Introduction to Heat Transfer
Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2, Problem 2.54P

The one-dimensional system of mass M with constant properties and no internal heat generation shown in the figure is initially at a uniform temperature T i . The electrical heater is suddenly energized, providing a uniform heat flux q o " at the surface x = 0. The boundaries at x = L and elsewhere are perfectly insulated.

Chapter 2, Problem 2.54P, The one-dimensional system of mass M with constant properties and no internal heat generation shown

  1. Write the differential equation, and identify the boundary and initial conditions that could be used to determine the temperature as a function of position and time in the system.
  2. On T x coordinates, sketch the temperature distributions for the initial condition t 0 and for several times after the heater is energized. Will a steady-state temperature distribution ever be reached?
  3. On q x " t coordinates, sketch the heat flux q x " x , t at the planes x = 0 , x = L / 2 , and x = L as a function of time.
  4. After a period of time t e has elapsed, the heater power is switched off. Assuming that the insulation is perfect, the system will eventually reach a final uniform temperature T f . Derive an expression that can be used to determine T f as a function of the parameters q o " , t e , T i , and the system characteristics M , c p , and A s (the heater surface area).

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Chapter 2 Solutions

Introduction to Heat Transfer

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