Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

T M Ajayi,A J Omowaye,I L Animasaun

doi:10.1155/2017/1697135

Abstract

The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases inRex1/2Cfxis guaranteed withStwhen magnitude ofβis large.Rex1/2Cfxdecreases withEcandm.

Highlights

Within the last thirty years, the study of non-Newtonian fluid flow over a stretching surface has received significant attention due to its industrial applications
Due to friction and internal heat generated between two layers of fluid, viscosity and thermal conductivity of fluid substance may be affected by temperature; for more details see Batchelor [34], Lai and Kulacki [35], and Abd El-Aziz [36]
Considering the fact that Prandtl number is strongly dependent on plastic dynamic viscosity and thermal conductivity, and it is assumed that both properties vary linearly with temperature; for more accurate analysis of boundary layer as suggested in [47, 48], the Pr in (14) is

Summary

Introduction

Within the last thirty years, the study of non-Newtonian fluid flow over a stretching surface has received significant attention due to its industrial applications. Due to friction and internal heat generated between two layers of fluid, viscosity and thermal conductivity of fluid substance may be affected by temperature; for more details see Batchelor [34], Lai and Kulacki [35], and Abd El-Aziz [36] Proper consideration of this fact in the study on inherent irreversibility in a variable viscosity Couette flow by Makinde and Maserumule [37], numerical investigation of micropolar fluid flow over a nonlinear stretching sheet taking into account the effects of a temperature-dependent viscosity by Rahman et al [38], effects of MHD on Casson fluid flow in the presence of Cattaneo-Christov heat flux by Malik et al [39], fluid flow through a pipe with variation in viscosity by Makinde [40], Casson fluid flow within boundary layer over an exponentially stretching surface embedded in a thermally stratified medium by Animasaun [41], steady fully developed natural convection flow in a vertical annular microchannel having temperature-dependent viscosity in the presence of velocity slip and temperature jump at the annular microchannel surfaces by Jha et al [42] have enhanced the body of knowledge on fluid flow, boundary layer analysis, and heat/mass transfer. The above literature review shows that there exists no published article on the effects of viscous dissipation in the flow of nonNewtonian Casson fluid over a upper horizontal thermally stratified melting surface of a paraboloid of revolution

Formulation of the Problem

Numerical Solution

Results and Discussion

Conclusion