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EX3: Non-Constant Conductivity I

Homework 5.5

Equation (5.6) gives the temperature distribution in an infinite slab of material of thickness bounded by planes at 0 and whose temperatures are and . Figure 6 shows that the thermal conductivity varies with temperature. can increase or decrease with or remain relatively constant.

The differential equation, (5.2) was solved to obtain the temperature distribution, equation (5.6).

What we want to do here is to obtain an equation which represents the solution for every possible specification of and . Note that in this problem is a linear function of .

Problem 51 - homework! :

Make equation (5.6) dimensionless in terms of



Equation 72



Equation 73

and one dimensionless parameter,



Equation 74

Use equations (5.1) and (5.3) to represent and .

Problem 52 - homework! :

Plot vs. for . See how the plot changes as is varied here.

Problem 53 - homework! :

What is your physical interpretation of the parameter ?

Problem 54 - homework! :

Determine the sensitivity of at any value of to the value of .

Hint: Obtain an expression for and calculate its value for 0.1, 0.2, 0.4, 0.6, and 1.

 
 
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