Answered: 5. Consider the following diagram from…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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$# Understanding Heat Transfer: Analyzing Temperature Distribution ## Diagram Explanation The diagram illustrates heat transfer through a plane wall and consists of two main parts: 1. **Temperature Distribution:** - Represents the flow of heat from a hot fluid with temperature $ T_{\infty,1} $ on one side to a cold fluid with temperature $ T_{\infty,2} $ on the other side. - Heat transfer occurs convectively from the hot fluid to the solid surface at $ x = 0 $, then through the solid, and finally to the cold fluid. - The red curve shows a nonlinear temperature profile within the solid, indicating the boundary layer effects on the fluid side. 2. **Equivalent Thermal Circuit:** - A thermal resistance circuit diagram is shown below the temperature profile. - Consists of resistances representing convective and conductive heat transfer: - $ R_{conv,1} $ for convective resistance at the hot fluid side. - $ R_{cond} $ for conductive resistance through the solid medium. - $ R_{conv,2} $ for convective resistance at the cold fluid side. ## Focus Areas - **Temperature Distribution from $ T_{\infty,1} $ to $ T_{s,1} $:** - Highlights convection from hot fluid to the solid surface at $ x = 0 $. - The distribution is nonlinear, reflecting the boundary layer influence of the fluid. - **Discussion Points:** - **(a)** While the function is nonlinear, we can still use electrical circuit analogies to model heat convection at $ x = 0 $ because the principles governing flow (Ohm’s Law and Fourier’s Law of Heat Conduction) are analogous. - **(b)** On the other hand, heat conduction in the solid requires a linear temperature distribution (from $ x = 0 $ to $ x = L $), which aligns with steady-state assumptions and allows reliable use of electrical circuit analogies. The reasons for this relate to the direct proportionality between temperature difference and heat flow within the solid, typical of linear systems.$

Transcribed Image Text:# Understanding Heat Transfer: Analyzing Temperature Distribution ## Diagram Explanation The diagram illustrates heat transfer through a plane wall and consists of two main parts: 1. **Temperature Distribution:** - Represents the flow of heat from a hot fluid with temperature $ T_{\infty,1} $ on one side to a cold fluid with temperature $ T_{\infty,2} $ on the other side. - Heat transfer occurs convectively from the hot fluid to the solid surface at $ x = 0 $, then through the solid, and finally to the cold fluid. - The red curve shows a nonlinear temperature profile within the solid, indicating the boundary layer effects on the fluid side. 2. **Equivalent Thermal Circuit:** - A thermal resistance circuit diagram is shown below the temperature profile. - Consists of resistances representing convective and conductive heat transfer: - $ R_{conv,1} $ for convective resistance at the hot fluid side. - $ R_{cond} $ for conductive resistance through the solid medium. - $ R_{conv,2} $ for convective resistance at the cold fluid side. ## Focus Areas - **Temperature Distribution from $ T_{\infty,1} $ to $ T_{s,1} $:** - Highlights convection from hot fluid to the solid surface at $ x = 0 $. - The distribution is nonlinear, reflecting the boundary layer influence of the fluid. - **Discussion Points:** - **(a)** While the function is nonlinear, we can still use electrical circuit analogies to model heat convection at $ x = 0 $ because the principles governing flow (Ohm’s Law and Fourier’s Law of Heat Conduction) are analogous. - **(b)** On the other hand, heat conduction in the solid requires a linear temperature distribution (from $ x = 0 $ to $ x = L $), which aligns with steady-state assumptions and allows reliable use of electrical circuit analogies. The reasons for this relate to the direct proportionality between temperature difference and heat flow within the solid, typical of linear systems.

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