Temperature dependent fluid properties effects on the heat function formulation of natural convective flow and heat transfer

To study quantitatively the effects of combined temperature dependent thermodynamics and transport fluid properties on the heat transfer rate, heat function fields and profiles in a fluid filled square enclosure.

Navier‐Stokes equations in two‐dimensions, which are the flow governing equations, were transformed into stream function and vorticity transport equations. These equations together with the energy and heat function equations were cast into their non‐dimensional forms. Numerical solutions of the resulting equations were done by the use of finite‐difference method.

The numerical investigations conducted covered the Rayleigh and Prandtl numbers in the range 10³≤Ra≤10⁶ and 0.01≤Pr≤450, respectively, and expansion parameter ε=(T_h−T_c)/T_R in the range 0.05≤ε≤1. Results show that Boussinesq‐approximation is not sufficient to simulate natural convective flow when the difference between T_h and T_c is high and close to the reference state temperature. The effects of the other fluids properties other than density can be disregarded in computation without significant loss of accuracy. Combined fluid properties have very strong effects on the heat transfer, heat function fields and profiles.

The results of this study will serve as baseline information to designers of heat transfer or process equipment in which fluid at very high temperature occurs.