Solution Manual for Principles of Heat Transfer 7th Edition by Krieth Full file at https://TestbankDirect.eu/ Principles of Heat Transfer, 7th Edition Chapter 1: Concept Review Solutions 1.1 Briefly respond to the following to review the primary concepts learned in this chapter: (a) Explain how heat transfer by conduction is different from that by radiation Conduction is a diffusion process and requires a medium (matter which could be solid, liquid, or gas) for the transport of thermal energy or heat from a high temperature region to that at a lower temperature Radiation, on the other hand, is an electromagnetic wave transmission process and hence, does not require an intervening material medium (between the high and low temperature regions) for the transport of heat (b) State Fourier’s law of conduction for a one-dimensional system in words and write its heat transfer rate equation Fourier’s law of conduction states that the heat flux q′k′ , or the transfer rate per unit surface area (qk A) through which heat is transferred by conduction, is proportional to the temperature gradient normal (or perpendicular) to the surface Mathematically, this can be expressed as qk′′∞ dT dn or qk ∞A dT dn where (dT dn) is the temperature gradient in a one dimensional system, and A is the surface area Note that in a two- or three-dimensional system, the gradient would be expressed by a partial differential, or as (∂T ∂n) The proportionality constant gives the definition of the thermal conductivity k of a homogeneous medium and qk = − kA dT dn which is the general form of Eq (1.1) (c) How is the convective heat transfer coefficient defined? The convective heat transfer coefficient is defined as the ratio heat flux q′k′ (or the transfer rate per unit area (qk A) of the surface with which a fluid (gas or liquid) exchanges heat) and the temperature difference between the surface and some reference location in the fluid The average convection heat transfer coefficient can be calculated from Eq (1.10) as © 2011 Cengage Learning Engineering All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Principles of Heat Transfer 7th Edition by Krieth Full file at https://TestbankDirect.eu/ Principles of Heat Transfer, 7th Edition hc = q′′ q = ∆T A∆T (d) Write the equation for heat loss from a spherical satellite in space when the satellite surface has an emissivity of 50% The spherical satellite can be modeled as a gray body of diameter ds, which has a surface temperature Ts and an emissivity ε, and the outer space (or surrounding) as a black enclosure at a temperature of T∞ Thus, the radiation heat loss can be calculated from Eq (1.17) as qr = As εσ(Ts4 − T∞4 ) = (π d s2 )(0.5)(Ts4 − T∞4 ) where σ is the Stefan-Boltzmann constant (e) Identify the thermo-physical property that characterizes a metal and a thermal insulating material, and comment upon the magnitude of the two The thermal conductivity k is the thermo-physical property that characterizes the difference between a metal (a good conductor of heat) and an insulating material (a poor conductor of heat) The relative magnitude or value of their respective thermal conductivity is such that kmetal >> kinsulation Often for an insulating material, because of its make up (packed fibers, cellular foams, etc which may have entrapped gas), an effective thermal conductivity of insulation keff is specified which encapsulates a combination of heat flow mechanisms through the material 1.2 In both thermodynamics and heat transfer, energy conservation with transfer of heat is considered (a) Explain the differences in modeling heat transfer in the two cases The thermodynamic model looks at a device as an open (or closed) system (or control volume) and simply considers the overall energy balance; how or by what mechanism the energy or heat is transferred is not modeled The heat transfer model, on the other hand, considers the mechanism(s) or mode(s) of heat transfer in the energy balance and the relative contribution of heat transfer by conduction, convection, and radiation is calculated (b) Pick a simple engineering system or device of your choice and describe both the thermodynamics and heat transfer models for the transfer of heat and energy conservation in this system/device As an example, consider a closed feedwater heater, which is typically a shell-andtube heat exchanger in a steam power plant wherein steam extracted from a turbine © 2011 Cengage Learning Engineering All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Principles of Heat Transfer 7th Edition by Krieth Full file at https://TestbankDirect.eu/ Principles of Heat Transfer, 7th Edition flows on the shell-side of the exchanger and boiler feedwater flows inside the tubes As the steam, which is at a higher temperature than that of the feedwater, condenses on the outside of the tubes it heats up the feedwater In the Thermodynamic model, all we can calculate is the rate heat transfer from the condensing steam received by the boiler feedwater This can be expressed by applying energy conservation (First Law of Thermodynamics) to the control volume of the heat exchanger (an open system) for steady-state conditions Assuming no heat loss to the surroundings, the following is then obtained: qsteam = q feedwater or ( mh fg ) steam = [m( hout − hin )] feedwater = [ mc p (Tout − Tin )] feedwater In the heat transfer model, we can calculate how or by what mechanism heat is transferred from the condensing steam to the feedwater Energy conservation in this case tells us that heat transfer rate by convection due to steam condensation on the outside of the tubes in the heat exchanger is equal to the heat transfer rate by conduction through the material of the tubes This in turn is equal to the heat transfer rate by convection from the tube wall to the flowing feedwater, or q = qc ,steam = qk ,tubewall = qc , feedwater where qc ,steam = hc ,s Ao (Ts − Tw,o ) ro qk ,tubewall = − k w ∫ ri convection from steam to outer surface of tubes, dT 2π k w L dA = (T − T ) dr ln(ro ri ) w,o w,i qc , feed water = hc , fw Ai (Tw,i − T fw ) conduction through tube walls, and convection from inner tube surface to feedwater Ts is the average steam temperature, Ao is the outside surface area of the tubes, Tw,o is the outside surface temperature of the tube walls, Tw,i is the inner surface temperature of the tube walls, ri and ro are the inner and outer radii of the tubes, Ai is the inside surface area of the tubes, and Tfw is the average bulk temperature of feedwater Note that the term after the second equality sign in the conduction equation will be derived in Chapter and the student need not be concerned with it at this stage Based on this example, students should identify a few other heat exchangers in different applications and develop both the thermodynamic and heat transfer models for each © 2011 Cengage Learning Engineering All Rights Reserved Full file at https://TestbankDirect.eu/ ... https://TestbankDirect.eu/ Solution Manual for Principles of Heat Transfer 7th Edition by Krieth Full file at https://TestbankDirect.eu/ Principles of Heat Transfer, 7th Edition flows on the shell-side of the exchanger.. .Solution Manual for Principles of Heat Transfer 7th Edition by Krieth Full file at https://TestbankDirect.eu/ Principles of Heat Transfer, 7th Edition hc = q′′ q = ∆T... the outside of the tubes in the heat exchanger is equal to the heat transfer rate by conduction through the material of the tubes This in turn is equal to the heat transfer rate by convection