A motor draws electric power Pelec from a supply line and delivers mechanical power Pmech to a pump through a rotating copper shaft of thermal conductivity ks, length L, and diameter D. The motor is mounted on a square pad of width W, thickness t, and thermal conductivity kp. The surface of the housing exposed to ambient air at T8 is of area Ah, and the corresponding convection coefficient is hh' Opposite ends of the shaft are at temperatures of Th and T8, and heat transfer from the shaft to the ambient air is characterized by the convection coefficient hs. The base of the pad is at Too.
(a) Expressing your result in terms of Pelec , Pmeeh, ks, L, D, W, t, kp, Ah , hh, and hs, obtain an expression for (Th - T8).
(b) What is the value of Tit if P e1ee = 25 kW, Pmeeh = 15kW, ks = 400 W/m . K, L = 0.5 m, D = 0.05 m, W = 0.7 m, t = 0.05 m, kp = 0.5 W/m · K, Ah = 2 m2, hh = 10 W/m2 · K, h, = 300 W/m2 · K, and Too = 25°C?