A radioactive material can be considered as a sphere of ro = 0.04 m. the sphere is generating heat at a constant rate of 4x107 W/m³. The heat generated is dissipated to the environment in a steady state. The thermal conductivity of the sphere is k=15 W/m.°C and the surface of the sphere is maintained at a constant temperature of 80°C. Assuming steady one-dimensional heat transfer, (a) drive the differential equation and the express boundary conditions for heat conduction through the sphere, (b) Get a relation for the variation of temperature in the sphere by solving the differential equation, and (c) Calculate the temperature at the center of the sphere.

A spherical container having an outer radius r2 and inner radius r1 (with thermal conductivity, k) is filled with radioactive material generating constant heat at a rate of qdot. Fluid flows across the container at Tinfinity and convection coefficient h. Obtain a relation for the variation of temperature through the spherical container assuming steady state.

Consider the rate of conductive heat transfer from the inside of an animal’s body (at 37 ˚C) tothe cooler surroundings (initially at 22 ˚C). Order the following from lowest to highestimpact. Justify your answer. The outside temperature increases to 27 ˚CThe thermal conductivity of the animal’s insulating layer is doubledThe thickness of the animal’s insulating layer is halvedThe volume of the animal is doubledThe surface of the animal becomes coated in an extremely thin layer of black oil

Heat Transfer A wall of an oven with a wire in it. Across the wire a voltage of 50 Volts and a current of 2 Amps is applied, and 80% of the electrical power is converted to thermal energy. The oven is a convection oven and has air flowing through it at 240 C and h = 10 W/m^2 K. The wall of the oven is 0.1 m thick and 1.5 m tall and 1.5 m wide and is made of steel (k = 15 W/m K). Find the surface energy balance on the inner wall of the oven and determine the temperature of the ineer wall at steady state. Then do an energy balance on the outer wall, assume that the oven is free standing and has an emissivity, e = 0.6, and the surrounding temperature is 25 C. The air in the surrounding has a convective heat transfer coefficient of 25 W/m^2 K. Just set up the balance equation that would enable to solve, no need to actually solve.