Multiple steady state solutions for natural convection in a shallow horizontal rectangular cavity filled with non‐Newtonian power‐law fluids and heated from all sides

Abstract

Purpose

The aim of this work is to study numerically and analytically flow and heat transfer characteristics and multiplicity of steady states for natural convection in a horizontal rectangular cavity, filled with non‐Newtonian power‐law fluids and heated from all sides.

Design/methodology/approach

The governing equations are discretised by using the well known second‐order central finite difference method and integrated by combining the ADI and PSOR techniques. The analytical approach is based on the parallel flow assumption.

Findings

Natural and anti‐natural flows existence is proved when the Rayleigh number exceeds a critical value and the side lateral heating intensity values is chosen inside a specific range. The analytical results are found to agree well with those obtained numerically. The fluid flow and the heat transfer are found to be rather sensitive to the non‐Newtonian power‐law behaviour.

Research limitations/implications

The obtained results are limited to non‐Newtonian power‐law fluids and cannot be extended to fluids having other behaviours.

Practical implications

The problem is implied in some industrial thermal processes.

Originality/value

Existence of multiple steady state‐solutions in the range of the side lateral heating intensity values ensuring, that is reduced by the shear‐thickening behaviour and extended by the shear‐thinning one for a given value of Rayleigh number.

Citation

Lamsaadi, M., Naïmi, M. and Hasnaoui, M. (2006), "Multiple steady state solutions for natural convection in a shallow horizontal rectangular cavity filled with non‐Newtonian power‐law fluids and heated from all sides", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 No. 7, pp. 779-802. https://doi.org/10.1108/09615530610683511