MHD Stokes flow and heat transfer in a lid‐driven square cavity under horizontal magnetic field

Abstract

This study considers the steady flow of a viscous, incompressible and electrically conducting fluid in a lid‐driven square cavity under the effect of a uniform horizontally applied magnetic field. The governing equations are obtained from the Navier‐Stokes equations including buoyancy and Lorentz force terms and the energy equation including Joule heating and viscous dissipation terms. These equations are solved iteratively in terms of velocity components, stream function, vorticity, temperature, and pressure by using radial basis function approximation. Particular solution, which is approximated by radial basis functions to satisfy both differential equation and boundary conditions, becomes the solution of the differential equation itself. Vorticity boundary conditions are obtained from stream function equation using finite difference scheme. Normal derivative of pressure is taken as zero on the boundary. The numerical results are obtained for several values of Hartmann number and Grashof number for the Stokes approximation (Re << 1). The results show that when the viscous dissipation is present, the flow and isolines concentrate through the cold wall forming boundary layers as Grashof number increases. An increase in the magnetic field intensity retards the effect of buoyancy force in the square cavity, whereas the movement of the upper lid causes buoyancy force to be dominant. The solution is obtained in a considerably low computational expense through the use of radial basis function approximations for the MHD equations. Copyright © 2017 John Wiley & Sons, Ltd.

Streamline analysis of MHD flow in a double lid-driven cavity

“…They also employed the RBF approximation to MHD convection flow in different channels. 32,33 Geridonmez and Oztop 34 adopted RBF to MHD natural convection in a cavity subjected to cross partial magnetic field. They reported that the augmentation of Lorentz force decreases the convective heat transfer.…”

Natural convection nanofluid flow with heat transfer analysis of carbon nanotubes–water nanofluid inside a vertical truncated wavy cone

“…In literature review, it appears that heat transfer in natural convection power law non‐Newtonian fluid flow through vertical truncated wavy cone with the Tiwari and Das 22 nanofluid model has not yet been investigated. However, several overlapping studies in one or other way can be found in previous studies 23–41 . In order to fill the gap in literature, the thermally stratified boundary layer CNT–water nanofluid flow suspended by a vertical truncated cone is considered.…”

“…However, several overlapping studies in one or other way can be found in previous studies. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] In order to fill the gap in literature, the thermally stratified boundary layer CNT-water nanofluid flow suspended by a vertical truncated cone is considered. Firstly, the system gives a nonsimilar solution; then it converts to a similar solution by using transformation to find its solution.…”

Numerical Solution of MHD Incompressible Convection Flow in Channels

“…They showed that temperature increases with increasing values of Eckert number. Gürbüz & Tezer-Sezgin (2018) studied the effect on viscous dissipation on MHD flow and heat transfer applying Stokes approximation (Re << 1) with small value of Grashof number 90. They found that both Stokes flow and isolines concentrate through the cold wall due to the viscous dissipation effect.…”