3) (35pts) Thermal Conductivity of a New Biomaterial Bioengineer Dr. Kaitlin ...d her graduate students have fabricated a new collagen-based biomaterial for culturing cells for their cervical cancer research. They need

to know the thermal conductivity of the biomaterial. They have asked the Rochefort Lab for help to devise an experiment to measure the thermal conductivity of the biomaterial. We will use a heated rod device to estimate the thermal conductivity of a new biomaterial. The biomaterial is wrapped around a cylindrical heating rod. The exposed ends of the device are sealed and insulated. The heating rod generates 50 kW/m³ of heat which is uniformly dissipated through the biomaterial. The heating rod dimensions are D = 5.0 cm and L=15 cm. The temperature at the surface of the heating rod is measured using a thermocouple to be 100 °C, and is constant down the length (L) of the rod. The thickness of the biomaterial surrounding the heating rod is 1.0 cm and the temperature of the surrounding bulk air is constant at 20 °C. The convective heat transfer coefficient of the air film surrounding the biomaterial is 25 W/m²-K. Show all your work (including UNITS). a) Sketch and label the experimental set-up, and state all your assumptions. b) What is the surface temperature at the outside of the biomaterial. c) What is the thermal conductivity of the biomaterial, kg?