MHD mixed convective slip flow of Casson fluid over a porous inclined plate with Joule heating, viscous dissipation and thermal radiation

Abstract In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.

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Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

Nonlinear Engineering ◽

10.1515/nleng-2017-0014 ◽

2017 ◽

Vol 6 (3) ◽

Cited By ~ 11

Author(s):

K. Ganesh Kumar ◽

N.G. Rudraswamy ◽

B.J. Gireesha ◽

M.R. Krishnamurthy

Keyword(s):

Differential Equations ◽

Thermal Radiation ◽

Ordinary Differential Equations ◽

Viscous Dissipation ◽

Joule Heating ◽

Stretching Sheet ◽

Three Dimensional ◽

Nonlinear Thermal Radiation ◽

Nonlinear Ordinary Differential Equations ◽

Three Dimensional Flow

AbstractPresent exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge–Kutta–Fehlberg fourth–fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

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Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220964843 ◽

2020 ◽

pp. 095440622096484

Author(s):

Muhammad Nazim Tufail ◽

Musharafa Saleem ◽

Qasim Ali Chaudhry

Keyword(s):

Differential Equations ◽

Viscous Dissipation ◽

Joule Heating ◽

Casson Fluid ◽

Graphical Analysis ◽

Thermal Transfer ◽

Fluid Parameter ◽

Two Parameters ◽

Unsteady Effects ◽

Physical Quantities

The model encountered an unsteady laminar and two-dimensional convective flow of Casson fluid passing through an inclined permeable vertical stretching sheet. The momentum, thermal and concentrated boundary layers (BLs) are used to analyze the unsteady effects of magnetohydrodynamics (MHD) (neglecting induced magnetic field), viscous dissipation, Joule heating and chemical reactions. The governed partial differential equations (PDEs) of the model are reduced to the ordinary differential equations (ODEs). The ξ and χ are selected as the two parameters of the scaling transformations. By using bvp4c with MATLAB, the ODEs are solved numerically and represent their results through the graphs and tables. After the non-dimensionalizing of the equations system, we get the emerging dimensionless parameters. The concentration process was enhanced by the Casson fluid parameter but it reduced the fluid flow and thermal transfer that can be found through the graphical results. The effect of Buoyancy is highlighted as it reduced the velocity profile function, but it is a growing function of the thermal and concentrated profiles. The physical quantities are integrated through the table and graphical analysis. In the center of the wall, the number Shx versus Sc decreases, but at the end it increases.

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