scholarly journals Dual Solutions of Non-Newtonian Casson Fluid Flow and Heat Transfer over an Exponentially Permeable Shrinking Sheet with Viscous Dissipation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Aurang Zaib ◽  
Krishnendu Bhattacharyya ◽  
Md. Sharif Uddin ◽  
Sharidan Shafie
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Flow ◽  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Shrinking Sheet ◽  
Nonlinear Odes ◽  
Flow And Heat Transfer

The two-dimensional boundary layer flow of a non-Newtonian Casson fluid and heat transfer due to an exponentially permeable shrinking sheet with viscous dissipation is investigated. Using similarity transformations, the governing momentum and energy equations are transformed to self-similar nonlinear ODEs and then those are solved numerically by very efficient shooting method. The analysis explores many important aspects of flow and heat transfer of the aforesaid non-Newtonian fluid flow dynamics. For the steady flow of non-Newtonian Casson fluid, more amount of wall mass suction through the porous sheet is required in comparison to that of Newtonian fluid flow. Dual similarity solutions are obtained for velocity and temperature. The viscous dissipation effect has major impact on the heat transfer characteristic. In fact, heat absorption at the surface occurs and it increases due to viscous dissipation. For higher Prandtl number, the temperature inside the boundary layer reduces, but with larger Eckert number (viscous dissipation) it is enhanced.

scholarly journals 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

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. M. Ajayi ◽  
A. J. Omowaye ◽  
I. L. Animasaun
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Dynamic Viscosity ◽  
Casson Fluid ◽  
Stratified Medium ◽  
Internal Space ◽  
Melting Surface

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.

scholarly journals Effects of Second-Order Slip and Viscous Dissipation on the Analysis of the Boundary Layer Flow and Heat Transfer Characteristics of a Casson Fluid

2016 ◽  
Vol 21 (1) ◽  
pp. 48 ◽  
Author(s):  
Mohammad M. Rahman ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Layer Flow ◽  
Casson Fluid ◽  
Shrinking Sheet ◽  
Solution Branch ◽  
Heat Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Layer Flow

The aim of the present study is to analyze numerically the steady boundary layer flow and heat transfer characteristics of Casson fluid with variable temperature and viscous dissipation past a permeable shrinking sheet with second order slip velocity. Using appropriate similarity transformations, the basic nonlinear partial differential equations have been transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters namely: shrinking parametersuction parameterCasson parameterfirst order slip parametersecond order slip parameter  Prandtl number  and the Eckert number  using the bvp4c function from MATLAB. A stability analysis has also been performed. Numerical results have been obtained for the reduced skin-friction, heat transfer and the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking surface for certain values of the parameter space. The stability analysis indicates that the lower solution branch is unstable, while the upper solution branch is stable and physically realizable. In addition, it is shown that for a viscous fluida very good agreement exists between the present numerical results and those reported in the open literature. The present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a Casson fluid. Therefore, this study has importance for researchers working in the area of non-Newtonian fluids, in order for them to become familiar with the flow behavior and properties of such fluids.  

Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of Nanofluids Past a Bidirectional Exponential Permeable Stretching/Shrinking Sheet With Viscous Dissipation Effect

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Rahimah Jusoh ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Volume Fraction ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Flow And Heat Transfer ◽  
Layer Flow

The problem of boundary layer flow and heat transfer of magnetohydrodynamic (MHD) nanofluids which consist of Fe3O4, Cu, Al2O3, and TiO2 nanoparticles and water as the base fluid past a bidirectional exponentially permeable stretching/shrinking sheet is studied numerically. The mathematical model of the nanofluid incorporates the effect of viscous dissipation in the energy equation. By employing a suitable similarity transformation, the conservative equations for mass, momentum, and energy are transformed into the ordinary differential equations. These equations are then numerically solved with the utilization of bvp4c function in matlab. The effects of the suction parameter, magnetic parameter, nanoparticle volume fraction parameter, Eckert number, Prandtl number, and temperature exponent parameter to the reduced skin friction coefficient as well as the local Nusselt number are graphically presented. Cu is found to be prominently good in the thermal conductivity. Nevertheless, higher concentration of nanoparticles leads to the deterioration of heat transfer rate. The present result negates the previous literature on thermal conductivity enhancement with the implementation of nanofluid. Stability analysis is conducted since dual solutions exist in this study, and conclusively, the first solution is found to be stable.

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