Effects of uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity

Abstract

Purpose

The purpose of this paper is to perform a numerical study for heat transfer through natural convection in the presence of a constant magnetic field in an incompressible steady nanofluid flow inside an isosceles triangular cavity.

Design/methodology/approach

For this flow problem, the left wall of the cavity subjected to uniform/nonuniform heat was considered, while right and bottom walls of the cavity were kept cold. The obtained equations were solved by using the Galerkin weighted residual technique. Results are computed for a wide range of parameters including Rayleigh number (Ra) (10^3 < Ra < 10^7), Hartman number (Ha) (0 < Ha < 60), and heat-generation/-absorption coefficient (q) (−10 < q < 10), while, Prandtl number (Pr) was kept fixed at 6.2. These computed results are presented in terms of stream functions, isotherms, Nusselt numbers and average Nusselt numbers through figures.

Findings

It is observed that, in case of uniform heating of the side wall, the strength of stream lines’ circulations increases with an increase in Ra and decreases with an increase in Ha. Similarly, by increasing heat-absorption coefficient q, an increase in the circulation strength is noted and the circulation cell moves towards the left wall in the presence of a heat sink (q < 0) and moves to the cold right wall in the presence of a heat source (q > 0). In the case of nonuniformly heated left wall in the presence of a heat source (q > 0), a higher-temperature gradient is observed in the cavity and isotherms are clustered to the left wall in the lower portion and to right wall in the upper portion; these appear to be straight and parallel to the x-axis near the bottom wall. On the other hand, the heat transfer rate along all the walls of the cavity is observed to be higher for smaller values of q. Whereas, Nusselt number along the bottom wall (Nu-B) increases with an increase in the values of x, while, that along the left wall (Nu-L) first increases and then decreases. But Nusselt number along the right wall (Nu-R) is found to be qualitatively opposite to Nu-L with an increase in distance x. Whereas, average Nusselt number increases with an increase in Rayleigh number Ra and heat-generation/-absorption coefficient q.

Research limitations/implications

The problem is formulated for an incompressible flow; viscous dissipation has been neglected, negligible induced magnetic field has been considered and local thermal equilibrium has been considered.

Originality/value

Results presented in this paper are original and new for the effects of a uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity. Hence, this study is important for researchers working in the area of heat transfer in cavity flows involving the nanofluid to become familiar with the flow behavior and properties.

Citation

Javed, T., Mehmood, Z., Siddiqui, M.A. and Pop, I. (2017), "Effects of uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 2, pp. 334-357. https://doi.org/10.1108/HFF-10-2015-0448