The temperature distribution in a moving cylindrical rod, shown in Figure P4.27, is given by the energy equation where U is the velocity of the moving rod of radius R, a is the thermal diffusivity, and the other variables are the same as in the preceding problem. The boundary conditions are Employing the finite-difference approach, compute T(x). Take U = 1 mm/s, h = 20 W/(m 2 K), a = 10-4 m 2 /s, k = 100 W/(mK), T o = 600 K, T a = 300 K, and R = 2 cm. Numerically simulate x ? 8 by taking a large value of x and ensuring that the results are independent of a further increase in this value.

The temperature distribution in a moving cylindrical rod, shown in Figure P4.27, is given by the energy equation where U is the velocity of the moving rod of radius R, a is the thermal diffusivity, and the other variables are the same as in the preceding problem. The boundary conditions are Employing the finite-difference approach, compute T(x). Take U = 1 mm/s, h = 20 W/(m 2 K), a = 10-4 m 2 /s, k = 100 W/(mK), T o = 600 K, T a = 300 K, and R = 2 cm. Numerically simulate x ? 8 by taking a large value of x and ensuring that the results are independent of a further increase in this value. Also, nondimensionalize this problem and determine the governing dimensionless variables. If the material and dimensions are fixed, what are the main design variables? Discuss how these may be varied to control the temperature decay over a given distance.

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