BOOKCOMP, Inc. — John Wiley & Sons / Page 895 / 2nd Proofs / Heat Transfer Handbook / Bejan FOULING 895 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [895], (99) Lines: 4121 to 4121 ——— 1.66077pt PgVar ——— Normal Page PgEnds: T E X [895], (99) TABLE 11.6 Fouling Resistances of Various Gas, Vapor, and Liquid Streams Fouling Fouling Resistance Resistance Fluid (10 4 m 2 · K/W) Fluid (10 4 m 2 · K/W) Liquid water streams Crude oil refinery streams Artificial spray pond water 1.75–3.5 Temperature ≈ 120°C 3.5–7 Boiler blowdown water 3.5–5.3 Temperature ≈ 120–180°C 5.25–7 Brackish water 3.5–5.3 Temperature ≈ 180–230°C 7–9 Closed-cycle condensate 0.9–1.75 Temperature > 230°C 9–10.5 Closed-loop treated water 1.75 Petroleum streams Distilled water 0.9–1.75 Lean oil 3.5 Engine jacket water 1.75 Liquefied petroleum gases 1.75–3 River water 3.5–5.3 Natural gasolene 1.75–3.5 Seawater 1.75–3.5 Rich oil 1.75–3.5 Treated boiler feedwater 0.9 Process liquid streams Treated cooling tower water 1.75–3.5 Bottom products 1.75–3.5 Industrial liquid streams Caustic solutions 3.5 Ammonia (oil bearing) 5.25 DEA solutions 3.5 Engine lube oil 1.75 DEG solutions 3.5 Ethanol 3.5 MEA solutions 3.5 Ethylene glycol 3.5 TEG solutions 3.5 Hydraulic fluid 1.75 Caustic solutions 3.5 Industrial organic fluids 1.75–3.5 Crude and vacuum liquids Methanol 3.5 Atmospheric tower bottoms 12.3 Refrigerants 1.75 Gasolene 3.5 Transformer oil 1.75 Heavy fuel oil 5.3–12.3 No. 2 fuel oil 3.5 Heavy gas oil 5.3–9 No. 6 fuel oil 0.9 Kerosene 3.5–5.3 Cracking and coking unit streams Light distillates and gas oil 3.5–5.3 Bottom slurry oils 5.3 Naphtha 3.5–5.3 Heavy coker gas oil 7–9 Vacuum tower bottoms 17.6 Heavy cycle oil 5.3–7 Industrial gas or vapor streams Light coker gas oil 5.3–7 Ammonia 1.75 Light cycle oil 3.5–5.3 Carbon dioxide 3.5 Light liquid products 3.5 Coal flue gas 17.5 Overhead vapors 3.5 Compressed air 1.75 Light-end processing streams Exhaust steam (oil bearing) 2.6–3.5 Absorption oils 3.5–5.3 Natural gas flue gas 9 Alkylation trace acid streams 3.5 Refrigerant (oil bearing) 3.5 Overhead gas 1.75 Steam (non-oil bearing) 9 Overhead liquid products 1.75 Overhead vapors 1.75 Reboiler streams 3–5.5 Chemical process streams Acid gas 3.5–5.3 Natural gas 1.75–3.5 Solvent vapor 1.75 Stable overhead products 1.75 Source: Adapted from Chenoweth (1988). BOOKCOMP, Inc. — John Wiley & Sons / Page 896 / 2nd Proofs / Heat Transfer Handbook / Bejan 896 HEAT EXCHANGERS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [896], (100) Lines: 4121 to 4381 ——— 0.20695pt PgVar ——— Short Page PgEnds: T E X [896], (100) to specify a fouling factor for a particular process stream along with some range of appropriate temperature differences. TEMA has made some attempt to anticipate temperature differences by classifying fouling factors according to various process services. The result is inexact, as there is much latitude in establishing a process service. In any event, fouling factors which are, in reality, fouling resistances are given by TEMA and may be specified by other standards. Chenoweth (1990) provided a summary of the fouling resistances for various gas, vapor, and liquid streams. A partial list of his fouling factors is given in Table 11.6. NOMENCLATURE Roman Letter Symbols A bp crossflow area for bypass, m 2 A c crossflow area, m 2 cold-side flow area, m 2 A CL centerline flow area, m 2 A f flow area, m 2 A fr frontal area, m 2 A fr,c cold-side frontal area, m 2 A fr,h hot-side frontal area, m 2 A fr,1 frontal area, side 1 of exchanger, m 2 A fr,2 frontal area, side 2 of exchanger, m 2 A w window flow area, m 2 A wg gross window area, m 2 A wt crossflow area for bypass, m 2 A 1 inlet nozzle area, m 2 A 2 bundle entry area, m 2 A 3 outlet nozzle area, m 2 A 4 bundle exit area, m 2 a coefficient, dimensionless separation or splitter plate thickness, m b coefficient, dimensionless distance between separation plates, m mean flow channel gap, m b f fin height, m b i inside fin height, m b o outside fin height, m C constant, dimensionless capacity rate, W/K C c cold-fluid capacity rate, W/K C h hot-fluid capacity rate, W/K coefficient, dimensionless C m matrix wall capacity rate, W/K BOOKCOMP, Inc. — John Wiley & Sons / Page 897 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 897 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [897], (101) Lines: 4381 to 4381 ——— 0.39796pt PgVar ——— Short Page PgEnds: T E X [897], (101) C max maximum capacity rate, W/K C min minimum capacity rate, W/K C mc cold-side matrix wall capacity rate, W/K C mh hot-side matrix wall capacity rate, W/K C 1 difference between shell inside diameter and outer tube limit, m ¯ C c cold-side heat capacitance, W/kg · K ¯ C h hot-side heat capacitance, W/kg · K ¯ C m matrix material heat capacitance, W/kg · K ¯ C mc cold-side matrix material heat capacitance, W/kg · K ¯ C mh hot-side matrix material heat capacitance, W/kg · K C ∗ capacity rate ratio, dimensionless c c contraction coefficient, dimensionless counterflow coefficient, dimensionless c m specific heat of rotor, J/kg · K c p specific heat at constant pressure, J/kg · K c pc cold-fluid specific heat at constant pressure, J/kg · K c ph hot-fluid specific heat at constant pressure, J/kg · K D depth of exchanger, m parameter defined where used D b baffle diameter, m D e equivalent diameter, m D e equivalent diameter of bypass lane, m D o outer tube limit diameter, m D s shell inside diameter, m d diameter, m d e equivalent diameter, m d h hydraulic diameter, m d i inner or inside diameter, m d o tube diameter (outside diameter), m F logarithmic mean temperature difference correction factor, dimensionless F C crossflow tube fraction, dimensionless F T transitional correction factor, dimensionless F w fraction of number of tubes in one window, dimensionless f friction factor, dimensionless G parameter, defined when used, dimensionless mass velocity, kg/m 2 · s G ch channel mass velocity, kg/m 2 · s Gr Graetz number, dimensionless g c proportionality factor in Newton’s second law, dimensionless H height of exchanger, m h heat transfer coefficient, W/m 2 · K h c cold-side heat transfer coefficient, W/m 2 · K h dc cold-side fouling heat transfer coefficient, W/m 2 · K BOOKCOMP, Inc. — John Wiley & Sons / Page 898 / 2nd Proofs / Heat Transfer Handbook / Bejan 898 HEAT EXCHANGERS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [898], (102) Lines: 4381 to 4381 ——— 1.00563pt PgVar ——— Normal Page PgEnds: T E X [898], (102) h dh hot-side fouling heat transfer coefficient, W/m 2 · K h h hot-side heat transfer coefficient, W/m 2 · K h i inside heat transfer coefficient, W/m 2 · K h io inside heat transfer coefficient referred to outside surface, W/m 2 · K h iη annulus heat transfer coefficient corrected for the weighted fin efficiency, W/m 2 · K h o annulus heat transfer coefficient including the effect of fouling, W/m 2 · K I modified Bessel function of the first kind, dimensionless J B correction factor for bundle bypass, dimensionless J C correction factor for baffle cut, dimensionless J L correction factor for baffle leakage, dimensionless J R correction factor for temperature gradient, dimensionless j h heat transfer parameter, dimensionless k thermal conductivity, W/m · K k m thermal conductivity of metal, W/m · K L exchanger length, m tube length, m length of plate, m L bc central baffle spacing, m L bi baffle spacing at inlet, m L bo baffle spacing at outlet, m L ∗ i baffle spacing parameter, dimensionless L ∗ o baffle spacing parameter, dimensionless l c baffle cut, m LMTD logarithmic mean temperature difference, K m mass of matrix, kg fin performance factor, m −1 ˙m mass flow rate, kg/s ˙m b bypass path mass flow rate, kg/s ˙m c cold-fluid mass flow rate, kg/s crossflow path mass flow rate, kg/s ˙m cr total crossflow mass flow rate, kg/s ˙m h hot-fluid mass flow rate, kg/s ˙m l leakage path mass flow rate, kg/s ˙m s shell-to-baffle leakage path mass flow rate, kg/s ˙m T total mass flow rate, kg/s ˙m t tube-to-baffle leakage path mass flow rate, kg/s ˙m w window mass flow rate, kg/s N cc group of length terms, dimensionless N cf number of transfer units for counter flow, dimensionless N CL number of tubes on shell centerline, dimensionless N cw number of tubes crossed in one window, dimensionless N p number of plates, dimensionless BOOKCOMP, Inc. — John Wiley & Sons / Page 899 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 899 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [899], (103) Lines: 4381 to 4381 ——— 0.0059pt PgVar ——— Normal Page PgEnds: T E X [899], (103) N r rotational speed, rev/s N ss number of sealing strip pairs, dimensionless N tu number of heat transfer units, dimensionless N tu,c number of heat transfer units based on cold side, dimensionless N tu,o overall number of heat transfer units, dimensionless n number of fins, dimensionless n b flow resistance of bypass path, N · s/m 2 · kg n c number of tubes crossed, dimensionless flow resistance of crossflow path, N · s/m 2 · kg n cr flow resistance of total crossflow path, N ·s/m 2 · kg n cw number of tubes crossed in one window, dimensionless n hp number of hairpins, dimensionless n i number of fins on inside, dimensionless n o number of fins on outside, dimensionless n p number of passes, dimensionless number of in-line pass partitions, dimensionless n r number of rows, dimensionless n s flow resistance of shell-to-baffle leakage path, N · s/m 2 · kg n t flow resistance of tube-to-baffle leakage path, N · s/m 2 · kg number of tubes, dimensionless n tw number of tubes in one window, dimensionless n w flow resistance of window path, N · s/m 2 · kg n we exit space window flow resistance, N · s/m 2 · kg n 1 number of stacks, side 1 of heat exchanger, dimensionless n 2 number of stacks, side 2 of heat exchanger, dimensionless n number of tubes in a row, dimensionless Nu Nusselt number, dimensionless Nu d Nusselt number based on diameter, dimensionless Nu ch channel Nusselt number, dimensionless P cold-side effectiveness, dimensionless perimeter of passage, m pressure, N/m 2 or Pa P c cold-fluid time period, s P d diagonal pitch, m P h hot-fluid time period, s P l longitudinal pitch, m P t transverse pitch, m P W 1 wetted perimeter for one channel, m ∆P pressure loss, N/m 2 or Pa ∆P AB pressure loss from A to B,N/m 2 or Pa ∆P b bypass path pressure loss, N/m 2 or Pa ∆P c crossflow path pressure loss, N/m 2 or Pa ∆P ch channel pressure loss, N/m 2 or Pa ∆P cr total crossflow path pressure loss, N/m 2 or Pa BOOKCOMP, Inc. — John Wiley & Sons / Page 900 / 2nd Proofs / Heat Transfer Handbook / Bejan 900 HEAT EXCHANGERS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [900], (104) Lines: 4381 to 4381 ——— 0.00563pt PgVar ——— Normal Page PgEnds: T E X [900], (104) ∆P e end-space pressure loss, N/m 2 or Pa ∆P f friction pressure loss, N/m 2 or Pa ∆P l leakage path pressure loss, N/m 2 or Pa ∆P n1 pressure loss at inlet nozzle, N/m 2 or Pa ∆P n2 pressure loss at outlet nozzle, N/m 2 or Pa ∆P port port pressure loss, N/m 2 or Pa ∆P s shell-to-baffle path pressure loss, N/m 2 or Pa ∆P t turn pressure loss, N/m 2 or Pa tube-to-baffle path pressure loss, N/m 2 or Pa ∆P w window pressure loss, N/m 2 or Pa p porosity of matrix surface, dimensionless p b baffle cut, m p pl plate pitch, m Pr Prandtl number, dimensionless Pr w Prandtl number based on wall thermal properties, dimensionless q heat flow, W tube pitch correction factor, dimensionless R capacity rate ratio, W/K thermal resistance, K/W R c cold-side thermal resistance, K/W R dc cold-side fouling thermal resistance, K/W R dh hot-side fouling thermal resistance, K/W R h hot-side thermal resistance, K/W R io sum of internal resistances referred to the outside of the inner pipe, K/W R is sum of internal resistances referred to gross outside surface, K/W R m metal thermal resistance, K/W r a area ratio, defined where used, dimensionless r b area ratio, defined where used, dimensionless r c area ratio, defined where used, dimensionless r di inside fouling resistance, m 2 · K/W r dio inside fouling resistance referred to tube outside, m 2 · K/W r do outside fouling resistance, m 2 · K/W r h hydraulic radius, m r io inside film resistance referred to tube outside, m 2 · K/W r mo pipe wall resistance referred to tube outside, m 2 · K/W r o annulus film resistance referred to tube outside, m 2 · K/W r oη annulus thermal resistance corrected for fouling, m 2 · K/W r o refers to outside or annulus resistance with fouling, m 2 · K/W r oη refers to outside or annulus resistance with fouling corrected for overall efficiency, m 2 · K/W Re Reynolds number, dimensionless Re c crossflow Reynolds number, dimensionless BOOKCOMP, Inc. — John Wiley & Sons / Page 901 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 901 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [901], (105) Lines: 4381 to 4444 ——— 12.00577pt PgVar ——— Normal Page PgEnds: T E X [901], (105) Re d Reynolds number based on diameter, dimensionless S surface area, m 2 S annulus surface per unit length, m 2 /m S b base or prime surface area, m 2 S bi inside base surface area, m 2 S bo outside base surface area, m 2 S c cold side surface area, m 2 S f finned surface area, m 2 S fi inside finned surface area, m 2 S fo outside surface area, m 2 S h hot surface area, m 2 S i inside surface area, m 2 S m metal or matrix surface area, m 2 S o outside surface area, m 2 S surface area per unit length of tube, m 2 /m St Stanton number, dimensionless T hot-fluid temperature, K T mc cold-side matrix temperature, K T mh hot-side matrix temperature, K T s surface temperature, K T w wall temperature, K T 1 inlet hot-fluid temperature, K T 2 outlet hot-fluid temperature, K t cold-fluid temperature, K t 1 inlet cold-fluid temperature, K t 2 outlet cold-fluid temperature, K U overall heat transfer coefficient, W/m 2 · K U c overall heat transfer coefficient referred to cold fluid, W/m 2 · K U h overall heat transfer coefficient referred to hot fluid, W/m 2 ·K u linear velocity, m/s V volume of exchanger, m 3 V void void volume, m 3 v specific volume of fluid, m 3 /kg W width of exchanger, m width of plate, m w effective plate width, m w p width of bypass divider lane, m X L longitudinal tube spacing, m X T transverse tube spacing, m Z parameter used in multistream arrangements, dimensionless z clear space between tubes, m pass partition width, m fin root width, m BOOKCOMP, Inc. — John Wiley & Sons / Page 902 / 2nd Proofs / Heat Transfer Handbook / Bejan 902 HEAT EXCHANGERS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [902], (106) Lines: 4444 to 4444 ——— 0.72923pt PgVar ——— Normal Page PgEnds: T E X [902], (106) Greek Letter Symbols α parameter defined where used, dimensionless ratio of total area on one side of the exchanger to the total volume on both sides of an exchanger, m 2 /m 3 packing density, m 2 /m 3 β parameter defined where used, dimensionless ratio of total area on to the total volume on one side of an exchanger, m 2 /m 3 chevron angle, deg Γ parameter defined where used, dimensionless γ correction factor for multipass arrangements, dimensionless parameter defined where used, dimensionless ∆ change in, dimensionless δ f fin thickness, m δ fi inside fin thickness, m δ fo outside fin thickness, m δ m metal thickness, m δ ov height of baffle overlap region, m δ pl plate thickness, m δ sb shell-to-baffle spacing, m δ sh tube sheet thickness, m δ tb tube-to-baffle spacing, m δ ts tube-to-shell gap thickness, m exchanger effectiveness, dimensionless ζ combination of terms, dimensionless η efficiency, dimensionless η c cold-side fin efficiency, dimensionless η f fin efficiency, dimensionless η fi inside fin efficiency, dimensionless η fo outside fin efficiency, dimensionless η h hot-side fin efficiency, dimensionless η ov overall efficiency, dimensionless η ov,c cold-side overall efficiency, dimensionless η ov,h hot-side overall efficiency, dimensionless η ov,i inner or inside efficiency, dimensionless η ov,o outer or outside efficiency, dimensionless θ m true temperature difference, K θ 1 angle between the horizontal and the point on the baffle edge on the baffle cut, rad θ 2 angle, rad θ 3 twice the angle between the vertical and the intersection of the baffle edge and the outer tube limit, rad Λ enlargement factor, dimensionless µ dynamic viscosity, N · s 2 /m ρ fluid density, dimensionless BOOKCOMP, Inc. — John Wiley & Sons / Page 903 / 2nd Proofs / Heat Transfer Handbook / Bejan NOMENCLATURE 903 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [903], (107) Lines: 4444 to 4550 ——— 0.20847pt PgVar ——— Normal Page PgEnds: T E X [903], (107) ratio of transverse to longitudinal tube spacing, dimensionless σ ratio of free flow area to frontal area, dimensionless τ dc cold-side dwell time, s τ dh hot-side dwell time, s Υ ratio of Prandtl numbers, dimensionless Φ parameter, defined where used, dimensionless φ viscosity correction factor, dimensionless φ c cold-side face angle in a regenerator, rad φ h hot-side face angle in a regenerator, rad φ sh shield face angle in a regenerator, rad φ t total face angle in a regenerator, rad ϕ group of length terms, dimensionless ψ ratio, dimensionless correction factor, dimensionless Subscripts a particular area ratio AB distance between A and B B bundle bypass b bypass path particular area ratio base or prime surface baffle bulk temperature bc central baffle spacing bi inside base surface bi inlet baffle spacing bo outside base surface bo outlet baffle spacing bp bypass area C baffle cut crossflow tube fraction CL tubes on shell centerline centerline flow area c contraction coefficient baffle cut cold fluid crossflow number of tubes crossed particular area ratio crossflow path cc group of length terms cf counterflow ch channel D diameter BOOKCOMP, Inc. — John Wiley & Sons / Page 904 / 2nd Proofs / Heat Transfer Handbook / Bejan 904 HEAT EXCHANGERS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [904], (108) Lines: 4550 to 4550 ——— 0.00604pt PgVar ——— Normal Page PgEnds: T E X [904], (108) d diameter diagonal dirt or fouling dc cold-side dwell time dh hot-side dwell time di inside fouling dio inside fouling condition referred to outside do outside fouling e end space equivalent f fin flow fi inside fin fo outside fin fr frontal area h heat transfer parameter hot fluid hydraulic i inner or inside id ideal condition L baffle leakage l longitudinal m matrix or metal max maximum min minimum mo metal condition referred to outside n 1 nozzle 1 location n 2 nozzle 2 location o outer or outside outer tube limit p number of bypass divider lanes width of bypass divider lane number of pass partitions number of bypass divider lanes pl plate port port S baffle spacing s shell surface sb shell-to-baffle leakage path shell-to-baffle spacing sh tube sheet shell shell ss sealing strips . T E X [898], (102) h dh hot-side fouling heat transfer coefficient, W/m 2 · K h h hot-side heat transfer coefficient, W/m 2 · K h i inside heat transfer coefficient, W/m 2 · K h io inside heat transfer coefficient referred. dimensionless H height of exchanger, m h heat transfer coefficient, W/m 2 · K h c cold-side heat transfer coefficient, W/m 2 · K h dc cold-side fouling heat transfer coefficient, W/m 2 · K BOOKCOMP,. dimensionless N tu number of heat transfer units, dimensionless N tu,c number of heat transfer units based on cold side, dimensionless N tu,o overall number of heat transfer units, dimensionless n