An attempt has been made to study the heat and mass transfer effect in a boundary layer flow through porous medium of an electrically conducting viscoelastic fluid over a shrinking sheet subject to transverse magnetic field in the presence of heat source. Effects of radiation, viscous dissipation, and uniform heat sink on the heat transfer have been considered. The method of solution involves similarity transformation. The coupled nonlinear partial differential equations representing momentum, concentration, and nonhomogenous heat equation are reduced into a set of nonlinear ordinary differential equations. The transformed equations are solved by applying Kummer’s function. The exact solution of temperature field is obtained for powerlaw surface temperature (PST) as well as powerlaw heat flux (PHF) boundary condition. The interaction of magnetic field is proved to be counterproductive in enhancing velocity and concentration distribution, whereas presence of porous matrix reduces the temperature field at all points.
The fluid flow over a stretching sheet is important in many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning, polymers in metal spring processes, the continuous casting of metals, drawing plastic films, and spinning of fibers, which all involve some aspects of flow over a stretching sheet or cylindrical fiber [
A chemical reaction can be codified as either a homogenous or a heterogeneous process. This depends upon whether it occurs on an interface or as a singlephase volume reaction. A reaction is said to be first order if its rate is directly proportional to the concentration itself.
Chamkha [
Ahmad and Khan [
The objective of the present study is to consider the heat and mass transfer of an electrically conducting viscoelastic fluid flow over a linearly shrinking sheet embedded in a porous medium.
The novelty of the present study is to investigate the effect of porous medium and mass transfer on the flow of a slightly elastic fluid over a shrinking sheet. The results of Midya [
Consider a steady twodimensional flow of an incompressible electrically conducting secondorder viscoelastic fluid over a shrinking surface. In our analysis we have taken
Equations (
The boundary conditions are
The shear stress at the wall is defined as
Powerlaw surface temperature (PST) and powerlaw wall heat flux (PHF) cases are to be considered.
In powerlaw surface temperature, the boundary conditions are given by
The boundary conditions (
The boundary conditions in case of PHF are given by
Introducing the similarity variable
The boundary conditions are assigned as
The present study considers the flow of a viscoelastic incompressible electrically conducting fluid flow past a stretching sheet through a porous medium in the presence of magnetic field, viscous dissipation, and uniform heat source/sink in the presence of chemical reaction. The aim of the following discussion is to bring out the effect of permeability of the medium, plate temperature, and chemical reaction on the flow phenomena.
The heat generation/absorption contributes significantly to nonisothermal heat transfer case. Another consideration of the present study is the saturated porous media. Porous media are very widely used to insulate a heated body to maintain its temperature. They are considered to be useful in diminishing the natural free convection which would otherwise occur intensely on the vertical surface.
Further, the effect of free convection on the flow through porous media plays an important role in agricultural engineering and in petroleum industry in extracting poor petroleum from the crude. Moreover, the present study considers the effect of viscous dissipation which accounts for the heat energy stored in the fluid due to frictional heating.
The following discussion presents the effects of various parameters exhibiting the above phenomena.
Figure
(a) Velocity profile. (b) Velocity profile for
Furthermore, it is interesting to note that when
Figures
Variation of temperature:
Variation of temperature:
Thus, it may be considered that the increase in
Temperature distribution for different values of
Variation of temperature:
Figure
Variation of temperature:
Figures
Variation of temperature.
Variation of temperature:
Variation of temperature:
Figures
Variation of temperature:
Variation of temperature:
Variation of temperature:
Variation of temperature:
Variation of temperature:
Figure
Concentration profile.
From Table
Skin friction coefficient.
Sl. number 





1  1.5  100  0.1  1.070259 
2  3  100  0.1  2.698484 
3  3  0.5  0.1  3.015113 
4  3  100  0.5  2.310844 
5  3  100  0.8  2.109502 
6  3  0.5  0.8  2.357023 
7  2  100  0.1  1.654196 
8  4  100  0.1  3.693975 
9  2  0.5  0.1  2.132007 
10  4  0.5  0.1  3.931227 
From Table
Nusselt number.
Sl. number 







Nu 






















































































































Table
Sherwood number.
Sl. number 




Sh 





































Presence of porous matrix enhances the velocity because porous matrix acts as an insulator to the vertical surface preventing energy loss due to free convection.
The resistive force of magnetic field is overcome due to the presence of porous matrix and elasticity of the fluid and hence the velocity increases due to the presence of both.
Further, absence of magnetic field and porous matrix leads to transitory motion of the fluid.
Presence of elasticity also leads to an increase in the temperature at all points but the presence of magnetic field reduces it.
The thinning of thermal boundary layer thickness is due to slow rate thermal diffusion in presence of magnetic field and porous matrix.
The variation in temperature is more sensitive due to presence of heat flux.
Presence of porous matrix with moderate values of magnetic parameter in case of heavier species enhances the concentration level in the presence of chemical reaction.
For higher value of magnetic field in conjunction with porous matrix reduces the concentration level.
Presence of elastic element is favorable in reducing the skin friction.
The effect of porous matrix is duly compensated, enhancing the magnetic strain in the absence of porous matrix on the rate of heat transfer.
Moreover, the rate of heat transfer in the present study is sensitive to the presence of porous matrix and magnetic parameter.
Porous matrix enhances the rate of mass transfer, whereas increase in chemical reaction has no impact in absence of porous matrix.
Nondimensional species concentration
Species concentration away from the wall
Nondimensional velocity in the
Nondimensional velocity in the
Volumetric rate of internal heat generation/absorption
Permeability of the medium
Thermal diffusivity
Elastic parameter
Prandtl number
Schmidt number
Nondimensional temperature
Nondimensional time
Density of the fluid
Kinematics coefficient of viscosity
StefanBoltzmann constant
Specific heat
Wall heat flux
Wall shear stress
Temperature far from sheet
Wall temperature
Porosity parameter
Magnetic parameter
Magnetic field of uniform strength
Heat source parameter
Temperature of the field
Time
Molecular diffusivity
Radiative heat flux
Absorption coefficient
Electrical conductivity
Radiation parameter
Eckert number
Skin friction coefficient
Dimensionless elastic parameter
Rate of mass flux.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the referees for their constructive comments and valuable suggestions.