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EX4: Non-Constant Conductivity II

Homework Problems

Equation (6.7-) gives the temperature distribution in an infinite circular tube with inner radius and outer radius and boundary temperatures . shows that the thermal conductivity varies with temperature. can increase or decrease with or remain relatively constant.

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 62 - homework! :

Make equation (6.7-) dimensionless in terms of



Equation 130



Equation 131

and one dimensionless parameter,



Equation 132

Use equations (6.1) and (6.6) to represent and . Recall that we have set , therefore .

Problem 63 - homework! :

Plot for . To see how the plot changes as is varied click here.

Problem 64 - homework! :

What is your physical interpretation of the parameter ?

Problem 65 - 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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