# Unsteady MHD forced flow due to a point sink

TL;DR: In this paper, an analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field.

Abstract: An analysis is performed to study the unsteady laminar incompressible boundary-layer flow of an electrically conducting fluid in a cone due to a point sink with an applied magnetic field. The unsteadiness in the flow is considered for two types of motion, viz. the motion arising due to the free stream velocity varying continuously with time and the transient motion occurring due to an impulsive change either in the strength of the point sink or in the wall temperature. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The magnetic field increases the skin friction but reduces heat transfer. The heat transfer and temperature field are strongly influenced by the viscous dissipation and Prandtl number. The velocity field is more affected at the early stage of the transient motion, caused by an impulsive change in the strength of the point sink, as compared to the temperature field. When the transient motion is caused by a sudden change in the wall temperature, both skin friction and heat transfer take more time to reach a new steady state. The transient nature of the flow and heat transfer is active for a short time in the case of suction and for a long time in the case of injection. The viscous dissipation prolongs the transient behavior of the flow.

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TL;DR: The unsteady, buoyancy-induced, hydromagnetic, thermal convection flow in a semi-infinite porous regime adjacent to an infinite hot vertical plate moving with constant velocity, is studied in the presence of significant thermal radiation.

Abstract: The unsteady, buoyancy-induced, hydromagnetic, thermal convection flow in a semi-infinite porous regime adjacent to an infinite hot vertical plate moving with constant velocity, is studied in the presence of significant thermal radiation. The momentum and energy conservation equations are normalized and then solved using both the Laplace transform technique and Network Numerical Simulation. Excellent agreement is obtained between both analytical and numerical methods. An increase in Hartmann number (𝑀2) strongly decelerates the flow and for very high strength magnetic fields (𝑀2=20), the flow is reversed after a short time interval. The classical velocity overshoot is also detected close to the plate surface for low to intermediate values of 𝑀2 at both small and large times; however this overshoot vanishes for larger strengths of the transverse magnetic field (𝑀2=10). An increase in radiation-conduction parameter (𝐾𝑟) significantly increases temperature throughout the porous regime at both small and larger times, adjacent to the plate, but decreases the shear stress magnitudes at the plate. Temperature gradient is reduced at the plate surface for all times, with a rise in radiation-conduction parameter (𝐾𝑟). Shear stress is reduced considerably with an increase in Darcian drag parameter (𝐾𝑝).

27 citations

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TL;DR: In this article, the velocity, temperature and concentration profiles are studied for different physical parameters like Suction parameter s, Heat sink F, thermal Grashof number Gr, mass Grashoff number Gc, chemical reaction parameter K, Prandtl number Pr and Schmidt number Sc.

Abstract: The aim of this study is to determine heat and mass transfer over a vertical plate in the presence of periodic suction and heat sink. The dimensionless governing equations are solved using perturbation technique. The velocity, temperature and concentration profiles are studied for different physical parameters like Suction parameter s, Heat sink F, thermal Grashof number Gr, mass Grashof number Gc, chemical reaction parameter K, Prandtl number Pr and Schmidt number Sc. It is observed that the velocity increases with increase in F and s. It is also observed that temperature increases with increasing F, Pr but s decreases with rise in temperature. While concentration increases with increasing Sc and K. the aim of the study is to determine the rate of heat and mass transfer of the system.

15 citations

### Cites background from "Unsteady MHD forced flow due to a p..."

...Eswara et al. (2004) studied unsteady MHD forced flow due to a point sink....

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01 Jan 2011

TL;DR: In this article, the steady incompressible mixed convection boundary layer flow with variable fluid properties and mass transfer inside a cone due to a point sink at the vertex of the cone have been investigated.

Abstract: The steady incompressible mixed convection boundary layer flow with variable fluid properties and mass transfer inside a cone due to a point sink at the vertex of the cone have been investigated. The fluid viscosity and thermal conductivity have been assumed to be temperature dependent. The governing fluid flow equations with boundary conditions have been transformed into set of coupled ordinary differential equations with the help of similarity transformations and solved Runge-Kutta method with shooting technique. The effects of Schmidt number, variable thermal conductivity parameter, mixed convection parameter, buoyancy parameter and chemical reaction parameter on velocity distribution, temperature distribution, concentration distribution, heat transfer rate and coefficient of skinfriction have been investigated. It is observed that concentration decreases with increasing Schmidt number and temperature increases with increasing values of thermal conductivity parameter. Also with increasing values of mixed convection parameter, velocity, temperature and concentration decreases. The present study is relevant in conical nozzle and diffuser flow problems exist in petroleum and chemical industries.

9 citations

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TL;DR: In this article, the effects of the magnetic field, mass flux diffusion and heat transfer on demixing of a binary mixture of incompressible viscous electrically conducting fluids in steady, laminar boundary layer flow in presence of a point sink at the vertex of a cone are discussed.

Abstract: The present problem concerns with the effects of the magnetic field, mass flux diffusion and heat transfer on demixing of a binary mixture of incompressible viscous electrically conducting fluids in steady, laminar boundary layer flow in presence of a point sink at the vertex of a cone. The momentum, energy and concentration equations are reduced to non-linear coupled ordinary differential equations by similarity transformations and are solved numerically by using MATLAB’s built in solver bvp4c. The local skin friction, the Nusselt number and the Sherwood number are tabulated for various values of the parameters. These numerical results have been demonstrated graphically from which it is observed that the effects of various parameters are to separate the components of the binary mixture by collecting the rarer and lighter component near the surface of the cone and throwing the heavier one away from it.

8 citations

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TL;DR: An analytical solution of the magnetohydrodynamic, steady, and incompressible laminar boundary layer flow in the presence of heat and mass transfer as well as magnetic field on a cone due to a point sink by using the homotopy analysis method (HAM) has been studied under the radiative fluid properties.

Abstract: An analytical solution of the magnetohydrodynamic, steady, and incompressible laminar boundary layer flow in the presence of heat and mass transfer as well as magnetic field on a cone due to a point sink by using the homotopy analysis method (HAM) has been studied under the radiative fluid properties. The HAM produces an analytical solution of the governing self-similar nonlinear two-point boundary layer equations. The effects of the suction/injection, magnetic, and radiation parameters over the obtained solution have been discussed. The effects of Prandtl number on temperature and Schmidt number on concentration profiles have also been studied. It has been observed that the temperature profiles exhibit an increasing trend with radiation in case of injection while an opposite trend is observed in case of suction. The results obtained in the present study have also been compared numerically as well as graphically with the corresponding results obtained by using other methods. An excellent agreement has been found between them. The analytical solution obtained by the HAM is very near to the exact solution for a properly selected initial guess, auxiliary, and convergence control parameters and for higher orders of deformations.

6 citations

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...[5] investigated the problem for the transient case....

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##### References

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01 Jan 1955

TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.

Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

17,321 citations

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01 Jan 1965

TL;DR: Quasilinearization and nonlinear boundary value problems as discussed by the authors, where the boundary value problem is formulated as a quadratic equation of the value of a boundary value.

Abstract: Quasilinearization and nonlinear boundary-value problems , Quasilinearization and nonlinear boundary-value problems , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

1,163 citations