A concentric tube arrangement, for which the inner and outer diameters are 80 mm and 100 mm, respectively, is used to remove heat from a biochemical reaction occurring in a 1-m-long settling tank. Heat is generated uniformly within the tank at a rate of 105 W/m3, and water is sup plied to the annular region at a rate of 0.2 kg/s.

(a) Determine the inlet temperature of the supply water that will maintain an average tank surface temperature of 37°C. Assume fully developed flow and thermal conditions. Is this assumption reasonable?

(b) It is desired to have a slight, axial temperature gradient on the tank surface, since the rate of the bio-chemical reaction is highly temperature dependent. Sketch the axial variation of the water and surface temperatures along the flow direction for the following two cases: (i) the fully developed conditions of part (a), and (ii) conditions for which entrance effects are important. Comment on features of the temperature distribution. What change to the system or operating conditions would you make to reduce the surface temperature gradient?

Reaction tank. 4 = 1 x 105 Wim, L=1m Kater i-0.2 kgis Insulation wrap D, = 80 mm D = 100 mm