Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated

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Textbook Question
Chapter 2, Problem 2.1P

Assume steady-state, one-dimensional heat conduction through the axisymmetric shape shown below.

Assuming constant properties and no internal heat generation, sketch the temperature distribution on T x coordinates. Briefly explain the shape of your curve.

To determine

To sketch: The temperature distribution on T-x coordinates and explain the shape.

### Explanation of Solution

Draw the axisymmetric shape as shown below:

Write the expression as per Fourier law.

qx=kAxdTdx

Here, qx is the heat conducted through the axisymmetric shape, k is the thermal conductivity of shape, Ax is the area of shape at position x , dT is change in temperature and dx is the change in position.

Since the heat transfer through the body remains constant and thermal conductivity of the body remains constant, the Fourier law can be explained as:

AxdTdx=constantdTdx1Ax

The above expression indicated that temperature and thickness is inversely proportional to one another.

On T-x curve the independent variable is x and the dependent variable is T .

Draw the T-x curve for axisymmetric shape as shown below:

The T-xcurve for axisymmetric shape is shown above and the slope dTdx decreases as distance increases.

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