17.5 The device shown in the figure below is used to estimate the thermal conductivity of a new biomaterial 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 biomaterial layer and then through the surrounding air film layer. The temperature at the surface of the 3-cm-diameter heating rod (r=R, 1.50 cm, T = To) 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 biomaterial surrounding the heating rod is 0.3 cm, the power load is 15 W, the measured surface temperature of the rod is To=70°C, and the temperature of the surrounding air re- mains constant at 20°C· The convective heat-transfer coefficient of the air film surrounding the biomaterial is 80 W/m2 .K. a. What are the appropriate boundary conditions for heat- transfer analysis through the biomaterial? What is the thermal conductivity of the biomaterial, km? Plot the temperature profile T(r) from r = Ro to r = Rm. b. c. insulated ends air bulk film: air 15 W heating rod (3.0 ㎝ diameter, 6 ㎝ length) biomaterial layer (0.3 cm thickness)
