Answered: A heat pack can be modeled as a plane…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A heat pack can be modeled as a plane wall of thickness L=2cm. Assume that the pack has a constant thermal conductivity (4.0 W/(m*K)) and constant heat generation (800 W/m3 ) with one side (x=0) maintained at a constant temperature T1 = 80°C and the other side (x=L) cooled by moving air at T∞ = 25°C with a heat transfer coefficient of h = 20 W/(m2K).
a. Reduce the heat equation with clearly stated assumptions
b. Find the steady-state temperature distribution T(x) in the pack.

Expert Solution

Step 1: Write the given data and what is to find

Given:

$table row L equals cell 2 space c m end cell row k equals cell 4 space W divided by m minus K end cell row cell q with dot on top subscript g e n end subscript end cell equals cell 800 space W divided by m cubed end cell row cell T subscript 1 end cell equals cell 80 to the power of o C end cell row cell T subscript infinity end cell equals cell 25 to the power of o C end cell row h equals cell 20 space W divided by m squared minus K end cell end table$

To find:

a. Reduce the heat equation with clearly stated assumptions
b. Find the steady-state temperature distribution T(x) in the pack.

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