Two large stainless steel plates at temperatures of 90°C and 70°C are separated by a stainless steel rod 0.3 m long and 2.5 cm in diameter. The thermal conductivity of type 304 stainless steel is k = 16.2 W/m K. The rod is welded to each plate. The space between the plates is filled with insulation so that no heat is lost from the circumference of the rod. Because of a voltage difference between the two plates, current flows through the rod, resulting in a uniform heat generation rate of 1.5 x 105 W/m3. a) Solve for the temperature distribution in the rod as a function of position x analytically (integrate the equation). b) Determine the maximum temperature in the rod. Where does it occur? c) Solve for the temperature distribution in the rod as a function of position x using the finite difference method. Assume a ∆x of 0.05 m. How does this compare to the exact solution?
Two large stainless steel plates at temperatures of 90°C and 70°C are separated by a stainless steel rod
0.3 m long and 2.5 cm in diameter. The thermal conductivity of type 304 stainless steel is k = 16.2
W/m K. The rod is welded to each plate. The space between the plates is filled with insulation so that
no heat is lost from the circumference of the rod. Because of a voltage difference between the two
plates, current flows through the rod, resulting in a uniform heat generation rate of 1.5 x 105 W/m3.
a) Solve for the temperature distribution in the rod as a function of position x analytically (integrate
the equation).
b) Determine the maximum temperature in the rod. Where does it occur?
c) Solve for the temperature distribution in the rod as a function of position x using the finite
difference method. Assume a ∆x of 0.05 m. How does this compare to the exact solution?
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