The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink

Abstract Steady two-dimensional non-Newtonian second grade fluid is studied under the influence of temperature dependent viscosity and thermal conductivity. The viscosity is assumed to vary inversely as linear function of temperature while the thermal conductivity varies directly as linear function of temperature. Also, effects of radiative heat, viscous dissipation and heat source/sink are considered in the energy equation. The basic governing partial differential equations for the velocity and temperature are transformed to ordinary differential equations (ODEs) using appropriate similarity variables. These coupled nonlinear ODEs have been solved approximately subject to appropriate boundary conditions by Runge–Kutta shooting technique. The quantitative effects of emerging dimensionless physical parameters on the velocity, temperature, skin friction and heat transfer rate are displayed graphically. The numerical investigation of the variable thermo-physical properties of a second grade fluid over a stretching sheet provides an extension to previous work.

[1]  S. Barış,et al.  Three-dimensional stagnation point flow of a second grade fluid towards a moving plate , 2006 .

[2]  K. Hsiao.  Viscoelastic Fluid over a Stretching Sheet with Electromagnetic Effects and Nonuniform Heat Source/Sink , 2010 .

[3]  Ahmad Naseem.  Visco-Elastic Boundary Layer Flow past a Stretching Plate and Heat Transfer with Variable Thermal Conductivity , 2011 .

[4]  M. Ramya,et al.  Study of Visco-Elastic Fluid Flow and Heat Transfer over a Stretching Sheet with Variable Viscosity and Thermal Radiation , 2014 .

[5]  S. Spartalis.  Similarity Approach to the Problem of Second Grade Fluid Flows over a Stretching Sheet , 2007 .

[6]  A Study for MHD Boundary Layer Flow of Variable Viscosity over a Heated Stretching Sheet via Lie-Group Method , 2015 .

[7]  M. Noor,et al.  Some Relatively New Techniques for Nonlinear Problems , 2009 .

[8]  Rahmat Ellahi,et al.  Study of magnetic and heat transfer on the peristaltic transport of a fractional second grade fluid in a vertical tube , 2015 .

[9]  T. Hayat,et al.  Flow of a second grade fluid with convective boundary conditions , 2011 .

[10]  G. Layek,et al.  Analysis of Boundary Layer Flow and Heat Transfer for two Classes of Viscoelastic Fluid Over a Stretching Sheet with Heat Generation or Absorption , 2012 .

[11]  R. Rivlin,et al.  Stress-Deformation Relations for Isotropic Materials , 1955 .

[12]  Rafael Cortell Bataller,et al.  Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet , 2007, Comput. Math. Appl..

[13]  R. Cortell,et al.  Fluid flow and radiative nonlinear heat transfer over a stretching sheet , 2014 .

[14]  M. Subhas Abel,et al.  Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation , 2008 .

[15]  T. C. Chiam.  Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet , 1998 .

[16]  Oluwole Daniel Makinde,et al.  Analysis of entropy generation in a variable viscosity fluid flow between two concentric pipes with a convective cooling at the surface , 2011 .

[17]  C. Mamaloukas.  Similarity Approach to the Problem of Second Grade Fluid Flows over a Stretching Sheet , 2006 .

[18]  Vivek,et al.  Effect of Variable Thermal Conductivity & Heat Source/Sink near a Stagnation Point on a Linearly Stretching Sheet using HPM , 2014 .

[19]  T. Roper,et al.  Flow and heat transfer in a second grade fluid over a stretching sheet , 1999 .

[20]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[21]  M. Massoudi,et al.  Fully developed flow of a modified second grade fluid with temperature dependent viscosity , 2001 .

[22]  O. Makinde,et al.  Natural Convection of Viscoelastic Fluid from a Cone Embedded in a Porous Medium with Viscous Dissipation , 2013 .

[23]  K. Das.  Effects of thermophoresis and thermal radiation on MHD mixed convective heat and mass transfer flow , 2013 .

[24]  T. Hayat,et al.  Influence of Thermal Radiation on Blasius Flow of a Second Grade Fluid , 2009, Zeitschrift für Naturforschung A.

[25]  M. Nandeppanavar,et al.  Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink , 2010 .

[26]  A. Megahed,et al.  Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity , 2013 .

[27]  A. Gupta,et al.  Viscoelastic Fluid over a Stretching Sheet with Electromagnetic Effects and Nonuniform Heat Source / Sink , 2010 .

[28]  M. Massoudi,et al.  Natural convection flow of a generalized second grade fluid between two vertical walls , 2008 .

[29]  R. Cortell.  A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet , 2006 .

[30]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[31]  Yasir Khan,et al.  Heat Transfer Analysis on the Magnetohydrodynamic Flow of a Non- Newtonian Fluid in the Presence of Thermal Radiation: An Analytic Solution , 2012 .

[32]  M. Mishra,et al.  Boundary layer flow and heat transfer past a stretching plate with variable thermal conductivity , 2010 .

[33]  Tasawar Hayat,et al.  Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space , 2008 .