Reconsider Prob. 2–101. Using the relation obtained for the variation of temperature in the sphere, plot the temperature as a function of the radius r in the range of r = 0 to r = r_o. Also, plot the center temperature of the sphere as a function of the thermal conductivity in the range of 10 W/m·K to 400 W/m·K. Discuss the results. Use the EES (or other) software.

Data from problem 101

Consider a homogeneous spherical piece of radioactive material of radius r_o = 0.04 m that is generating heat at a constant rate of ė_gen = 5 × 10⁷ W/m³. The heat generated is dissipated to the environment steadily. The outer surface of the sphere is maintained at a uniform temperature of 110°C and the thermal conductivity of the sphere is k = 15 W/m · K. Assuming steady one-dimensional heat transfer,

(a) Express the differential equation and the boundary conditions for heat conduction through the sphere,

(b) Obtain a relation for the variation of temperature in the sphere by solving the differential equation,

(c) Determine the temperature at the center of the sphere.

Transcribed Image Text:

è gen 0 110°C To