International Journal of Scientific & Engineering Research, Volume 6, Issue 1, January-2015 182 ISSN 2229-5518 IJSER © 2015 http://www.ijser.org Boundary Layer Flow & Heat Transfer of an Unsteady Dusty Fluid over a Stretching Sheet S.K.Mishra and A.K.Rauta Abstract- The unsteady flow and heat transfer of a viscous incompressible dusty fluid over a vertical stretching sheet is studied. The governing partial differential equations are solved by reducing into ordinary differential equations using similarity transformations and the solutions have been found using well known Runge-Kutta method with help of Shooting technique. The effect of pertinent flow parameters such as Unsteady parameter, Froud number, Grashof number, Prandtl number, Eckert number, Volume fraction, fluid interaction parameter etc on heat transfer are investigated with help of tables and graphs. We have found that our result is good agreement with previously published results. It is found that the thermal and momentum boundary layer thickness decreases on the increase of unsteady parameter and the temperature of both fluid phase as well as particle phase are enhancing on the increase of Eckert number. It is also noticed that the rate of cooling is faster for higher prandtl number and unsteady parameter. AMS classification: 76T10, 76T15 Keywords: Boundary layer flow, Eckert number, Fluid – particle interaction parameter, Froud number, Grashof number, Prandtl number, Shooting techniques, Stretching sheet, Unsteady parameter, Volume fraction. —————————————————————————————————————————————————————————————— 1. Introduction: The unsteady flow and heat transfer of two phase viscous incompressible flow over a stretching sheet is occurring in several industrial applications and technologies. The practical applications are underground disposable of radioactive waste materials, exothermic and endothermic reactions , centrifugal separation of particles, blood rheology, flow through packed beds, sedimentation etc .The momentum and Heat transfer in the laminar boundary layer flow on a moving surface is also important for both practical as well as theoretical point of view because of their wide application in heat removal from nuclear fuel debris, the aerodynamic extrusion of plastic sheet, glass blowing, cooling or drying of papers, drawing plastic films , extrusion of polymer melt-spinning process and heat treated materials traveling on conveyer belt etc .Due to this fact several researchers motivated to study the effect of momentum and heat transfer. The study of the boundary layer flow over a stretched surface moving with a constant velocity was initiated by Sakiadis B.C.[18] in 1961.Then many researchers extended the above study with the effect of Heat Transfer .Tsou et.al [20] studied the effect of Heat Transfer and experimentally confirmed the numerical result of Sakiadis . Grubka et.al[9] investigated the temperature field in the flow over a stretching surface when subject to uniform heat flux .Sharidan[19] presented similarity solutions for unsteady boundary layer flow and heat Transfer due to stretching sheet .A numerical solution for laminar thermal boundary over a flat plate with convective surface boundary condition was analyzed by Aziz[1].Chen [6] investigated mixed convection of a power law fluid past a stretching surface in presence of thermal radiation and magnetic field .Crane [13] has obtained the Exponential solution for planar viscous flow of linear stretching sheet. Chamakha et.al.[7] Investigated the unsteady magneto hydrodynamics boundary layer flow of viscous incompressible electrical conducting fluid along a semi infinite vertical permeable plate. Nandkeolyar et.al. [16] have studied the effect of ramped surface temperature on the flow and heat transfer of a viscous, incompressible and electrically conducting dusty fluid in presence of transverse magnetic fluid,M Das et.al. [14] recently have studied the unsteady hydro magnetic flow of a Heat absorbing Dusty Fluid past a permeable vertical plate with ramped temperature. B.J. Gireesha et.al[4] have studied the effect of hydrodynamic laminar boundary layer flow and heat Transfer of a dusty fluid over an unsteady stretching surface in presence of non uniform heat source/sink .They have examined the Heat Transfer characteristics for two type of boundary conditions namely variable wall temperature and variable Heat flux. G.K.Ramesh et.al [8] have investigated the momentum and heat transfer characteristics in hydrodynamic flow of dusty fluid over an inclined stretching sheet with non uniform heat source/sink .B.G. Gireesh et.al [3] also studied the mixed convective flow a dusty fluid over a stretching sheet in presence of thermal radiation, space dependent heat source/sink. In this paper the study of effect of different flow parameters on unsteady boundary layer and heat transfer of a dusty fluid over a stretching sheet have investigated. The problem of two phase suspension flow is solved in the IJSER