For the following descriptions, please write the appropriate form of the heat (c

Question

For the following descriptions, please write the appropriate form of the heat (conduction) equation: a) A cylindrical rod having constant thermal conductivity, whose side surfaces are perfectly insulated while the opposite ends are maintained at different temperatures, which do not change with time b) Electrical current flows through a cylindrical rod having constant thermal conductivity, whose side surfaces are perfectly insulated while the opposite ends are maintained at different temperatures, which do not change over time. The flow of electrical current results in uniform heat generation within the rod c) Electrical current starts to flow through a cylindrical rod having constant thermal conductivity, whose side surfaces are exposed to air at constant temperature. The flow of electrical current results in uniform heat generation within the rod. d) Electrical current flows through a cylindrical rod for a long period of time. One half of rod

Explanation / Answer

a) d^2T/dx^2 = 0
b)d^2T/dx^2 +(q*)/k=0
q* =i^2r
c) d^2T/dx^2 +d^2T/dy^2 +(q*)/k=0
d) equation b for length l/2 and eq c for next length l/2 and at boundary T is same
e)d^2T/dx^2 +d^2T/dy^2 =(1/ )(dT/dt)

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