Overlapping Multi-Domain Spectral Method for Conjugate Problems of Conduction and MHD Free Convection Flow of Nanofluids over Flat Plates

Abstract

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag-water nanofluid has higher skin friction and surface temperature than the Cu-water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement.

Numerical solution of time-dependent Emden-Fowler equations using bivariate spectral collocation method on overlapping grids

“…where α is the overlapping distance between two intervals. We note that 8) which upon rearranging and making Lx the subject of the formula gives Eq. (23).…”

“…In the non-overlapping multi-domain BSQLM, the multi-domain technique was only applied in time. Recently, Mkhatshwa et al [8,9] found that the accuracy of the BSQLM can be improved by applying the overlapping multi-domain technique in the space interval and the non-overlapping multi-domain technique in the time interval. Teleei and Dehghan [10] introduced a numerical scheme for the solution of sine-Gordon equation when only space discretization is performed by an overlapping multi-domain pseudo-spectral technique.…”

MHD mixed convective radiative flow of Eyring‐Powell fluid over an oscillatory stretching sheet using bivariate spectral method on overlapping grids

“…[46][47][48][49] In all these studies, the overlapping multidomain approach was applied only in the spatial domain, and it was found that the accuracy of pseudospectral methods improved through the use of overlapping grid procedure. Mkhatshwa et al 48 and Mkhatshwa et al 49 considered nonlinear PDEs modeling problems that arise in fluid mechanics. The BSQLM on overlapping grids was introduced by Mkhatshwa et al 38 and implemented to solve time-dependent Emden-Fowler equations.…”

“…The single‐domain BSQLM method uses quasilinearization technique, 45 the Chebyshev spectral collocation method, as well as the bivariate Lagrange interpolation polynomial with Chebyshev‐Gauss‐Lobatto grid points. The overlapping multidomain technique with pseudospectral methods has been considered by several researchers 46‐49 . In all these studies, the overlapping multidomain approach was applied only in the spatial domain, and it was found that the accuracy of pseudospectral methods improved through the use of overlapping grid procedure.…”

Effects of Convection on Sisko Fluid with Peristalsis in an Asymmetric Channel

“…Heat transfer with convective boundary conditions is implicated in mechanisms like gas turbines, thermal energy storage, nuclear power plants etc.. In this context, some recent studies [26][27][28][29][30][31] are observed in which the study of non-Newtonian fluid flows with peristalsis are conducted in the vicinity of convective conditions.…”