4.62 A steady-state, finite-difference analysis has been performed on a cylindrical fin with a diameter of 12 mm and a thermal conductivity of 15W/m K. The convection process is characterized by a fluid temperature of 25°C and a heat transfer coefficient of 25W/m2 K. If the temperature of the first three nodes, separated by a spatial increment of delta x = 10 mm, are T0 =100 degree C, T1 =93.4 degree C, and T2 = 89.5 degree C, determine the fin heat transfer rate. Determine the temperature at the node 3, T3.

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.