Lie group analysis for the effect of viscosity and thermophoresis particle deposition on free convective heat and mass transfer in the presence of suction/injection

Abstract

An analysis has been carried out to study heat and mass transfer characteristics of an incompressible and Newtonian fluid having temperature-dependent fluid viscosity and thermophoresis particle deposition over a vertical stretching surface with variable stream condition. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The vertical surface is assumed to be permeable so as to allow for possible wall suction or injection. The governing differential equations are derived and transformed using Lie group analysis. The transformed equations are solved numerically by applying Runge-Kutta Gill scheme with shooting technique. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity, temperature and concentration profiles for a prescribed temperature-dependent fluid viscosity and thermophoresis particle deposition parameters are presented graphically to elucidate the influence of the various physical parameters.Proucavaju se karakteristike prenosa toplote i mase nestisljivog Njutnovskog fluida koji ima viskoznost zavisnu od temperature i talozenje cestica termoforezom preko vertikalne zategnute povrsi sa promenljivim uslovom struje. Roslendova aproksimacija se koristi za dobijanje toplotnog fluksa radijacije u energijskoj jednacini. Za vertikalnu povrs se pretpostavlja da je propustljiva dozvoljavajuci usisavanje ili ubrizgavanje. Diferencijalne jednacine problema su izvedene i transformisane analizom Liove grupe. Transformisane jednacine su resene primenom Runge-Kuta-Gilove seme sa snimajucom tehnikom. Uporedjenja sa objavljenim radovima su povoljna. Numericki rezultati za brzinu, temperaturu i koncentracione profile za propisane zadate parametre viskoznosti i talozenja su prikazani graficki da bi objasnili uticaj raznih fizickih parametara.