temperature distribution

Project Description:

heat is generated within a spherical catalyst particle because of chemical reaction. the particle is 8 mm in diameter, has thermal conductivity of 0.003 cal/m.s.k, and has a surface temperature of 300 oc. the generation of heat decreases linearly towards the center of the particle because of the decrease in the amount of material that reacts (longer diffusion path). the generation is given by 67.5 (r/ro) cal/s cm3. assume that the generation of the heat is exactly balanced by the loss of heat at the surface. determine the temperature distribution and more particularly the maximum temperature. the catalyst tends to lose activity above 700 oc; is this temperature exceeded?
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