Stagnation-Point Flow Towards a Heated Porous stretching Sheet Through a Porous Medium with Thermal Radiation and Variable Viscosity

2015 ◽  
Vol 11 (3) ◽  
pp. 3081-3090
Author(s):  
Faiza Ahmed Salama
Keyword(s):  
Porous Medium ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Stagnation Point Flow ◽  
Stream Velocity ◽  
Fluid Temperature ◽  
Governing Equations ◽  
Scaling Group Of Transformations

An analysis is made for the steady two-dimensional stagnation-point flow in a porous medium of an incompressible viscous fluid towards a permeable stretching surface with variable viscosity and thermal radiation. The viscosity of the fluid is assumed to be an inverse linear function of the fluid temperature. The stretching velocity  and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The governing equations for the problem where changed to dimensionless ordinary differential equations using scaling group of transformations. The transformed governing equations in the present study were  solved numerically by using  Rung-Kutta and Shooting method. Favorable comparison with previously published work is performed. A comparison between the analytical and numerical solutions has  been included. The numerical  solutions are presented to illustrate the influence of the various values of the ratio of free stream velocity and stretching velocity, the viscosity variation parameter and the porosity parameter. These effects of the different parameter on the velocity and temperature profiles in the boundary layer as well as the coefficient of heat flux and shearing  stress at the surface are presented graphically to show interesting aspects of the solution.

scholarly journals SCALING GROUP OF TRANSFORMATIONS FOR BOUNDARY LAYER STAGNATION‐POINT FLOW THROUGH A POROUS MEDIUM TOWARDS A HEATED STRETCHING SHEET

2006 ◽  
Vol 11 (2) ◽  
pp. 187-197 ◽  
Author(s):  
G. C. Layek ◽  
S. Mukhopadhyay ◽  
SK. A. Samad
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Stream Velocity ◽  
Scaling Group Of Transformations ◽  
Scaling Group

An analysis is performed to investigate the structure of the boundary layer stagnation‐point flow and heat transfer of a fluid through a porous medium over a stretching sheet. A scaling group of transformations is applied to get the invariants. Using the invariants, a third and a second order ordinary differential equations corresponding to the momentum and energy equations are obtained respectively. The equations are then solved numerically. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity (ax) and the stretching velocity (ax). The temperature decreases in this case. At a particular point of the stretching sheet, the fluid velocity decreases or increases with the increase of the permeability of the porous medium when the free stream velocity is less or grater than the stretching velocity.

scholarly journals Heat Transfer due to Magnetohydrodynamic Stagnation-Point Flow of a Power-Law Fluid towards a Stretching Surface in the Presence of Thermal Radiation and Suction/Injection

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Tapas Ray Mahapatra ◽  
Sabyasachi Mondal ◽  
Dulal Pal
Keyword(s):  
Heat Transfer ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Power Law ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Stream Velocity ◽  
Stretching Surface ◽  
Power Law Fluid

An analysis is made on the study of two-dimensional MHD (magnetohydrodynamic) boundary-layer stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point in the presence of thermal radiation and suction/injection. The paper examines heat transfer in the stagnation-point flow of a power-law fluid except when the ratio of the free stream velocity and stretching velocity is equal to unity. The governing partial differential equations along with the boundary conditions are first brought into a dimensionless form and then the equations are solved by Runge-Kutta fourth-order scheme with shooting techniques. It is found that the temperature at a point decreases/increases with increase in the magnetic field when free stream velocity is greater/less than the stretching velocity. It is further observed that for a given value of the magnetic parameter M, the dimensionless rate of heat transfer at the surface and |θ′(0)| decreases/increases with increase in the power-law index n. Further, the temperature at a point in the fluid decreases with increase in the radiation parameter NR when free stream velocity is greater/less than the stretching velocity.

Thermal Radiation Effects on the Mixed Convection Stagnation-Point Flow in a Jeffery Fluid

2011 ◽  
Vol 66 (10-11) ◽  
pp. 606-614 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
Saleem Obaidat
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Deborah Number ◽  
Stagnation Point Flow ◽  
Suction Parameter

This study describes the mixed convection stagnation point flow and heat transfer of a Jeffery fluid towards a stretching surface. Mathematical formulation is given in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux. Similarity transformations are employed to reduce the partial differential equations into the ordinary differential equations which are then solved by a homotopy analysis method (HAM). A comparative study is made with the known numerical solutions in a limiting sense and an excellent agreement is noted. The characteristics of involved parameters on the dimensionless velocity and temperature are also examined. It is noticed that the velocity increases with an increase in Deborah number. Further, the temperature is a decreasing function of mixed convection parameter. We further found that for fixed values of other parameters, the local Nusselt number increases by increasing suction parameter and Deborah number.

scholarly journals Magnetic Dipole and Thermal Radiation Impacts on Stagnation Point Flow of Micropolar Based Nanofluids over a Vertically Stretching Sheet: Finite Element Approach

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1089
Author(s):  
Shahid Ali Khan ◽  
Bagh Ali ◽  
Chiak Eze ◽  
Kwun Ting Lau ◽  
Liaqat Ali ◽  
...  
Keyword(s):  
Finite Element ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Magnetic Dipole ◽  
Fluid Velocity ◽  
Stagnation Point Flow ◽  
Fluid Temperature ◽  
Finite Element Scheme ◽  
Physical Consideration ◽  
Element Scheme

An analysis for magnetic dipole with stagnation point flow of micropolar nanofluids is modeled for numerical computation subject to thermophoresis, multi buoyancy, injection/suction, and thermal radiation. The partial derivative is involved in physical consideration, which is transformed to format of ordinary differential form with the aid of similarity functions. The variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear ordinary differential problem. The fluid temperature, velocity, tiny particles concentration, and vector of micromotion are studied for two case of buoyancy (assisting 0<λ, and opposing 0>λ) through finite-element scheme. The velocity shows decline against the rising of ferromagnetic interaction parameter (β) (assisting 0<λ and opposing 0>λ), while the inverse behaviour is noted in micro rotation profile. Growing the thermo-phoresis and microrotation parameters receded the rate of heat transfer remarkable, and micromotion and fluid velocity enhance directly against buoyancy ratio. Additionally, the rate of couple stress increased against rising of thermal buoyancy (λ) and boundary concentration (m) in assisting case, but opposing case shows inverse behavior. The finite element scheme convergency was tested by changing the mesh size, and also test the validity with available literature.

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