Heating of Bodies in a Limited Volume of Well-Stirred Fluid

Consider long cylinders of radius placed in a limited volume of well-stirred fluid. The uniform temperature of the fluid varies because heat is exchanged by convection with the long cylinders. Initially the fluid and the bodies are at dimensionless temperatures equal to 1 and 0, respectively.
The dimensionless constant , a measure of the heat storage capacity of the bodies relative to the fluid, is given by: , where is the number of long cylinders, , , and are the fluid's specific heat, density and volume, respectively, and , , and are the body's specific heat, density and volume, respectively.
The Biot number is defined as , where is the heat transfer coefficient of the fluid, the thermal conductivity of the long cylinder, and its radius.
This Demonstration displays the average temperature in the bodies (the blue curve) and the fluid's temperature (the orange curve) as a function of time for various Biot numbers. For low Biot numbers, the two temperatures will become equal only after a long time, as expected, because the fluid's heat transfer coefficient is very low. Again as expected, the temperatures of the fluid and the bodies are both equal to if . As increases, the steady-state fluid's temperature and the steady-state bodies' average temperature will be smaller.


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Reference: M. D. Mikhailov and M. N. Özisik, Unified Analysis and Solutions of Heat and Mass Diffusion, New York: Dover, 1994.
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