Magnetohydrodynamic Fluid Flow due to an Unsteady Stretching Sheet with Thermal Radiation, Porous Medium, and Variable Heat Flux

A shooting method has been introduced for determining the numerical solution of the ordinary differential equations which describe the Newtonian magnetohydrodynamic laminar fluid flow due to an unsteady stretching sheet together with the presence of thermal radiation and variable heat flux. The variable viscosity and variable conductivity are taken into consideration. Absence of magnetic field in some studies restricts the development of the energy-efficient heat transfer mechanism as is desired in numerous applications. The present study encompasses parameters such as unsteadiness parameter, porous parameter, viscosity parameter, magnetic number, radiation parameter, and conductivity parameter. It has been consummated that the proposed model is superior to other existing models for the industrial fluid.

Heat transfer in natural convection flow of nanofluid along a vertical wavy plate with variable heat flux

The present analysis is concerned to examine the enhancement of heat transfer in natural convection flow of nanofluid through a vertical wavy plate assumed at variable heat flux. The rate of heat transfer in nanofluid flow as compared to pure water can be increased due to increase the density of nanofluid which depends on the density and concentration of nanoparticles. For this analysis, Tiwari and Das model is used by considering two nanoparticles i. e. Al2O3 and Cu are suspended in a base fluid (water). A very efficient implicit finite difference technique converges quadratically is applied on the concerning PDE for numerical solution. The effects of pertinent parameters namely, volume fraction parameter of nanoparticle, wavy surface amplitude, Prandtl number and exponent of variable heat flux on streamlines, isothermal lines, local skin friction coefficient and local Nusselt number are shown through graphs. In this analysis, a maximum heat transfer rate is noted in Cu-water nanofluid through a vertical wavy surface as compared to Al2O3-water and pure water.