Insight into the Boundary Layer Flows of Free Convection and Heat Transfer of Nanofluids over a Vertical Plate using Multi-Step Differential Transformation Method

Abstract

This paper presents an insight into the boundary layer of free convection and heat transfer of nanofluids over a vertical plate at very low and high Prandtl number. Suitable similarity variables are used to convert the governing systems of nonlinear partial differential equations of the flow and heat transfer to systems of nonlinear ordinary differential equations which are solved using multi-step differential transformation method. The approximate analytical solutions are verified with numerical solutions. From the parametric studies, it is observed that the velocity and temperature of the nanofluid decreases and increases, respectively as the Prandtl number and volume-fraction of the nanoparticles in the base fluid increase. Also, the decrease in velocity and increase in temperature are highest in lamina shaped nanoparticle followed by platelets, cylinder, bricks and sphere shaped nanoparticles, respectively. Using a common base fluid to all the nanoparticle type, it is observed that the decrease in velocity and increase in temperature are highest TiO2 followed by CuO, Al2O3 and SWCNTs nanoparticles, in that order. The present study will enhance the understanding of free convection boundary-layer problems.