In the present problem a magnetohydrodynamic (MHD) three dimensional Casson fluid flow past a porous linearly stretching sheet is investigated, introducing convective boundary condition at the surface where the thermal conductivity of the fluid varies linearly with respect to the temperature. Computations are performed for the velocity and temperature fields for different parameters. Spectral Relaxation Method (SRM) is used to solve the governing equations. The present results are compared with existing limited solutions, showing good agreement with each other and with different parameters. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. The influence of the skin friction and local Nusselt number for different parameters is discussed and presented in tabular form. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
In this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are Pr (0.3-0.8), ( β 0.5-1.5), M (1-5), A (0.5-1.5), L (0.1-0.9) 0 , D (0.2-4) f , Sr (0.3-6.3), and Sc (0.05-0.15). It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number,whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.
The Marangoni flow is involved with microgravity and earth gravity, which causes undesirable effects in crystal growth experiments. Crystal growth experiments were designed in such a manner so as to appraise MIR (space station), which is one of the best platforms for protein crystallization and radiation experiments. In this article, a model is proposed with a stagnation point and a Casson fluid flow at the interface of the plate in the presence of Marangoni convection influenced by a magnetic field and chemical reaction. Furthermore, it is considered that both temperature and concentration surface tension vary linearly with the interface. It is important to choose similarity transformations for implementing nonlinear differential equations into linear ordinary differential equations. We solved the system of differential equations using fourth order Range‐Kutta method with suitable shooting techniques, and the results are displayed through graphs. A comparison is made with the earlier existing literature, and it shows a very good agreement. The results and a detailed discussion of velocity, temperature, and concentration have been shown graphically. The favorable and unfavorable buoyancy force to Marangoni flow, the features of temperature and concentration field, have been investigated.
In the present paper, we have discussed the thermosolutal Marangoni force acting on the electrically conducting Casson fluid flow over a permeable horizontal stretching surface. It is presumed that the condition at the interfaces is influenced by the surface tension, which is proportional to the temperature and concentration profiles. At the interface, both concentration and temperature are heated in such a way that they are quadratic functions in x. Furthermore, we have introduced the magnetic field in the transverse direction of the fluid flow along with heat generation/absorption, thermal radiation, viscous dissipation, and first-order chemical effect with heat and mass flux into the present system. Similarity transformations have been used to convert the system of the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The reduced ODEs are then solved using the MATLAB program bvp4c, which is based on the fourth-order Runge-Kutta and shooting method.The impact of various pertinent flow parameters on the flow field, temperature, and species concentration has been studied through graphs. To know the characteristics of shear stress, heat and mass rate near the boundary, numerical values of them are also calculated and given in the tabular form. The resultsshow that the momentum boundary layer's thickness is getting thicker with an increase in solutal surface tension ratio, while its opposite trends have been observed in the thermal boundary layer region, this is due to the Marangoni effect. This Marangoni effect is very much important in the field of melting metals, crystal growth, welding, and electron beam. K E Y W O R D S Casson fluid, chemical effect, heat generation, Marangoni force, Soret and Dufour effect, thermal radiation, viscous dissipation
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