Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge. (English) Zbl 1200.76172
The authors analyze the flow and heat transfer characteristics of an incompressible viscous electrically conducting fluid over a permeable non-isothermal wedge in the presence of thermal radiation. It is assumed that the fluid is heat-generating/absorbing having temperature-dependent viscosity. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The effects of viscous dissipation, Joule heating and stress work are also included in the model. The governing partial differential equations are derived and transformed using a non-similarity transformation. Thus, the problem is reduced to two partial differential equations with the corresponding boundary conditions. The problem is governed by eight non-dimensional parameters, namely, the Prandtl number \(Pr\), thermal radiation parameter \(Nr\), heat generation parameter \(\lambda\), Eckert number \(Ec\), viscosity parameter \(\theta_r\), suction/injection parameter \(f_0\), pressure gradient parameter \(m\) and magnetic parameter \(\xi\). The transformed equations are solved numerically following the local non-similarity method. The system of four ordinary differential equations with the corresponding boundary conditions is also solved numerically for some values of the governing parameters using the Runge-Kutta-Fehlberg scheme with shooting method. The accuracy of the numerical method has been checked by performing comparisons with previously known results for a constant viscosity fluid (\(\theta_r\to\infty\)). A good agreement has been found. Velocity and temperature profiles for a prescribed magnetic field parameter \(\xi\) as well as the development of the local skin friction coefficient and local Nusselt number with the magnetic (\(\xi\)) and radiation parameter \(Nr\) are presented in 15 figures and 4 tables. It is shown that the effect of increasing Eckert number \(Ec\) is to decrease the dimensionless temperature distribution \(\theta\) in the thermal boundary layer. This temperature decreases with the similarity variable \(\eta\) rapidly at first, till it reaches a negative minimum value and then increases more gradually to its free surface value (\(\eta\to\infty\)) due to reversed heat flow between the wall and the surrounding fluid in the presence of thermal radiation. Physically, this situation of negative \(\theta\) may arise when excess heating of the ambient fluid takes place due to viscous dissipation and as the value of \(Ec\) increases. This clearly shows that higher values of \(Ec\) result in extremely high temperature.
Reviewer: Ioan Pop (Cluj-Napoca)
MSC:
| 76R10 | Free convection |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
Keywords:
non-similarity solution; boundary layer; Rosseland approximation; Runge-Kutta-Fehlberg scheme; shooting methodReferences:
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