(d) Is the thermal conductivity of the medium constant or variable? Q3. A spherical container of inner radius r1=2m, outer radius r2=2.1m, and thermal conductivity k=30W/m.C is filled with iced water at 0C. The container is gaining heat by convection from the surrounding air at T=25C with a heat transfer coefficient of h=18W/m2.C. Assuming the inner surface temperature of the container to be 0C, (a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container (b) Obtain a relation for the variation of temperature in the conatiner by solving the differential equation (c) Evaluate the rate of heat gain to the iced water. Q4. A long homogeneous resistance wire of radius r0=5mm is being used to heat the air in a room by the passage of electric current. Heat is generated in the wire uniformly at a rate of 5X107W/m3 as a result of resistance heating. If the temperature of the outer surface of the wire remains at 180C, determine the temperature at r=3.5mm after steady operation conditions are reached. Take the thermal conductivity of the wire to be k=8W/m.C