Heat transfer in nano fluid from a stretching (shrinking), porous and heated sheet of variable thickness

Abstract

Heat transfer in Nano fluid from a stretching (shrinking) and porous sheet of variable thickness is investigated in this paper. A set of unseen transformations is generated and the new variables are consequently used for the solution of partial differential equations under consideration. The classical models of heat transfer in Nano fluids from rigid/porous and stretching/shrinking sheets with Brownian motion and thermophoresis effects will be the special case of current study. The set of generalized similarity variables is introduced into the systems of boundary layer equations and boundary conditions and a system of coupled and non-linear ODE’s is formed. The final ODE’s are characterized by several dimensionless parameters and their effects are examined on field quantities. The governing parameters are: suction (injection), stretching (shrinking) parameters, Brownian motion number ( Nb), Thermophoresis number ( Nt) and Lewis number ( Le). The numerical observations are shown in different graphs and tables, whereas, effects of physical parameters are seen on the rate of heat transfer [Formula: see text] and mass transfer [Formula: see text], defined at the surface of the sheet. Moreover, the new results are presented in the respective sections. The remarkable aspects of the present simulations are scrutinized, however, special cases of current simulations give the previous problems, which are highlighted in the consequent sections.