Find the steady-state temperature distribution u in a semi-infinite solid cylinder (Fig. 2) of radius a if the base (at z-0) is held at 60° and the curved sides at 0'.

2. A rectangular block has thickness B in the x-direction. The side at x = 0 is held at temperature T, while the side at x = B is held at T2. The other four sides are well insulated. Heat is generated in the block at a uniform rate per unit volume of [. (a) Use the conduction equation to derive an expression for the steady-state temperature profile, T(x). Assume constant thermal conductivity. (b) Use the result of part (a) to calculate the maximum temperature in the block for the following values of the parameters: T₁-120 °C k-0.2 W/(m K) B-1.0 m T₂-0 F-100 W/m³

Q 2: A rod 10cm long, has its ends A and B kept at 50°C and 100°C, respectively, until steady state conditions prevail. The temperature at each end is then suddenly reduced to 0°C and kept so. Find the funetion of distribution temperature along the rod?

#4: A rod of length L. coincides with the interval [0, L] on the x-axis. Let u(x, t) be the temperature. Consider the following conditions. (A) The left end is held at temperature 0°. (B) The right end is insulated. (C) There is heat transfer from the lateral surface of the rod into the surrounding medium, which is held at temperature 0° (D) The left end is insulated. (E) The initial temperature is 0° throughout. (F) The right end is held at temperature 0°. (G) There is heat transfer from the right end into the surrounding medium, which is held at a constant temperature of 0°. (H) There is heat transfer from the left end into the surrounding medium, which is held at a constant temperature of 0°. In each part below, determine which of the above conditions corresponds to the given initial or boundary condition for the heat equation. (a) u(x, 0) = 0 (b) u(0, 1) = 0 (c) du (d) ou x=L ox|x=0 = -hu(L, 1) = hu(0, 1)