Scaling investigation of natural convection heat transfer and fluid flow of low Prandtl fluids over a heated vertical wall

Matthew N.  Ottah; Olayinka O.  Adewumi; Ayowole A.  Oyediran

Matthew N. Ottah
Olayinka O. Adewumi
Ayowole A. Oyediran

Keywords: Newtonian fluid, Grashof number, Prandtl number, Scale analysis, boundary layer

Abstract

This work presents numerical analysis for two-dimensional laminar free convection over a vertical isothermal and constant heat flux wall of low Prandtl number Newtonian fluids. The Bejan’s method of scale analysis is used to obtain the governing partial differential equations while similarity transformation is employed to transform the partial differential equations to ordinary differential equations. Bejan’s method of scale analysis shows the influence of balance of forces that affects the boundary layer flow and heat transfer. In this study, results show that Grashof number is the relevant dimensionless group describing the flow as against Raleigh number which was used to generalize the flow for both inner and outer layer other researchers. The velocity layer which is the inner layer closest to the solid wall dominated by the friction – buoyancy force balance is considered in this study. The governing equations are solved using the classical fourth order Runge – Kutta numerical method coupled with shooting method; multi-step differential transformation method and Keller box method and results obtained are compared. Results for velocity, temperature, local Nusselt number and skin friction were obtained for Prandtl numbers of 0.001, 0.01, 0.1, 0.5, and 0.72. The scales derived for low Prandtl flows in this study show that Grashof number is only applicable to the velocity boundary layer for low Prandtl flows. Results obtained were compared to those reported in open literature and there was 29% difference in the values obtained for local skin friction while the results for Nusselt number there was a difference factor of Pr1/2.

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