Numerical study of forced convection in a 3D flow of a non‐Newtonian fluid through a porous duct

Abstract

Purpose

To investigate the forced convection heat transfer to hydrodynamically and thermally fully developed laminar steady flow of power‐law non‐Newtonian fluid in a partially porous square duct.

Design/methodology/approach

The modified Brinkmann‐Forchheimer extended Darcy model for power‐law fluids is used in the porous layer. The solutions for the velocity and temperature fields are obtained numerically using the finite volume method. Computations are performed over a range of Darcy number, power‐law indices, porous insert thickness and thermal conductivity ratio.

Findings

The average Nusselt number and the Fanning factor, so obtained are found to be in good agreement with the literature. It is highlighted that a heat transfer improvement is obtained when the channel is entirely porous and this enhancement is maximized at low permeability. While depending on the working conditions, heat transfer enhancement can also be obtained by filling partially the duct with the porous insert, even if the conductivity ratio is equal to 1. The results indicate also that the conductivity ratio has a strong impact on the heat transfer enhancement at high permeability, while this impact is significant beyond a critical thickness of the porous layer at low permeability. It is found that both shear‐thinning (n<1) and shear‐thickening (n>1) fluids allow obtaining the highest Nusselt number according to the properties of the porous insert. The presence of the porous insert causes a significant increase in pressure drop. This added pressure drop is found to be more important with shear thickening fluids (n>1).

Research limitations/implications

The results of this paper are valid for square ducts and H1 thermal boundary condition, corresponding to an axially uniform heat flux and peripherally uniform temperature. The inertial effects are neglected in the porous region.

Practical implications

The obtained results can be used in the design of heat exchangers and in the cooling of electronic equipments.

Originality/value

This work investigates some interesting ways to enhance heat transfer in three‐dimensional square ducts by using porous substrates and non‐Newtonian fluids. It is believed that the case studied in this paper has not previously been investigated.

Citation

Nebbali, R. and Bouhadef, K. (2006), "Numerical study of forced convection in a 3D flow of a non‐Newtonian fluid through a porous duct", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 No. 8, pp. 870-889. https://doi.org/10.1108/09615530610702041