# HW_C6_1 - Hint use the following expression for the...

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Homework Set #6: Due date: 10/27/06, by 11:00 am. Problem #1 : Solve problem 10.A.1 in BSL Problem #2 : Solve problem 10.B.1 in BSL: Answer questions (a), (b), and (c). Do not work on question (d). Problem #3 : Read the statement of Problem 10.B.4 in BSL, but do NOT answer questions (a) and (b) in the text. Answer the followings: (a) Derive a differential equation for temperature T. (b) Show that the differential equation in (a) can be converted into the following form ( 29 ( 29 1 1 0 0 1 0 C d T T k k k dr r Θ - - + - Θ = where 0 1 0 T T T T   - Θ=  ÷ -   and C1 is an integration constant (c) State boundary conditions in terms of (d) Solve the equation in (b) using boundary conditions in (c). Note that you only need to determine C1. You do not need to determine C2. (e) Determine the heat flow through the wall. In your derivation, show that the determination of C2 is not necessary.

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Unformatted text preview: Hint: use the following expression for the temperature dependence of the thermal conductivity k ( 29 ( 29 1 1 1 1 T T k k k k k k k T T T T T T -= + - ≡ + - Θ ÷- -Θ= ÷- When you obtain a differential equation for temperature T, you may want to make the following variable transformation ( 29 1 dT d T T dr dr Θ =-Using this transformation to convert the differential equation for T into a differential equation for Θ . Θ To solve the equation in (b), you multiply both sides of this equation with dr . As a result, the left- and right-hand sides of the resulting equation (i.e. after multiplying by dr) are two separate differential equations, which can be integrated separately. Problem #4 : Solve problem 10.B.9 in BSL: only question (a)...
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HW_C6_1 - Hint use the following expression for the...

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