An engineered tissue system consists of a slice of cell mass immobilized on a scaffold measuring 5 cm in length and 0.5 cm in thickness. The top face of the tissue scaffold is exposed to water, dissolved oxygen, and organic nutrients maintained at 30°C. The bottom face of the tissue is thermally insulated. At present, the specific oxygen consumption of the tissue mass is 0.5 mmol 0₂/cm³cells-hr, and from respiration energetics, the energy released by respiration is 468 J/mmol 0₂ consumed. We are interested in knowing the temperature at the bottom face of the tissue next to the insulated boundary. If this temperature remains below 37°C, the tissue will not die. The thermal conductivity of the tissue scaffold is k = 0.6 W/m · K.

a. Using the information given predict the temperature profile within the tissue slab the slab.

b. What is the heat generated per unit volume of tissue?

c. Estimate the temperature at x = L (the insulated boundary).