Answered: 2. Consider a large plane wall of…

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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$2. Consider a large plane wall of thickness $ L = 0.05 \, \text{m} $. The wall surface at $ x = 0 $ is insulated, while the surface at $ x = L $ is maintained at a temperature of $ 30^\circ \text{C} $. The thermal conductivity of the wall is $ k = 30 \, \text{W/m}\cdot\text{K} $, and heat is generated in the wall at a rate $ \dot{q} = \dot{q}_0 e^{-0.5x/L} $ where $ \dot{q}_0 = 8 \times 10^6 \, \text{W/m}^3 $. Assume steady-state one-dimensional heat transfer. (a) Write the appropriate form of the energy equation. (b) Specify boundary conditions for solving the energy equation for the temperature profile. (c) Solve for the temperature profile within the wall. (d) Determine the maximum temperature within the wall and its location. (e) Calculate the rate of heat transfer per unit area from the wall.$

Transcribed Image Text:2. Consider a large plane wall of thickness $ L = 0.05 \, \text{m} $. The wall surface at $ x = 0 $ is insulated, while the surface at $ x = L $ is maintained at a temperature of $ 30^\circ \text{C} $. The thermal conductivity of the wall is $ k = 30 \, \text{W/m}\cdot\text{K} $, and heat is generated in the wall at a rate $ \dot{q} = \dot{q}_0 e^{-0.5x/L} $ where $ \dot{q}_0 = 8 \times 10^6 \, \text{W/m}^3 $. Assume steady-state one-dimensional heat transfer. (a) Write the appropriate form of the energy equation. (b) Specify boundary conditions for solving the energy equation for the temperature profile. (c) Solve for the temperature profile within the wall. (d) Determine the maximum temperature within the wall and its location. (e) Calculate the rate of heat transfer per unit area from the wall.

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