ĐẠI HỌC QUỐC GIA TP HCM TRƯỜNG ĐẠI HỌC BÁCH KHOA TRẦN THẾ BẢO PHÂN TÍCH VÀ TỐI ƯU HĨA EXERGY-KINH TẾ COLLECTOR KHƠNG KHÍ CĨ NHÁM NHÂN TẠO Chuyên ngành : Kỹ thuật Nhiệt Mã số: 60520115 LUẬN VĂN THẠC SĨ TP HỒ CHÍ MINH, tháng 08 năm 2020 CƠNG TRÌNH ĐƯỢC HỒN THÀNH TẠI TRƯỜNG ĐẠI HỌC BÁCH KHOA –ĐHQG -HCM Cán hướng dẫn khoa học : PGS.TS NGUYỄN MINH PHÚ Chữ ký…………………………… Cán chấm nhận xét : Chữ ký…………………………… Cán chấm nhận xét : Chữ ký…………………………… Luận văn thạc sĩ bảo vệ Trường Đại học Bách Khoa, ĐHQG Tp HCM ngày 08 tháng 09 năm 2020 Thành phần Hội đồng đánh giá luận văn thạc sĩ gồm: CT: GS.TS Lê Chí Hiệp TK: TS Hà Anh Tùng UV: TS Lê Minh Nhựt PB1: TS Tạ Đăng Khoa PB2: PGS.TS Lê Anh Đức Xác nhận Chủ tịch Hội đồng đánh giá LV Trưởng Khoa quản lý chuyên ngành sau luận văn sửa chữa (nếu có) CHỦ TỊCH HỘI ĐỒNG TRƯỞNG KHOA సඤ ඤ $ ඤ ˘ —————————— —————————— མ ọ tên học viên: $RẦN $ Ế BẢO S V: 1670209 Ngày, tháng, năm, sinh: 16-06-1992 Nơi sinh: Bình ịnh ඤhun ngành: Kỹ thuật Nhiệt Â Í Ố མ Ơ ã số: 60520115 Ĩ E E Y Ế Í Ĩ E  མ 17 $ìm hiểu tổng quan collector khơng khí (Solar ir eater - S 27 Xây dựng mơ hình tính tốn S ) có sử dụng nhám nhân tạo 37 $hực tính tốn phân tích kết dựa định luật nhiệt động thứ hai 47 $ối ưu hóa hiệu suất exergy-kinh tế 57 Kết luận kết nghị Y 24 02 2020 Y ᓸ 2020 མYỄ $p7 ඤ , ngày ᓸ guyễn tháng năm 2020 Ô inh hú nh ùng R LỜI CẢM ƠN Trải qua thời gian dài nỗ lực học tập nghiên cứu, để đến kết ngày hôm em nhiều giúp đỡ gia đình, thầy cô bạn Qua em xin gửi lời cảm ơn chân thành với lòng biết ơn sâu sắc tới thầy giáo PGS TS Nguyễn Minh Phú, người hết lịng giúp đỡ em hồn thành luận văn Em xin chân thành gửi lời cảm ơn đến Thầy, Cô môn Công Nghệ Nhiệt Lạnh Phòng Đào tạo Sau đại học Trường Đại học Bách Khoa HCM tận tình truyền đạt kiến thức tạo điều kiện thuận lợi cho em q trình học tập nghiên cứu để hồn thành luận văn Cuối cùng, em xin gửi lời cám ơn đến gia đình người bạn ln động viên, ủng hộ giúp đỡ em suốt trình học tập hồn thành luận văn Mặc dù có nhiều cố gắng để hồn thành luận văn tất nhiệt tình khả mình, nhiên luận văn khơng thể tránh khỏi thiếu sót hạn chế Kính mong nhận chia sẻ đóng góp ý kiến Thầy, Cô bạn đồng nghiệp Trân trọng cảm ơn / Trần Thế Bảo TÓM TẮT Đối tượng nghiên cứu luận văn áp dụng nguyên lý định luật nhiệt động thứ hai phân tích kinh tế vào SAH có sử dụng nhám nhân tạo phoi kim loại có hình dạng xoắn ốc Trong nghiên cứu trước chúng tôi, đặc điểm nhiệt dòng chảy, hiệu suất thủy lực nghiên cứu thực nghiệm Trong luận văn này, tập trung phân tích hiệu suất nhiệt, hiệu suất hiệu dụng, hiệu suất exergy tối ưu hóa exergy-kinh tế SAH Những ảnh hưởng yếu tố bước nhám tương đối, độ cao tương đối nhám, diện tích bề mặt hấp thụ SAH số Reynolds kiểm tra Các tham số nhám nghiên cứu tối ưu để đạt hiệu suất exergy tốt xây dựng dựa kết tính tốn biểu diễn đồ thị SAH Phương pháp tổng trọng số sử dụng để tối ưu hóa mục tiêu SAH bao gồm hiệu suất exergy tổng chi phí hàng năm Kết cho thấy số Reynolds cao dẫn đến hiệu suất hiệu dụng thấp hiệu suất exergy thấp mong đợi Trong trường hợp này, việc sử dụng nhám với độ cao tương đối nhỏ chiều cao tương đối lớn nghiên cứu Nguyên nhân số Reynolds lớn làm cho tổn thất áp suất khơng khí SAH lớn Trong luận văn này, diện tích bề mặt hấp thụ SAH xác định 1.3 m2 để đạt hiệu suất exergy tối đa tối thiểu chi phí hàng năm SAH ABSTRACT The current study is the authors’ next work from the perspectives of the second law and economics of an air collector having artifcial roughness of metal waste In a previous study, heat and fuid fow characteristics and thermohydraulic performance were experimentally investigated In the present paper, thermal efciency, efective efciency, exergetic efciency and economic-based optimization are analytically appraised The infuences of the relative roughness pitch, relative roughness height, collector area and Reynolds number on the above parameters are examined The optimal roughness parameters to achieve the best exergetic performance are formulated as design plots for the design and operation of a solar air heater The weighted sum method is used to optimize the objectives of exergetic performance and total annual cost The results reveal that too high Reynolds numbers result in low efective performance and unexpected exergetic performance In that case, a lower roughness should be used, i.e a smaller relative roughness height and larger relative roughness pitch This is because the pressure loss penalty and irreversibility are quite large at high Reynolds numbers An absorber plate area of 1.3 m2 was found to achieve the maximum exergetic performance and minimum total annual cost MỤC LỤC DANH MỤC BẢNG DANH MỤC HÌNH DANH MỤC KÝ HIỆU CHƯƠNG 1: TỔNG QUAN VỀ SAH 11 1.1 Tổng quan SAH tình hình nghiên cứu SAH có sử dụng nhám nhân tạo giới 11 1.2 Mục đích đề tài 34 1.3 Đối tượng phạm vi nghiên cứu 34 1.3 Đối tượng nghiên cứu 34 1.3 Phạm vi nghiên cứu 34 1.4 Ý nghĩa khoa học nội dung nghiên cứu 34 1.4.1 Ý nghĩa khoa học đề tài 34 1.4.2 Nội dung nghiên cứu đề tài 34 CHƯƠNG 2: XÂY DỰNG MƠ HÌNH TỐN CỦA SOLAR AIR HEATER CÓ SỬ DỤNG NHÁM NHÂN TẠO 36 2.1 Mơ tả mơ hình vật lý SAH 36 2.2 Hiệu suất nhiệt 37 2.2.1 Tính tốn lượng có ích Q u 37 2.2 Tính tổn thất nhiệt toàn phần 41 2.3 Hiệu suất hiệu dụng 49 2.4 Hiệu suất exergy 50 CHƯƠNG 3: Q TRÌNH TÍNH TỐN VÀ KẾT QUẢ 53 PHÂN TÍCH ĐỊNH LUẬT NHIỆT ĐỘNG THỨ HAI 53 3.1 Sơ đồ tính tốn thơng số nhập vào 53 3.2 Kết tính tốn 62 CHƯƠNG 4: TỐI ƯU HÓA HIỆU SUẤT EXERGY VÀ KINH TẾ 75 4.1 Hàm mục tiêu, biến định điều kiện ràng buộc 75 4.2 Lựa chọn phương pháp tối ưu hóa đa mục tiêu 77 4.3 Tối ưu hóa exergy-kinh tế sử dụng phương pháp tổng trọng số 86 CHƯƠNG 5: KẾT LUẬN VÀ KIẾN NGHỊ 92 5.1 Kết luận 92 5.2 Kiến nghị 93 TÀI LIỆU THAM KHẢO 94 PHỤ LỤC 101 Phần 1: Chương trình EES tính tốn hiệu suất nhiệt, hiệu suất exergy, hiệu suất hiệu dụng 101 Phần 2: Chương trình EES tính tốn hàm mục tiêu theo phương pháp tổng trọng số 104 Phần 3: Công bố quốc tế ISI liên quan đến nội dung luận văn 109 DANH MỤC BẢNG Bảng 1.1: Các thông số kích thước nhám Bảng 1.2: Tình hình nghiên cứu nhám nhân tạo phần lượng exergy Bảng 4.1: Giá bán điện tham khảo số đối tượng khách hàng DANH MỤC HÌNH Hình 1.1: Sơ đồ lắp đặt SAH cho nhà kính Hình 1.2: So sánh nhiệt độ trước sau lắp đặt SAH nhà kính Hình 1.3: Sự khác tải nhiệt nhà kính vào mùa đơng Hình 1.4: Tải nhiệt tính tốn vào ngày 17-01-2013 Hình 1.5: Đồ thị thể biến đổi lượng nhiệt hữu ích theo luồng khơng khí Hình 1.6: Hiệu suất hoạt động hệ thống sưởi ấm vào mùa đơng Hình 1.7: Mơ hình thí nghiệm sấy tơm Việt Nam Hình 1.8: Tỉ lệ độ ẩm thân tơm thời gian sấy Hình 1.9: Khác nhiệt độ phần thân đuôi tôm với thời gian sấy Hình 1.10: Sơ đồ mơ hình nghiên cứu Hình 1.11: Cấu tạo ống trao đổi nhiệt Hình 1.12: Sự ảnh hưởng hệ số ma sát nhám tới số Reynolds Hình 1.13: Ảnh hưởng hệ số ma sát (thực nghiệm) hệ số ma sát (dự đốn) tới số Reynolds Hình 1.14: Hình học gân lớp nhám Hình 1.15: Mơ hình thí nghiệm Karwa Hình 1.16: Ảnh hưởng góc vát gân hệ số ma sát nhám nhân tạo tới số Stanton số Reynolds qua kênh ống hình chữ nhật Hình 1.17: Số Stanton hệ số ma sát với góc vát trường hợp p/e=4.5 Re = 10000 Hình 1.18: (a) Ảnh hưởng góc vát ( ≥ 14.5°) trường hợp số Stanton (p/e = 5.5) (b) Ảnh hưởng góc vát ( ≥ 15°) trường hợp số Stanton (p/e = 7) (c) Ảnh hưởng góc vát ( ≥ 14.5°) trường hợp số Stanton (p/e = 7) (d) Ảnh hưởng góc vát ( ≥ 15°) trường hợp số Stanton (p/e = 7) Hình 1.19: Mơ hình thực nghiệm Ahn Hình 1.20: Các loại gân nhám đem vào khảo sát mơ hình Ahn Hình 1.21: Sự phân bố nhiệt độ kênh chữ nhật sử dụng loại nhám khác Hình 1.22: Chỉ số hiệu đạt với loại nhám khác Hình 1.23: Mơ hình nghiên cứu thực nghiệm Karmare Hình 1.24: Mơ hình hình học nhám Hình 1.25: Ảnh hưởng số Reynolds tới số Nusselt loại nhám khác Hình 1.26a: Mơ hình nhám nhân tạo dạng W-down Hình 1.26b: Mơ hình nhám nhân tạo dạng W-up Hình 1.27: Ảnh hưởng số Reynolds tới trình trao đổi nhiệt sử dụng nhám W-down với độ cao nhám tương đối 0.03375 Hình 1.28: Ảnh hưởng số Reynolds tới trình trao đổi nhiệt sử dụng nhám W-up với độ cao nhám tương đối 0.03375 Hình 1.29: Mơ hình dịng chảy qua gân nhám hình dạng chữ S Hình 1.30: Ảnh hưởng độ dày nhám tương đối, bước nhám tương đối, góc vát nhám hình dạng chữ S tới số Nusselt Hình 2.1: Mơ hình SAH có nhám nhân tạo Hình 2.2: Mơ hình liên kết ống mối hàn Hình 2.3: Phương trình truyền nhiệt từ trung tâm cánh vào ống Hình 2.4: Sơ đồ tính tốn nhiệt Ut Hình 2.5: Cân lượng phần tử thể tích chất lỏng Hình 2.6: Đồ thị thể số Nusselt hàm số phụ thuộc vào số Reynolds Hình 2.7: Đồ thị thể hàm số Nur/Re0,901077 theo độ cao lớp nhám nhân tạo Hình 2.8: Đồ thị thể hàm số Nur/[Re0,901077(e/Dh)0.169444] phụ thuộc vào bước nhám Hình 2.9: Cân exergy SAH Hình 2.10: Các tổn thất exergy Hình 3.1: Sơ đồ giải thuật tính tốn thơng số hiệu suất SAH Hình 3.2: Đồ thị thể hiệu hiệu suất nhiệt phụ thuộc vào số Reynolds độ cao nhám tương đối Hình 3.3: Đồ thị thể hiệu suất hiệu dụng phụ thuộc vào số Reynolds độ cao nhám tương đối Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-020-09787-5 Analytical predictions of exergoeconomic performance of a solar air heater with surface roughness of metal waste Nguyen Minh Phu1,2 · Tran The Bao1,2 · Hoang Nam Hung3 · Ngo Thien Tu1,2 · Nguyen Van Hap1,2 Received: 29 January 2020 / Accepted: May 2020 © Akadémiai Kiadó, Budapest, Hungary 2020 Abstract The current study is the authors’ next work from the perspectives of the second law and economics of an air collector having artificial roughness of metal waste In a previous study, heat and fluid flow characteristics and thermo-hydraulic performance were experimentally investigated In the present paper, thermal efficiency, effective efficiency, exergetic efficiency and economic-based optimization are analytically appraised The influences of the relative roughness pitch, relative roughness height, collector area and Reynolds number on the above parameters are examined The optimal roughness parameters to achieve the best exergetic performance are formulated as design plots for the design and operation of a solar air heater The weighted sum method is used to optimize the objectives of exergetic performance and total annual cost The results reveal that too high Reynolds numbers result in low effective performance and unexpected exergetic performance In that case, a lower roughness should be used, i.e a smaller relative roughness height and larger relative roughness pitch This is because the pressure loss penalty and irreversibility are quite large at high Reynolds numbers An absorber plate area of 1.3 m2 was found to achieve the maximum exergetic performance and minimum total annual cost Keywords Metal waste · Solar air heater · Second law · Weighted sum method List of symbols Ac Area of the absorber plate (m2) Cj Thermal energy conversion factor CC Capital cost ($) C1 Constant ($ m−2 s) cp Air specific heat at a constant pressure (J kg−1 K−1) Dh Hydraulic diameter (m) f Friction factor Fp Collector efficiency factor FR Heat removal factor h Convective heat transfer coefficient (W m−2 K−1) hw Convective heat transfer coefficient due to wind (W m−2 K−1) I Solar radiation (W m−2) i Interest rate k Thermal conductivity of air (W m−1 K−1) * Nguyen Minh Phu nmphu@hcmut.edu.vn Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City, Viet Nam Viet Nam National University, Ho Chi Minh City, Viet Nam Quality Assurance and Testing Center of Binh Duong, Ho Chi Minh City, Binh Duong Province, Viet Nam ki Thermal conductivity of insulation (W m−1 K−1) kel Unit price of electricity ($ kW h−1) L Length of the collector (m) Li Thickness of insulation (m) M Mass flow rate number ṁ Air mass flow rate (kg s−1) N Number of glass covers (–) n SAH lifetime (year) Ns Entropy generation number Nu Nusselt number OC Operating cost ($ year−1) p Pressure (Pa) Pm Pumping power (W) Q̇ u Useful heat gain (W) Re Reynolds number s Constant TAC Total annual cost ($ year−1) Ta Ambient temperature (K) Tap Temperature of the absorber plate (K) Tf Average air temperature (K) Ti Air inlet temperature (K) To Air outlet temperature (K) Tsun Sun temperature (K) t Operational hours in a year (h) Ub Bottom loss coefficient (W m−2 K−1) 13 Vol.:(0123456789) Ue Edge loss coefficient (W m−2 K−1) UL Total loss coefficient (W m−2 K−1) Ut Top loss coefficient (W m−2 K−1) V Air velocity (m s−1) Vw Wind velocity (m s−1) W Width of the collector (m) w1 Weighted value w2 Weighted value Z Depth of the collector (m) Greek symbols βt Tilt angle of the collector (°) εab Emissivity of the absorber plate εg Emissivity of glass cover ηI Thermal efficiency ηII Exergetic efficiency ηEff Effective efficiency μ Air dynamic viscosity (kg m−1 s−1) ρ Air density (kg m−3) σ Stefan’s constant τα Effective transmittance–absorptance product Δ Difference Introduction A solar air heater (SAH) is a device that converts solar thermal energy into a hot air stream It is widely used due to its low investment and operating costs and high reliability SAHs are often used to provide hot air for space heating applications [1] and for drying agricultural products and seafood [2] In the early stages of SAH technology development, flat plate absorbers were known and exploited However, a flat plate absorber exposes the inherent disadvantage of a laminar sub-layer existing close to the absorber surface, causing poor heat transfer Therefore, an increasing number of different types of roughness have been proposed and studied to diminish the laminar sub-layer and create secondary flow On the other hand, roughness results in a pressure loss penalty that increases the pumping power Therefore, the balance between heat transfer enhancement and operating cost is considered by various criteria, such as thermohydraulic performance parameters, thermal efficiency, effective efficiency and exergy efficiency The evaluation of the thermo-hydraulic performance of different types of roughness has been the subject of numerous experimental and numerical studies Gupta et al [3] studied the effect of the transverse wire roughness in a transitionally rough flow region for a rectangular solar air heater duct They found that the correlations for the flow region showed good agreement between the predicted and experimental results The effects of chamfered rib roughness in rectangular ducts were investigated by Karwa et al [4, 5] 13 N. M. Phu et al The results showed that the highest heat transfer and the highest friction factor occurred for a chamfered rib angle of 15° Ahn [6] investigated the heat transfer and friction factor characteristics in rectangular ducts for five different configurations of roughness The results revealed that a triangular rib had the highest heat transfer performance The heat transfer and friction characteristics in a square duct were determined by Wang and Sundén [7] They found that trapezoidal ribs with decreased height in the flow direction attained the highest heat transfer enhancement factor Karmare et al [8] investigated metal grit ribs of circular cross sections in a staggered manner The results showed that the optimum performance was attained at the relative length of the grit, relative roughness height of the grit and relative roughness pitch of the grit of 1.72, 0.044 and 17.5, respectively In addition, there have been many studies on other rib shapes and their arrangements aiming to achieve the highest heat transfer performance, such as the W-shape [9], the S-shape [10], the V-shape [11, 12], metal shavings [13] and the broken arc shape [14] Over the last decade, due to the strong growth of computer science and numerical algorithms, computational fluid dynamics (CFD) studies on artificial roughness have been conducted to save time and cost CFD studies of various rib shapes in SAHs can be found in the literature [15, 16] Kesavan et al [17] used a triple-pass SAH to dry an agricultural product The second pass used a wire mesh to intensify heat transfer Moreover, sand was used as a thermal storage material to extend the drying time The results revealed that the highest outlet air temperature and maximum thermal efficiency were 62 °C and 66%, respectively Spherical roughness in an SAH was experimentally investigated by Maithani et al [18] The maximum thermo-hydraulic performance of 2.98 was found at a Reynolds number of 10,500 The combination of a V-groove and pin–fins on the absorber plate of a doublepass SAH was studied by Sudhakar and Cheralathan [19] This arrangement yields an increase of 12% in outlet air temperature compared to a traditional SAH Exergy performance is based on the second law of thermodynamics The second law is a powerful tool for assessing the maximum work potential and is a criterion for evaluating the effectiveness of a thermal system [20–23] However, the evaluation of parameters of SAHs based on the second law has not received much attention from researchers [24, 25] A few studies can be found as follows: Matheswaran et al [26] performed an analytical investigation of an SAH with jet impingement From the SAH’s optimal geometric values, they recorded that the largest exergy efficiency reached 0.0436 Kumar and Layek [27] appraised the performance of an SAH roughened with twisted ribs They concluded that the exergetic efficiency was 1.81 times higher than that of a smooth SAH Matheswaran et al [28] studied a jet impingement SAH with multiple arc protrusion ribs They found that Analytical predictions of exergoeconomic performance of a solar air heater with surface… the largest exergetic efficiency was 0.105 Matheswaran et al [29] evaluated a parallel pass jet plate SAH with several types of roughness They showed that a single-pass doubleduct jet plate SAH improves the annual exergy gain to 1.856 times that of a single-pass single-duct SAH Velmurugan and Kalaivanan [30] determined the energy and exergy efficiencies of four different models of SAHs The analysis yielded that a wire mesh dual-pass SAH provided better exergy output Yadav et al [31] performed an exergy-based performance evaluation of an SAH with protruding obstacles in an arc shape They revealed that a flat plate SAH should be used if the Reynolds number is greater than 20,000 due to the very low exergetic efficiency of the ribbed plate Chamoli and Thakur [32] tested V-down perforated baffles in an SAH in terms of the exergy method They found a 76% increase in exergetic efficiency compared to that of a smooth duct solar air heater The roughnesses of discrete V-down ribs and V-corrugated, arcuate-shaped and chamfered rib grooves have also been investigated on the basis of the second law of thermodynamics in the literature [33–36] The largest exergetic efficiency can reach approximately 17% at a collector area of 2.6 m2 with arcuate-shaped ribs [35] Recently, Rashidi et al [24] have applied CFD to determine the local irreversibility inside a solar nanofluid heater They verified that the entropy generation due to heat transfer decreases by approximately 11.1% when using nanofluid A l2O3–water An exergy analysis of a triangular SAH duct roughened with a V rib was analytically conducted by Kottayat et al [37] The ribbed triangular duct contributed a higher exergetic efficiency than other ribs in a rectangular duct They also found that a rib inclination of 45° achieved the minimum entropy generation Exergy-based evaluations of multi-pass SAHs have received attention from researchers [38, 39] The results showed that exergy efficiency increases with the number of passes due to better heat transfer of the glass cover and absorber plate with air Packed beds play a role of extended absorbing media Therefore, they are inserted into SAH ducts and evaluated for feasibility in both energy and exergy views Öztürk and Demirel [40] experimentally showed that an SAH packed with Raschig rings obtained a maximum exergy efficiency of 1.16% Table 1 presents researchers’ efforts to comprehensively examine the aspects of hydraulics, energy and exergy for different types of roughness in SAHs Few studies have given both the standpoints of the first and second laws of thermodynamics for artificial roughness on absorber plates Furthermore, helically coiled roughness elements have not been investigated, although their shape is similar to those of a twisted tape [41, 42], spring tape [41] and swarf, which are employed successfully in asphalt mixtures to absorb and conduct thermal energy [43] or in combination with paraffin wax in solar energy accumulators [44] From the above Table 1 Roughened absorber plate studies investigating both energy and exergy No Roughness shape Twisted rib Researchers and remarks in thermo-hydraulic research Kumar and Layek [45] Nusselt number and friction factor 2.46 and 1.78 times higher than those of a smooth plate Jet impingement and arc-shaped rib Nadda et al [46] Largest thermo-hydraulic performance parameter of 3.64 Jet impingement and metallic wires Chauhan and Thakur [47] Maximum increase in Nusselt number of 2.67 times and friction factor of 3.5 times V-corrugated Hollands and Shewen [48] Highest increase in collector efficiency of 12% V-down perforated baffles Chamfered rib groove Protruded ribs in arc shape Discrete V-down ribs Researchers and remarks in exergy research Anup and Apurba [27] Exergetic efficiency 1.81 times higher than that of a smooth plate Matheswaran et al [28] Maximum exergetic efficiency of 10.5% Matheswaran et al [26] Maximum exergetic efficiency of 4.36% Hedayatizadeh et al [34] Exergy output increased with number of glass covers Chamoli and Thakur [32] Chamoli and Thakur [49, 50] Highest increase in heat transfer of 2.2 times and Highest increase in exergetic efficiency of 76% friction factor of 5.2 times Apurba et al [36] Karwa et al [4] Larger relative roughness height, smaller entropy twofold increase in Stanton number and threegeneration fold increase in friction factor Sanjay et al [31] Yadav et al [51] Maximum exergetic efficiency of 2.25% Maximum increase in Nusselt number of 2.89 times and friction factor of 2.93 times Sukhmeet et al [33] Singh et al [52] Maximum exergetic efficiency of 2% Maximum increase in Nusselt number of 3.04 times and friction factor of 3.11 times 13 N. M. Phu et al literature survey, two objectives that should be covered in the current study are specified The first is the completion of a study on a solar air heater with metal waste from the points of view of both laws of thermodynamics and economics In the authors’ previous work [13], the heat and fluid flow characteristics and thermo-hydraulic performance were experimentally evaluated for an SAH having helically coiled metal waste The second objective is to theoretically analyse the economic aspects associated with exergetic performance To the best of the authors’ knowledge, the latter objective has not been noted in studies of artificial roughness in SAHs Thermal efficiency, effective efficiency, exergetic efficiency and economic optimization were analytically investigated to provide a comprehensive overview that is able to facilitate the design and operation of solar air heaters with metal waste Thermal efficiency The useful heat gain of the air flow acquired from solar radiation can be calculated by the following equations [27, 34]: ) ( Q̇ u = Ac [I(𝜏𝛼)] − UL Tap − Ta (1) ) ( Q̇ u = mc ̇ p T o − Ti (2) )] ( [ Q̇ u = Ac FR I(𝜏𝛼) − UL To − Ti Mathematical model and validation Figure 1 presents a schematic diagram with notations of an SAH roughened with helically coiled metal waste The roughness is from the waste of a steel shaft turning process, which is almost free of charge and has high availability The two ends of the helical roughness are locked at the collector edges, and the contact positions between the roughness and the absorber plate are tightly glued with a super glue Indoor testing conditions with different air speeds showed that the roughness of the metal waste remains stable, and the peak of the roughness moves slightly in the direction of flow due Fig. 1 Solar air heater having an absorber plate roughened with metal waste to the influence of the drag force Such an obstacle in a fluid channel generates turbulent recirculation flow and secondary flow, which enhance heat transfer characteristics [13, 27, 41, 53] An analytical model for evaluating the efficiencies and cost equations for optimization is described in the following sub-sections (3) where Ac is the absorber plate area, I is the solar radiation, τα is the effective transmittance–absorptance product, ṁ is the mass flow rate of air, cp is the air specific heat at a constant pressure, FR is the heat removal factor of the solar collector and UL is the total loss coefficient Tap, Ta, Ti and To are the mean temperature of the absorber plate, ambient temperature, air inlet temperature and air outlet temperature, respectively The total loss coefficient from the solar collector to the surroundings can be estimated as: l) n( tio a i d lar o S Air inlet Glass cover Helically coiled metal waste W P Absorber plate H e 13 Analytical predictions of exergoeconomic performance of a solar air heater with surface… (4) UL = Ut + Ub + Ue where Ut, Ub and Ue are the loss coefficients at the top, bottom and edge sides of the solar air heater, respectively The top loss coefficient is determined as [34] −1 ⎛ ⎞ ⎜ ⎟ N Ut = ⎜ � �� Tap −Ta �e + 1∕hw ⎟ ⎜ Ct ∕Tap ⎟ N+ft ⎝ ⎠ 2 T � � ap + Ta + 𝜎 Tap + Ta 2N+ft −1+0.133𝜀ap + −N 𝜀 +0.00591Nh 𝜀 ap w g (5) where ( ) Ct = 520 − 0.000051𝛽t2 ( ) e = 0.43 − 100∕Tap ( ) ft = + 0.089hw − 0.1166hw 𝜀ap (1 + 0.07866N) (6) The bottom and edge loss coefficients are defined as: Ub = ki ∕Li Ue = (L + W)Zki LWLi (7) (8) where ki and Li are the thermal conductivity and thickness of insulation, respectively L, W and Z are the length, width and depth of the solar air heater duct, respectively The heat removal factor is calculated as: [ ( ) ] Fp mc ̇ p exp UL Ac −1 FR = (9) UL Ac mc ̇ p where Fp is the collector efficiency factor This factor is expressed as: h Fp = h + UL (10) where h is the convective heat transfer coefficient between the air and absorber plate h = Nu k Dh Nu = 0.0753297Re0.901077 (e∕Dh )0.169444 (P∕e)−0.668855 (12) where e/Dh and P/e are the relative roughness height and relative roughness pitch, respectively The hydraulic diameter of the passage (Dh) and the Reynolds number (Re) are stated as: Dh = 4WZ 2(W + Z) (13) Re = mD ̇ h 𝜇WZ (14) The thermal efficiency is defined as the ratio of the useful heat gain of the air flow to the solar radiation on the surface of the SAH as follows: in which βt, εap, εg and N are the title angle of the heater, emissivity of the absorber plate, emissivity of the glass cover and number of glass covers, respectively The convective heat transfer due to wind (hw) is calculated by: hw = 5.7 + 3.8Vw A Nusselt number correlation (Nu) developed based on the simulation data obtained by Phu et al [13] is as follows: (11) 𝜂I = Q̇ u IAc (15) Effective efficiency The first law efficiency merely considers the useful heat received compared to the solar energy on the SAH surface However, the energy consumed to transport the working fluid through the SAH is not taken into account Hence, the effective efficiency is defined as follows [28]: 𝜂Eff = Q̇ u Pm − IAc IAc Cj (16) where Cj is the thermal energy conversion factor Cj is recommended to be 0.2 [28] The pumping power is calculated as Pm = mΔp ̇ 𝜌 (17) where ρ is the density of air and Δp is the pressure difference of the air flow The air pressure difference is expressed as: Δp = 4f 𝜌 LV 2Dh (18) where the mean air velocity inside the SAH duct (V) is computed as: V= ṁ 𝜌WZ (19) The friction factor equation (f) reported for conic-curve profile ribs [13] is given as: 13 N. M. Phu et al f = 16.9194Re−0.358125 (e∕Dh )0.527405 (P∕e)−0.875926 (20) The Nusselt and friction factor correlations were developed with a deviation of ± 10% and correlation coefficients of 0.996 and 0.982, respectively The exergetic efficiency can be calculated from the total exergy losses and input exergy summation as: ∑ ∑ 𝜂II = − EXloss ∕ EXinlet (28) Exergetic efficiency Exergoeconomic objective function Exergy analysis is a tool for finding components in a heating system that have great exergy destruction and high irreversibility From this analysis, a solution can be sought to maximize the exergetic efficiency or minimize the entropy generation For an SAH, the following exergy loss components are included [28]: Optical exergy losses: This section defines a model that is used to predict expenditures associated with investment and operation of an SAH Therefore, an objective function of total annual cost and exergetic efficiency is formed and optimized using the weighted sum method There are many methods of multi-objective optimization, such as a preference selection index method [54], a response surface method [55], a numerical orthogonal test [56], a genetic algorithm and Pareto optimality [57] In this study, the weighted sum method is used due to its simplicity, explicitness and popularity The multi-objective optimization problem is reduced to single-objective optimization, as pointed out in the literature [58, 59] The capital cost (CC) of an air collector is mostly dominated by its absorber plate area Ac The cost can be fit to the following equation [60]: [ )4 ] ) ( ( EXloss,opt = IAc (1 − 𝜏𝛼) − (4∕3) Ta ∕Tsun + (1∕3) Ta ∕Tsun (21) where Tsun is the sun temperature Exergy losses by convection and radiation heat transfer from the absorber plate to the environment: ) )( ( EXloss,Qloss = UL Ac Tap − Ta − Ta ∕Tap (22) Exergy losses by absorption of radiation by the absorber plate: CC = C1 Asc where C1 and s are assumed to be constant [ )] )4 ( ) ( ( EXloss,Tap ,Tsun = IAc 𝜏𝛼 − (4∕3) Ta ∕Tsun + (1∕3) Ta ∕Tsun − − Ta ∕Tap Exergy losses by heat transfer to the working air ) ( EXloss,Tap ,Tf = IAc 𝜂I Ta 1∕Tf − 1∕Tap (24) where T f is the mean temperature of the working air, Tf = 0.5(Ti + To) Frictional exergy losses of the working air EXloss,friction mΔpT ̇ a = 𝜌Tf (25) The first two kinds of exergy losses are outer losses The remaining kinds are known as inner losses The total exergy losses are the summation of the above-mentioned exergy losses as follows: ∑ EXloss = EXloss,opt + EXloss,Qloss + EXloss,Tap ,Tsun + EXloss,Tap ,Tf + EXloss,friction (26) The input exergy of the SAH is constituted by the air inflow and solar radiation source as: [ ∑ )4 ] ) ( ( EXinlet = IAc − (4∕3) Ta ∕Tsun + (1∕3) Ta ∕Tsun (27) 13 (29) (23) The operating cost (OC) of an SAH is mainly due to the electrical consumption used to draw the air flow Therefore, the cost can be estimated as [61]: OC = kel tΔpV̇ 𝜂b 𝜂m (30) where the efficiencies of the blower and motor are ηb = 0.80 and ηm = 0.85, respectively [62], V̇ is volumetric flow rate of the air flow inside the SAH, t is the hours of operation per year and kel is unit price of electricity The total annual cost (TAC) is the sum of the capital cost and the operating cost [60, 63]: TAC = crf ⋅ CC + OC (31) where crf is the capital recovery factor This factor can be defined as [60]: crf = i − (1 + i)−n (32) where i and n denote the bank interest rate and SAH lifetime, respectively Analytical predictions of exergoeconomic performance of a solar air heater with surface… (33) where w1 is the weighted value of the total annual cost function and w2 is the weighted value of the exergetic efficiency function WS, TAC and 𝜂II are normalized functions of the objective function, total annual cost, and exergetic efficiency, respectively The normalized functions can be written as [64]: WS − WSmin WSmax − WSmin TAC − TACmin TAC = TACmax − TACmin 𝜂II − 𝜂II 𝜂II = 𝜂II max − 𝜂II WS = The thermal–physical properties of air (viscosity µ, thermal conductivity k, specific heat cp, and density ρ) were estimated at the average temperature Tf and taken from EES software [65] The design and operation parameters of the SAH used in this study are listed in Table 2 These are commonly used to calculate and evaluate SAHs [66] The equations in “Thermal efficiency”–“Exergoeconomic objective function” sections were solved using an iterative procedure in EES The analytical model was first tested using V-down ribs, and the thermal and exergy efficiencies were compared with published results [33] Figure 2 shows these comparisons It is concluded that there is good agreement between the results The next section of this paper discusses the performance results of an SAH roughened with helical metal waste Results and discussion The influence of the relative roughness height and Reynolds number on the SAH performance is shown in Figs. 3–5 Figure shows that the thermal efficiency decreases slightly with a decrease in the relative roughness height and increases dramatically with the Reynolds number This is because the Nusselt number decreases as the relative roughness height decreases [13] As the Reynolds number increases, there is an increase in the airflow rate in the SAH duct, thus increasing the Nusselt number, which leads to an increase in the useful heat gain However, the first law efficiency does not reflect a penalty for pressure loss when the air speed increases This negative effect can be observed via Parameter Value Air inlet temperature (Ti) Ambient temperature (Ta) Depth of the collector (Z) Effective transmittance–absorptance product (τα) Emissivity of glass cover (εg) Emissivity of the absorber plate (εap) Length of the collector (L) Number of glass covers (N) Reynolds number (Re) Solar radiation (I) Sun temperature (Tsun) Thermal conductivity of insulation (ki) Thickness of insulation (Li) Width of the collector (W) Wind velocity (Vw) Weighted value (w1) Weighted value (w2) Constant (C1) Constant (s) Unit price of electricity (kel) Lifetime (n) Interest rate (i) Operational hours in a year (t) 300 K 300 K 0.025 m 0.8 0.88 0.9 1.5 m 1200–20,000 1000 W m−2 5800 K 0.037 W m−1 K−1 20 mm 1 m 1 m s−1 0.4 0.6 57.5 $ m−2 s 0.6 0.1186 $ kW h−1 10 years 7.5% 1800 h 0.02 0.8 0.7 0.01 0.6 0.5 η I (Singh et al.) η I (Present study) 0.4 η II (Singh et al.) η II (Present study) – 0.01 5000 10000 15000 0.3 20000 25000 Thermal efficiency, η I WS = w1 ⋅ TAC − w2 ⋅ 𝜂II Table 2 Values of operating and design parameters Exergetic efficiency, η II In this study, the minimum total annual cost and maximum exergetic efficiency at a certain size of an SAH are investigated Therefore, an objective function is defined as the following equation To minimize the objective function, the exergetic efficiency is multiplied by negative one 0.2 30000 Re Fig. 2 Validation of the present model formulation (curves) with the previous work (symbols) in the case of V-down ribs [33] the effective efficiency When considering the effect of the rapidly increasing pressure loss with the Reynolds number, the effective efficiency increases to the maximum at a Reynolds number of approximately 12,000 (Fig. 4) Then, the effective efficiency decreases with increasing Reynolds number The increase in heat transfer is not commensurate with the increase in the work consumed by friction, which leads to a decrease in the effective efficiency at very large Reynolds numbers The largest ηEff is approximately 0.66 There 13 N. M. Phu et al 1200 0.8 P/e = 1000 0.6 0.6 e/Dh = 0.6 0.45 0.3 0.15 0.4 0.3 5000 15000 10000 20000 Reynolds number Exergy loss components/W Thermal efficiency 0.7 800 1106 600 EXloss,friction 1104 EXloss,opt 1102 EXloss,Qloss EXloss,Tap,Tf EXloss,Tap,Tsun 400 ΣEXloss 1100 1098 1096 Fig. 3 Thermal efficiency as a function of the Reynolds number and relative roughness height 1000 2000 3000 4000 5000 6000 200 0.7 e/Dh P/e = 0 5000 10000 15000 20000 Reynolds number Effective efficiency 0.6 Fig. 6 Variation in exergy loss components with the Reynolds number 0.5 0.4 e/Dh = 0.6 0.45 0.3 0.15 0.3 0.2 5000 10000 15000 20000 Reynolds number Fig. 4 Effective efficiency as a function of the Reynolds number and relative roughness height 0.03 P/e = Exergetic efficiency 0.02 0.01 e/Dh 0 – 0.01 e/Dh = 0.6 0.45 0.3 0.15 – 0.02 – 0.03 – 0.04 5000 10000 15000 20000 Reynolds number Fig. 5 Exergetic efficiency as a function of the Reynolds number and relative roughness height 13 is an inversion of the influence of the relative roughness height on the effective efficiency At low Reynolds numbers, as the relative roughness height increases, the effective efficiency increases However, this effect shows the opposite trend at large Re numbers In other words, when the Reynolds number is relatively large, the metal waste roughness seems to be ineffective It can be seen from the trend that if the relative roughness height is relatively close to zero (i.e without roughness), the effective efficiency is maximized when the Reynolds number is large (Re > 12,000) Figure shows that the largest exergetic efficiency occurs at a Reynolds number of approximately 2000 This phenomenon is caused by the trade-off of exergetic loss components with the Reynolds number As the Reynolds number increases, EXloss,Tap,Tsun and EXlos,friction increase, and EXloss,Tap,Tf and E Xloss,Qloss decrease; E Xloss,opt does not change with the Reynolds number, as shown in Fig. 6 This leads to increasing and decreasing trends of total exergy losses (∑EXloss) with the Reynolds number The largest ηII is approximately 0.023 In comparison with that of other types of roughness, the highest exergetic efficiency of 2.3% is very competitive for a kind of artificial roughness from metal waste As shown by the monotonically decreasing trend of ηII as the Reynolds number increases, ηII becomes a negative value This is because the input exergy does not overcome the exergy losses due to friction associated with a large air flow rate An inversion behaviour can also be observed when considering the effect of the relative roughness height on Analytical predictions of exergoeconomic performance of a solar air heater with surface… 360 0.14 350 0.12 0.1 340 Tap 0.08 η Carnct 330 0.06 320 0.04 310 300 Carnot efficiency Absorber plate temperature/K the exergetic efficiency At Reynolds numbers greater than 7000, a smaller relative roughness height exhibits a better exergetic efficiency Figures 4 and show that the maximum exergy efficiency occurs at the largest e/Dh of 0.6, but the maximum effective efficiency happens at the smallest e/Dh of 0.15 This is because the maximum effective efficiency occurs at a small Reynolds number (Re 18,000, a flat plate collector should be used Fortunately, in practical applications Fig. 7 Ranges of absorber plate temperature and Carnot efficiency for an SAH 13 N. M. Phu et al ANSYS Velocity R19.2 m s–1 Absorber plate Airflow penetrating roughness elements 0.02 0.04 (m) 0.03 0.01 (a) 3D streamlines Separation point Dead zone Laminar sub-layer Recirculation Absorber plate Reattachment point (b) Forward curve side Separation point Recirculation Laminar sub-layer Reattachment point (c) Backward curve side Fig. 8 Flow pattern in a duct fitted with helically coiled metal waste 13 Analytical predictions of exergoeconomic performance of a solar air heater with surface… 0.8 0.7 Relative roughness height e/Dh = 0.3 Thermal efficiency 0.6 0.4 P/e = 10 0.2 0 5000 10000 15000 0.6 0.5 0.3 0.2 0.1 20000 l = 1000 W m–2 900 800 700 0.4 5000 10000 15000 20000 Reynolds number Reynolds number Fig. 9 Variation in thermal efficiency with the Reynolds number and relative roughness pitch Fig. 12 Optimal relative roughness height 11 10 P/e e/Dh = 0.3 ∞ Effective efficiency 0.6 0.5 0.4 0.3 P/e = 10 0.2 0.1 l = 1000 W m–2 900 800 700 5000 10000 15000 20000 Reynolds number 0 5000 10000 15000 20000 Reynolds number Fig. 13 Optimal relative roughness pitch Fig. 10 Variation in effective efficiency with the Reynolds number and relative roughness pitch 0.03 e/Dh = 0.3 0.02 Exergetic efficiency Relative roughness pitch 0.7 0.01 P/e ∞ – 0.01 P/e = 10 – 0.02 – 0.03 5000 10000 15000 20000 Reynolds number Fig. 11 Variation in exergetic efficiency with the Reynolds number and relative roughness pitch such as drying, the range of Re is 3500–16,000 [70] Therefore, the presence of roughness in an SAH is still effective from the perspective of the second law Figures 5 and 11 show that the exergetic efficiency can reach a maximum at a certain value of e/Dh and P/e Figures 12 and 13 show the optimal values of e/Dh and P/e as design plots In a specific application, given the air flow and known solar radiation intensity, the relative roughness height and relative roughness pitch can be easily selected from these plots to ensure maximum second law performance The trend of the curves in Figs. 12 and 13 is explained as follows For example, at I = 1000 W m−2 and from Fig. 5, we can see that if Re is less than 5000, we should use e/Dh = 0.6, and for Re over 6500, we should use e/Dh of 0.15 to obtain the highest exergetic performance This is shown by two horizontal lines at e/Dh = 0.6 and e/Dh = 0.15, where Re is less than 5000 and greater than 6500, respectively, in Fig. 12 13 N. M. Phu et al e/Dh = 0.6; P/e = 4; I = 1000 W m–2; ∆T/l = 0.03 K m2 W–1; W = m 20 0.026 0.024 15 ηII TAC 0.022 1.5 2.5 3.5 Conclusions 25 Total annual cost/$ year–1 Energetic efficiency 0.028 10 4.5 Area of the absorber plate/m2 Fig. 14 Change in exergetic efficiency and total annual cost with the absorber area Normalized objective function 1.1 e/Dh = 0.6; P/e = 4; I = 1000 W m–2; ∆T/l = 0.03 K m2 W–1 0.9 W = 0.5 m 0.75 1.25 1.5 0.7 0.5 0.3 0.1 – 0.1 Area of the absorber plate/m2 Fig. 15 Search for a minimum value of the objective function with respect to the absorber area In this paper, an analytical investigation of second law performance and exergoeconomic optimization was conducted for a solar air heater duct roughened with helical metal waste This study provides comprehensive quantitative results of metal waste roughness in an SAH, including thermal efficiency, effective efficiency, exergetic efficiency and economic optimization Among several figures of merit, the authors recommend that effective efficiency and exergetic efficiency should be used as criteria to evaluate the performance of a solar air heater because these efficiencies represent the first law and second law of thermodynamics and show the critical effects of the roughness parameters The roughness parameters are optimized to obtain the best exergetic performance The best exergetic performance is achieved at a Reynolds number of approximately 2000, the largest relative roughness height and the smallest relative roughness pitch When the Reynolds number is greater than 10,000, a flat plate collector should be chosen from the viewpoint of the second law The largest exergy efficiency of 2.7% is achieved at an absorber plate aspect ratio of A greater aspect ratio leads to a smaller exergetic efficiency mainly due to the increase in frictional exergy loss The optimal collector area to achieve the best exergetic performance is also presented Under certain conditions, an absorber area of 1.3 m2 was found to optimize the objectives of exergetic efficiency and total annual cost Acknowledgements This research is funded by Ho Chi Minh City University of Technology, VNU-HCM, under Grant Number T-CK-2019-07 References Figure 14 presents the effect of the absorber plate area on the exergetic performance and the total annual cost The width of the absorber plate is fixed as 1 m It can be seen that TACincreases sharply with the area due to an increase in both investment and operating costs However, when the area increases, the input exergy increases, and the exergy losses also increase, resulting in a maximum exergetic efficiency of 0.0271 for an area of approximately 3 m2, i.e an aspect ratio of Based on these behaviours, a multi-objective optimization of the maximum exergetic performance and minimum TACwas performed using the weighted sum method with the model parameters shown in Table 2 Figure 15 shows the results of the objective function with respect to absorber size To fulfil the minimization of the objective function, an absorber size of 2.6 m × 0.5 m = 1.3 m2 (L × W = Ac) is most suitable The optimization of larger dimensions can be obtained from the figure 13 Khalid J, Farhan AF Greenhouse heating by solar air heaters on the roof Renew Energy 2014;72:406–14 Nguyen MP, Ngo TT, Le TD Experimental and numerical investigation of transport phenomena and kinetics for convective shrimp drying Case Stud Therm Eng 2019;14:100465 Gupta D, Solanki SC, Saini JS Heat and fluid flow in rectangular solar air heater ducts having transverse rib roughness on absorber plates Sol Energy 1993;51(1):31–7 Karwa R, Solanki SC, Saini JS Heat transfer coefficient and friction factor correlations for the transitional flow regime in rib-roughened rectangular ducts Int J Heat Mass Transf 1999;42(9):1597–615 Karwa R Experimental studies of augmented heat transfer and friction in asymmetrically heated rectangular ducts with ribs on the heated wall in transverse, inclined, v-continuous and v-discrete pattern Int Commun Heat Mass Transf 2003;30(2):241–50 Ahn SW The effects of roughness types on friction factors and heat transfer in roughened rectangular duct Int Commun Heat Mass Transf 2001;28(7):933–42 Analytical predictions of exergoeconomic performance of a solar air heater with surface… Wang L, Sundén B Experimental investigation of local heat transfer in a square duct with various-shaped ribs Heat Mass Transf 2006;43(8):759 Karmare SV, Tikekar AN Heat transfer and friction factor correlation for artificially roughened duct with metal grit ribs Int J Heat Mass Transf 2007;50(21):4342–51 Lanjewar A, Bhagoria JL, Sarviya RM Experimental study of augmented heat transfer and friction in solar air heater with different orientations of W-Rib roughness Exp Therm Fluid Sci 2011;35(6):986–95 10 Kumar K, Prajapati DR, Samir S Heat transfer and friction factor correlations development for solar air heater duct artificially roughened with ‘S’ shape ribs Exp Therm Fluid Sci 2017;82:249–61 11 Hans VS, Saini RP, Saini JS Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with multiple v-ribs Sol Energy 2010;84(6):898–911 12 Kabeel E, Khalil A, Shalaby SM, Zayed ME Investigation of the thermal performances of flat, finned, and v-corrugated plate solar air heaters J Sol Energy Eng 2016;138(5):051004–7 13 Nguyen MP, Vo T, Ngo TT Augmented heat transfer and friction investigations in solar air heater artificially roughened with metal shavings J Mech Sci Technol 2019;33(7):3521–9 14 Hans VS, Gill RS, Singh S Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with broken arc ribs Exp Therm Fluid Sci 2017;80:77–89 15 Yadav S, Bhagoria JL Heat transfer and fluid flow analysis of solar air heater: a review of CFD approach Renew Sustain Energy Rev 2013;23:60–79 16 Ngo TT, Phu NM Computational fluid dynamics analysis of the heat transfer and pressure drop of solar air heater with coniccurve profile ribs J Therm Anal Calorim 2020;139:3235–46 https://doi.org/10.1007/s10973-019-08709-4 17 Kesavan S, Arjunan TV, Vijayan S Thermodynamic analysis of a triple-pass solar dryer for drying potato slices J Therm Anal Calorim 2019;136:159–71 https://doi.org/10.1007/s1097 3-018-7747-0 18 Maithani R, Kumar A, Gholamali Zadeh P, et al Empirical correlations development for heat transfer and friction factor of a solar rectangular air passage with spherical-shaped turbulence promoters J Therm Anal Calorim 2020;139:1195–212 https ://doi.org/10.1007/s10973-019-08551-8 19 Sudhakar P, Cheralathan M Thermal performance enhancement of solar air collector using a novel V-groove absorber plate with pin-fins for drying agricultural products: an experimental study J Therm Anal Calorim 2019 https: //doi.org/10.1007/s1097 3-019-08952-9 20 Kalogirou SA, Karellas S, Badescu V, Braimakis K Exergy analysis on solar thermal systems: a better understanding of their sustainability Renew Energy 2016;85:1328–33 https:// doi.org/10.1016/j.renene.2015.05.037 21 Nguyen MP Overall optimization and exergy analysis of an air conditioning system using a series-series counterflow arrangement of water chillers Int J Air Cond Refrig 2019;27(04):1950034 22 Bejan A, Kearney DW, Kreith F Second law analysis and synthesis of solar collector systems ASME J Sol Energy Eng 1981;103(1):23–8 https://doi.org/10.1115/1.3266200 23 Nguyen MP Energy and exergy estimation for a combined cycle of solid C O production and N H3–H 2O single effect absorption chiller Sci Technol Dev J 2016;19(1):61–9 https://doi org/10.32508/stdj.v19i1.611 24 Rashidi S, Javadi P, Esfahani JA Second law of thermodynamics analysis for nanofluid turbulent flow inside a solar heater with the ribbed absorber plate J Therm Anal Calorim 2019;135:551 25 Mukesh KS, Radha KP Exergy based performance evaluation of solar air heater with arc-shaped wire roughened absorber plate Renew Energy 2016;96:233–43 26 Matheswaran MM, Arjunan TV, Somasundaram D Analytical investigation of solar air heater with jet impingement using energy and exergy analysis Sol Energy 2018;161:25–37 27 Anup K, Apurba L Energetic and exergetic performance evaluation of solar air heater with twisted rib roughness on absorber plate J Clean Prod 2019;232:617–28 28 Matheswaran MM, Arjunan TV, Somasundaram Analytical investigation of exergetic performance on jet impingement solar air heater with multiple arc protrusion obstacles J Therm Anal Calorim 2019;137(1):253–66 29 Matheswaran MM, Arjunan TV, Somasundaram Energetic, exergetic and enviro-economic analysis of parallel pass jet plate solar air heater with artificial roughness J Therm Anal Calorim 2019;136(1):5–19 30 Velmurugan P, Kalaivanan R Energy and exergy analysis of solar air heaters with varied geometries Arab J Sci Eng 2015;40:1173 31 Sanjay Y, Maneesh K, Varun S Exergetic performance evaluation of solar air heater having arc shape oriented protrusions as roughness element Sol Energy 2014;105:181–9 32 Chamoli S, Thakur NS Exergetic performance evaluation of solar air heater having V-down perforated baffles on the absorber plate J Therm Anal Calorim 2014;117:909 33 Sukhmeet S, Subhash C, Saini JS Exergy based analysis of solar air heater having discrete V-down rib roughness on absorber plate Energy 2012;37(1):749–58 34 Hedayatizadeh M, Ajabshirchi Y, Sarhaddi F Analysis of exergy and parametric study of a v-corrugated solar air heater Heat Mass Transf 2012;48:1089 35 Gholami A, Ajabshirchi Y, Ranjbar SF Thermo-economic optimization of solar air heaters with arcuate-shaped obstacles J Therm Anal Calorim 2019;138:1395–403 https: //doi.org/10.1007/s1097 3-019-08273-x 36 Apurba L, Saini JS, Solanki SC Second law optimization of a solar air heater having chamfered rib–groove roughness on absorber plate Renew Energy 2007;32(12):1967–80 37 Kottayat N, Kumar S, Yadav AK, Anish S Enhanced thermohydraulic performance in a V-ribbed triangular duct solar air heater: CFD and exergy analysis Energy 2020 https://doi org/10.1016/j.energy.2020.117448 38 Velmurugan P, Kalaivanan R Energy and exergy analysis in double-pass solar air heater Sadhana 2016;41(3):369–76 39 Velmurugan P, Kalaivanan R Energy and exergy analysis of multi-pass flat plate solar air heater—an analytical approach Int J Green Energy 2015;12(8):810–20 https: //doi.org/10.1080/15435 075.2014.888662 40 Öztürk HH, Demirel Y Exergy-based performance analysis of packed-bed solar air heaters Int J Energy Res 2004;28:423–32 https://doi.org/10.1002/er.974 41 Bhattacharyya S The effects of short length and full length swirl generators on heat transfer and flow fields in a solar air heater tube J Therm Anal Calorim 2019 https://doi.org/10.1007/s1097 3-019-08764-x 42 Kumar A, Layek A Thermo-hydraulic performance of solar air heater having twisted rib over the absorber plate Int J Therm Sci 2018;133:181–95 https : //doi.org/10.1016/j.ijthe r mals ci.2018.07.026 43 González A, Norambuena-Contreras J, Storey L, Schlangen E Self-healing properties of recycled asphalt mixtures containing metal waste: an approach through microwave radiation heating J Environ Manag 2018;214:242–51 44 Reyes A, Negrete D, Mahn A, Sepúlveda F Design and evaluation of a heat exchanger that uses paraffin wax and recycled 13 45 46 47 48 49 50 51 52 53 54 55 56 57 58 N. M. Phu et al materials as solar energy accumulator Energy Convers Manag 2014;88:391–8 Kumar A, Layek A Nusselt number and friction factor correlation of solar air heater having twisted-rib roughness on absorber plate Renew Energy 2019;130:687–99 https://doi.org/10.1016/j.renen e.2018.06.076 Nadda R, Kumar A, Maithani R Developing heat transfer and friction loss in an impingement jets solar air heater with multiple arc protrusion obstacles Sol Energy 2017;158:117–31 Chauhan R, Thakur NS Heat transfer and friction factor correlations for impinging jet solar air heater Exp Therm Fluid Sci 2013;44:760–7 https : //doi.org/10.1016/j.expth e rmfl usci.2012.09.019 Hollands KGT, Shewen EC Optimization of flow passage air-heating, plate-type solar collector J Sol Energy Eng 1981;103:323–30 Chamoli S, Thakur NS Heat transfer enhancement in solar air heater with V-shaped perforated baffles J Renew Sustain Energy 2013;5:023122 Chamoli S, Thakur NS Correlations for solar air heater duct with V-shaped perforated baffles as roughness elements on absorber plate Int J Sustain Energy 2013 https://doi.org/10.1080/14786 451.2013.857318 Yadav S, Kaushal M, Varun VS Nusselt number and friction factor correlations for solar air heater duct having protrusions as roughness elements on absorber plate Exp Therm Fluid Sci 2013;44:895–907 Singh S, Chander S, Saini JS Heat transfer and friction factor correlations of solar air heater ducts artificially roughened with discrete v-down ribs Energy 2011;36(8):5053–64 Phu NM, Trinh NTM Modelling and experimental validation for off-design performance of the helical heat exchanger with LMTD correction taken into account J Mech Sci Technol 2016;30:3357–64 Chauhan R, Singh T, Thakur NS, Patnaik A Optimization of parameters in solar thermal collector provided with impinging air jets based upon preference selection index method Renew Energy 2016;99:118–26 https://doi.org/10.1016/j.renene.2016.06.046 Wang G, Deng Y, Xin X, He X, Zhao Y, Zou Y, Liu Z, Yue J Optimization of air jet impingement drying of okara using response surface methodology Food Control 2016;59:743–9 https://doi.org/10.1016/j.foodcont.2015.06.047 Hu J, Liu K, Ma L, Sun X Parameter optimization of solar air collectors with holes on baffle and analysis of flow and heat transfer characteristics Sol Energy 2018;174:878–87 https:// doi.org/10.1016/j.solener.2018.09.075 Tuyen V, Van Hap N, Phu NM Thermal-hydraulic characteristics and optimization of a liquid-to-suction triple-tube heat exchanger Case Stud Therm Eng 2020 https: //doi.org/10.1016/j.csite 2020.100635 Bouchekara HREH, Kedous-Lebouc A, Yonnet JP, Chillet C Multiobjective optimization of AMR systems Int J Refrig 2014;37:63–71 https://doi.org/10.1016/j.ijrefrig.2013.09.009 13 59 Holik M, Živić M, Virag Z, Barac A Optimization of an organic Rankine cycle constrained by the application of compact heat exchangers Energy Convers Manag 2019;188:333–45 https:// doi.org/10.1016/j.enconman.2019.03.039 60 Steven G, Penoncello Thermal energy systems-design and analysis Boca Raton: CRC Press; 2015 61 Hajabdollahi Z, Hajabdollahi H, Kim KC Heat transfer enhancement and optimization of a tube fitted with twisted tape in a fin-and-tube heat exchanger J Therm Anal Calorim 2019;140:1015–1027 62 Arul KR, Ganesh Babu B, Mohanraj M Thermodynamic performance of forced convection solar air heaters using pin–fin absorber plate packed with latent heat storage materials J Therm Anal Calorim 2016;126:1657–78 63 Nguyen MP, Lee GS Effects of inlet water temperature and heat load on fan power of counter-flow wet cooling tower Trans Korean Soc Mech Eng B 2013;37:267–73 64 Wechtaisong C, Sutthitep T, Prommak C Multi-objective planning and optimization for base station placement in WiMAX network In: 11th International conference on electrical engineering/ electronics, computer, telecommunications and information technology (ECTI-CON), Nakhon Ratchasima; 2014, pp 1–4 65 Klein SA Engineering equation solver (EES) London: F-Chart Software; 2013 66 Singh S, Kumar PA, Gupta A Review and performance evaluation of roughened solar air heaters Renew Sustain Energy Rev 2018;81:954–77 67 Singh S, Singh B, Hans VS, Gill RS CFD (computational fluid dynamics) investigation on Nusselt number and friction factor of solar air heater duct roughened with non-uniform cross-section transverse rib Energy 2015;84:509–17 https: //doi.org/10.1016/j energy.2015.03.015 68 Meibodi SS, Kianifar A, Mahian O, et al Second law analysis of a nanofluid-based solar collector using experimental data J Therm Anal Calorim 2016;126:617–25 https://doi.org/10.1007/s1097 3-016-5522-7 69 Chu SX, Liu LH Entropy generation analysis of twodimensional high-temperature confined jet Int J Therm Sci 2009;48(5):998–1006 70 Sunil C, Lu R, Xu D, Yu P Thermal performance improvement of a solar air heater fitted with winglet vortex generators Sol Energy 2018;159:966–83 https://doi.org/10.1016/j.solener.2017.11.046 Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations PHẦN LÝ LỊCH TRÍCH NGANG Họ tên: Trần Thế Bảo Ngày, tháng, năm sinh: 16-06-1992 Nơi sinh: Bình Định Địa liên lạc: Căn hộ A2-5.04 Chung cư Ehome 3, 103 Hồ Học Lãm, Phường An Lạc, Quận Bình Tân, TP Hồ Chí Minh Q TRÌNH ĐÀO TẠO - Từ năm 2010-2015: Học chuyên ngành Kỹ thuật Cơ khí (Hệ quy)Đại học Bách Khoa - Đại học Quốc gia Thành phố Hồ Chí Minh - Năm 2016 đến nay: Học viên cao học chuyên ngành Kỹ thuật Nhiệt- Đại học Bách Khoa - Đại học Quốc gia Thành phố Hồ Chí Minh Q TRÌNH CƠNG TÁC - Năm 2015 - 2016: Kỹ sư Cơ khí Cơng ty TNHH JaCon Việt Nam - Năm 2016-2018: Kỹ sư quản lý dự án- Công ty TNHH China Ecoteck Việt Nam - Năm 2018- Đến nay: Quản lý Công ty TNHH Giải pháp Công nghệ AIT ... CHƯƠNG 4: TỐI ƯU HÓA HIỆU SUẤT EXERGY VÀ KINH TẾ 75 4.1 Hàm mục tiêu, biến định điều kiện ràng buộc 75 4.2 Lựa chọn phương pháp tối ưu hóa đa mục tiêu 77 4.3 Tối ưu hóa exergy- kinh tế sử... thời tối ưu hóa hàm exergy- kinh tế SAH 1.3 Phạm vi nghiên cứu Phạm vi nghiên cứu luận văn phân tích hiệu suất, tối ưu hóa hàm exergy- kinh tế với số Reynolds khảo sát từ 1,200 đến 20,000, độ cao nhám. .. này, tập trung phân tích hiệu suất nhiệt, hiệu suất hiệu dụng, hiệu suất exergy tối ưu hóa exergy- kinh tế SAH Những ảnh hưởng yếu tố bước nhám tương đối, độ cao tương đối nhám, diện tích bề mặt