Soret and Dufour Effects in the Flow of Williamson Fluid over an Unsteady Stretching Surface with Thermal Radiation

2015 ◽  
Vol 70 (4) ◽  
pp. 235-243 ◽  
Author(s):  
Tasawar Hayat ◽  
Yusra Saeed ◽  
Sadia Asad ◽  
Ahmed Alsaedi
Keyword(s):  
Thermal Radiation ◽  
Energy Equation ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Soret And Dufour Effects ◽  
Williamson Fluid ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Unsteady Stretching Surface ◽  
Biot Numbers

AbstractThis paper looks at the simultaneous effects of heat and mass transfer in the flow of Williamson fluid over an unsteady stretching surface. The effects of thermal radiation and viscous dissipation are considered in an energy equation. Besides, the energy and concentration equations are coupled with the combined effects of Soret and Dufour. The convective conditions for both temperature and mass concentration are employed. The transformation procedure reduces the time-dependent boundary layer equations of momentum, energy, and concentration to the non-linear ordinary differential equations. Through graphs and numerical values, the velocity, temperature, and concentration fields are discussed for different physical parameters. It is found that the thermal and concentration Biot numbers have an increasing impact on both temperature and concentration fields, respectively.

Thermal Radiation Effect on Non-Newtonian Fluid Flow over a Stretched Sheet of Non-Uniform Thickness

2017 ◽  
Vol 377 ◽  
pp. 242-259 ◽  
Author(s):  
Ram Prakash Sharma ◽  
K. Avinash ◽  
N. Sandeep ◽  
Oluwole Daniel Makinde
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Newtonian Fluid ◽  
Stretching Surface ◽  
Soret And Dufour Effects ◽  
Williamson Fluid ◽  
Cross Diffusion ◽  
Diffusion Parameters ◽  
Matlab Package ◽  
Thermal Radiation Effect

The influence of thermal radiation on a two-dimensional non-Newtonian fluid flow past a slendering stretching surface is investigated theoretically. Casson and Williamson fluid models are considered with Soret and Dufour effects. The transformed ODEs are solved numerically using the bvp5c Matlab package and dual solutions are executed for Casson and Williamson fluid cases. The influence of various parameters, namely, thermal radiation parameter, cross diffusion parameters and slip parameters on velocity, thermal and concentration distributions are discussed with the assistance of graphs. The local Nusselt and Sherwood numbers are computed and presented through tables. It is observed that the influence of cross diffusion is higher on Williamson flow when equated with the Casson flow.

scholarly journals Effects of thermal radiation and heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of heat source or sink

2011 ◽  
Vol 15 (2) ◽  
pp. 477-485 ◽  
Author(s):  
Elsayed Elbashbeshy ◽  
T.G. Emam
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Source ◽  
Thermal Radiation ◽  
Skin Friction Coefficient ◽  
Integration Scheme ◽  
Stretching Surface ◽  
Boundary Layer Equations ◽  
Unsteady Stretching Surface ◽  
Permeability Parameter

The effects of thermal radiation and heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of heat source or sink are studied. The governing time dependent boundary layer equations are transformed to ordinary differential equations containing radiation parameter, permeability parameter, heat source or sink parameter, Prandtl number, and unsteadiness parameter. These equations are solved numerically by applying Nachtsheim-Swinger shooting iteration technique together with Rung-Kutta fourth order integration scheme. The velocity profiles, temperature profiles, the skin friction coefficient, and the rate of heat transfer are computed and discussed in details for various values of the different parameters. Comparison of the obtained numerical results is made with previously published results.

scholarly journals Unsteady double-diffusive natural convective MHD flow along a vertical cylinder in the presence of chemical reaction, thermal radiation and Soret and Dufour effects

2011 ◽  
Vol 8 (1) ◽  
pp. 25-36 ◽  
Author(s):  
Ali J. Chamkha ◽  
M. F. Al-Amin ◽  
Abdelraheem Aly
Keyword(s):  
Thermal Radiation ◽  
Numerical Solution ◽  
Chemical Reaction ◽  
Fluid Velocity ◽  
Vertical Cylinder ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Time Step ◽  
Soret And Dufour Effects ◽  
Double Diffusive

This work is focused on the numerical solution of unsteady double-diffusive free convective flow along a vertical isothermal cylinder in the presence of a transverse magnetic field, first-order homogeneous chemical reaction, thermal radiation and Soret and Dufour effects. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations are formulated and a numerical solution is obtained by using an explicit finite-difference scheme. The solutions at each time step have been found to reach the steady state solution properly. Representative results for the fluid velocity, temperature and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms. DOI: http://dx.doi.org/10.3329/jname.v8i1.7250

Multiple Analytic Solutions of Heat and Mass Transfer of Magnetohydrodynamic Slip Flow for Two Types of Viscoelastic Fluids Over a Stretching Surface

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Viscoelastic Fluid ◽  
Power Law ◽  
Multiple Solutions ◽  
Slip Flow ◽  
Analytic Solutions ◽  
Physical Parameters ◽  
Main Concern ◽  
Stretching Surface ◽  
Boundary Layer Equations ◽  
Nusselt Numbers

This paper focuses on the magnetohydrodynamic (MHD) slip flow of an electrically conducting, viscoelastic fluid past a stretching surface. The main concern is to analytically investigate the structure of the solutions and determine the thresholds beyond which multiple solutions exist or the physically pure exponential type solution ceases to exist. In the case of the presence of multiple solutions, closed-form formulae for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walter’s liquid B fluids. Heat transfer analyzes are also carried out for two general types of boundary heating processes, either by a prescribed quadratic power law surface temperature or by a prescribed quadratic power law surface heat flux. The flow field is affected by the presence of several physical parameters, whose influences on the unique/multiple solutions of velocity and temperature profiles, and Nusselt numbers are examined and discussed.

An Initial Value Method for the Solution of MHD Boundary-Layer Equations

1970 ◽  
Vol 21 (1) ◽  
pp. 91-99 ◽  
Author(s):  
T. Y. Na
Keyword(s):  
Boundary Layer ◽  
Iteration Process ◽  
Physical Parameters ◽  
Point Boundary ◽  
Initial Value ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

SummaryAn initial value method is introduced in this paper for the solution of the two-point non-linear ordinary differential equations resulting from an analysis of the MHD boundary-layer flow originally treated by Greenspan and Carrier. By using this method, the iteration process is eliminated. The method is seen to be applicable to the solution of similar two-point boundary value problems where certain physical parameters appear either in the differential equation or in the boundary conditions and solutions for a range of the parameter are sought.

scholarly journals Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation

2013 ◽  
Vol 18 (4) ◽  
pp. 1151-1164 ◽  
Author(s):  
G.V.R. Reddy ◽  
B.A. Reddy ◽  
N.B. Reddy
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Convection Flow ◽  
Physical Parameters ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Porous Stretching Surface

Abstract The effects of thermal radiation and mass transfer on an unsteady hydromagnetic boundary layer mixed convection flow along a vertical porous stretching surface with heat generation are studied. The fluid is assumed to be viscous and incompressible. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables. Numerical solutions of these equations are obtained by using the Runge-Kutta fourth order method along with the shooting technique. Velocity, temperature, concentration, the skin-friction coefficient, Nusselt number and Sherwood number for variations in the governing thermo physical parameters are computed, analyzed and discussed.

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