Laminar natural convection from an isothermal vertical surface to pseudoplastic and dilatant fluids

This paper reports the results of a numerical study of natural convective heat transfer from a vertical isothermal surface to pseudoplastic and dilatant fluids. The analysis calculates the average Nusselt number in the laminar regime when the surface is exposed to an otherwise quiescent fluid. Because the solution utilizes constitutive equations that are valid over the entire shear rate range, the results map the behavior regardless of the shear rates that exist in the flow field. The Nusselt number is shown to approach Newtonian values when the shear rates throughout the flow field are predominantly either in the zero or in the high shear rate Newtonian regions of the flow curve. When they are principally in the power law regime, and if the fluid is also strongly non-Newtonian, then the Nusselt number approaches power law values. For all other cases, it is seen to attain intermediate values. Furthermore, a shear rate parameter is identified that determines the shear rate regime where the system is operating. The average Nusselt number is presented in both graphical and tabular forms over a broad range of system parameters.