Casson fluid flow over a stretching surface with variable thermal conductivity and partial slip (original) (raw)

2017, International Journal of Engineering and Technology

The flow and heat transfer of aCasson fluid flow over an impermeable stretching surface with variable thermal conductivity and non-uniform heat source/sink in the presence of partial slip is investigated. The resulting partial differential equations are reduced to a set of non-linear ordinary differential equation using similarity transformation and solved numerically using Runge-Kutta method along with shooting technique. The effects of the governing parameter on velocityand temperature fields are discussed. Key words-Casson fluid, Partial slip, Variable thermal conductivity, Non-uniform heat source/sink 1. INTRODUCTION The flow over a stretching sheet is significant due to its much application in engineering processes such as in the extraction of polymer sheets, paper production, wire drawing and glass-fiber production.Sakiadis [1,2] initiated the study of the boundary layer flow over a continuous solid surface moving with constant speed.The boundary layer problem considered by Sakiadis differs from the classical boundary-layer problem of Blasius [3], mainly due to the entrainment of the ambient liquid. Here the surface is assumed to be constant (u w =0) whereas most of the physical situations are concerned with extensible surface (u w = cx) moving in a cooling liquid. Crane [4], for the first time, considered the boundary-layer behavior over an extensible surface, where he assumed the velocity of the surface to vary linearly with the distance from the slit. Carrayher and Crane [5] analyzed the heat transfer due to a continuous stretching sheet. The pioneering work of Crane was extended by many authors Gupta and Gupta [6], Grabka and Babba [7], Chen and Chur [8], and Chaim [9]. In engineering applications, homogeneous or heterogeneous reactions often lead to a significant heat release accompanied by non-isothermal conditions that require the introduction of a heat source/sink term in the energy equation.Cartel [10-12] studied the flow and heat transfer characteristics with linearly and Non-linearly stretching sheet for both Newtonian and Non-Newtonian fluids with internal heat generation/absorption and suction/injection.The study of flow and heat transfer for electrically conducting fluids under the influence of a magnetic field has attracted the interest of many investigators. MHD flows have great significance for the application in the field of satellite and planetary magnetospheres, aeronautics and chemical engineering. Sarpakaya [13] was the first to study the MHD effects on the flow of a non-Newtonian fluid. Pal and Mondal [14, 15] considered the MHD fluid for their study. The MHD fluids have been considered by many researchers [16-21,41]. Abel et al. [22] studied the effect of variable viscosity on the heat transfer of viscoelastic fluid due to stretching sheet. Vajravelu and Rollins [23] and Vajravelu and Nayfeh [24] have studied the effect of a uniform heat source/sink on the heat transfer from a stretching sheet. Bhattacharya and Vajravelu [26] studied the stagnation-point flow over an exponential stretching sheet. Abo-Eldahub and Elaziz [27] investigated heat transfer considering a non-uniform heat source/sink. Recent work of Nandep-Panavar et al. [28], Abel et al. [29] and Bataller [30] in the case of a visco elastic liquid flow due to a stretching sheet. The no-slip boundary condition is known as the central tenet of the Navier-Stokes theory. But there are situations wherein such a condition is not approximate. Especially the no-slip condition is insufficient for the most non-Newtonian liquids. The liquids exhibiting boundary slip find applications in technology such as polishing of artificial heart valves and internal cavities. Navier [31] suggested a slip boundary condition in terms of shear stress. The work of Navier was extended by many authors [32,40,43,44]. Mustafa et al. [45] studied the effect of non-uniform heat source on heat transfer of non-Newtonian power law fluid over a non-linear stretching sheet. John and Kumaran studied the heat transfer due to a heat source in MHD unsteady stretching sheet flow. Mahantish M. et al. [47] studied the MHD flow and heat transfer over a stretching surface with variable thermal conductivity and partial slip. In the above work, theCasson fluid flow over a stretching surface with variable thermal conductivity and partial slip has not investigated yet.