A concentric tube arrangement, for which the inner
Chapter 8, Problem 8.99(choose chapter or problem)
A concentric tube arrangement, for which the inner andouter diameters are 80 mm and 100 mm, respectively, isused to remove heat from a biochemical reaction occur-ring in a 1-m-long settling tank. Heat is generated uni-formly within the tank at a rate of 105W/m3, and wateris supplied to the annular region at a rate of 0.2 kg/s.Reaction tank,q = 1 105 W/m3,L = 1 mm = 0.2 kg/sWaterDi = 80 mmDo = 100 mmInsulation wrap a) Determine the inlet temperature of the supply waterthat will maintain an average tank surface tempera-ture of 37C. Assume fully developed flow andthermal conditions. Is this assumption reasonable? (b) It is desired to have a slight, axial temperature gra-dient on the tank surface, since the rate of the bio-chemical reaction is highly temperature dependent.Sketch the axial variation of the water and surfacetemperatures along the flow direction for the fol-lowing two cases: (i) the fully developed conditionsof part (a), and (ii) conditions for which entranceeffects are important. Comment on features of thetemperature distributions. What change to the sys-tem or operating conditions would you make toreduce the surface temperature gradient?
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