DRBEM solution of natural convection flow of nanofluids with a heat source

This paper presents the dual reciprocity boundary element method (DRBEM) solution of the unsteady natural convective flow of nanofluids in enclosures with a heat source. The implicit Euler scheme is used for time integration. All the convective terms are evaluated in terms of DRBEM coordinate matrix. The vorticity boundary conditions are obtained from the Taylor series expansion of stream function equation. The results report that the average Nusselt number increases with the increase in both volume fraction and Rayleigh number. It is also observed that an increase in heater length reduces the heat transfer. The average Nusselt number of aluminum oxide-water based nanofluid is found to be smaller than that of copper-water based nanofluid. Results are given in terms of streamlines, isotherms, vorticity contours, velocity profiles and tables containing average Nusselt number for several values of Rayleigh number, heater length, volume fraction, and number of iterations together with CPU times.