(a) Assume that there is a negligible thermal gradient in the wall of the container (dT/dr is negligible) and that the heat flux qi” is constant, write an equation that expresses how the temperature of the wall of the container changes with time (dT/dt) and evaluate the initial rate of change of wall temperature (dT/dt ) when qi”=106 W/m2. (b) What is the steady state temperature of the wall?
A spherical container is used to store reacting chemicals, which results in a uniform heat flux (qi”) applied to the inner surface of the container. The initial temperature of the inner wall of the container, Ti, is 500K. The container has an inner radius of 0.4 m and an outer radius of 0.5 m, the density of the container’s walls are 8055 kg/m3, and its heat capacity is 535 J/(kg-K). The container is then suddenly submerged in a liquid bath with a temperature T∞=300K. The convective heat transfer coefficient for the bath: h= 450 W/(m2 K).
(a) Assume that there is a negligible thermal gradient in the wall of the container (dT/dr is negligible) and that the heat flux qi” is constant, write an equation that expresses how the temperature of the wall of the container changes with time (dT/dt) and evaluate the initial rate of change of wall temperature (dT/dt ) when qi”=106 W/m2.
(b) What is the steady state temperature of the wall?
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