The device shown in the figure below is used to estimate the thermal conductivity of a new bio material by measuring the steady-state heat-transfer rate and temperature. The bio material is wrapped around the cylindrical heating rod as shown in the figure. The exposed ends of the device are sealed and insulated. A constant power load is passed through the heating rod. The power transferred to the heating rod is dissipated as heat through the bio material layer and then through the surrounding air film layer. The temperature at the surface of the 3-cm diameter heating rod (r = R_o= 1.50 cm, T = T₀) is measured, and is constant along the length, L, of the 6-cm long rod.
For the present set of measurements, the thickness of the bio material surrounding the heating rod is 0.3 cm, the power load is 15 W, the measured surface temperature of the rod is T₀= 70°C, and the temperature of the surrounding air remains constant at 20°C. The convective heat-transfer coefficient of the air film surrounding the bio material is 80 W/m²· K.
a. What are the appropriate boundary conditions for heat transfer analysis through the bio material?
b. What is the thermal conductivity of the bio material, k_m?
c. Plot the temperature profile T(r) from r = R_oto r = R_m.

Transcribed Image Text:

insulated ends air bulk film air :T=T 15 W heating rod (3.0 cm diameter, 6 cm length) biomaterial layer : (0.3 cm thickness) r= Rm T =Ts r = R. T =T. r = 0