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:
is the number of long cylinders,
are the fluid's specific heat, density and volume, respectively, and
are the body's specific heat, density and volume, respectively.
The Biot number is defined as
is the heat transfer coefficient of the fluid,
the thermal conductivity of the long cylinder, and
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
increases, the steady-state fluid's temperature and the steady-state
bodies' average temperature will be smaller.