Unsteady Hydromagnetic Free Convection Flow Research Articles

Transient flow and heat transfer characteristics of single-phase nanofluid past a stretching sheet under the influence of thermal radiation and heat source

This work aims to investigate the unsteady hydromagnetic free convective flow of a viscous, electrically incompressible fluid influenced by an inclined magnetic field, radiation, and heat source. Specifically, it explores the behavior of water-based nanofluids under these conditions. The Newton-Raphson shooting technique combines the 4th-order Runge-Kutta approach to obtain dimensionless and accurate solutions to the governing equations. The study assesses flow characteristics and heat transfer properties over various parameter values. The outcomes are visualized through graphical representations of velocity, temperature, skin friction coefficient, and the local Nusselt number. The present study examines the impact of copper (Cu), silver (Ag), alumina (Al2O3), and titanium dioxide (TiO2) nanoparticles in water as the base fluid on the percentage increase in skin friction and Nusselt number under various physical conditions. Suction increases skin friction by 10–15 % and the Nusselt number by a similar margin, whereas injection can reduce these metrics. Radiation enhances heat transfer, resulting in a 5–10 % increase in skin friction and a 10–15 % rise in the Nusselt number, with nanoparticles like Ag showing the most substantial effects due to their superior thermal properties.

Mathematical modelling of the effects of heat and mass transfer on an unsteady hydro-magnetic free convective flow over an infinite vertical plate embedded in a porous medium

Mathematical modelling of the effects of heat and mass transfer on an unsteady hydro-magnetic free convective flow over an infinite vertical plate embedded in a porous medium

Unsteady MHD natural convection flow past an infinite vertical porous plate with radiation absorption effects

AbstractIn this paper, we have explored the unsteady hydromagnetic free convective flow over an infinite perpendicular porous plate with temperature resource and/or radiation absorption. The prevailing equations are subsequently resolved systematically by utilizing perturbation methodology. The velocity, temperatures as well as concentrations sketches are shown in graphics. The impacts in the flow area for dissimilar leading parameters have been explored. Also, the skin friction, Nusselt quantity along with Sherwood quantity are computed with different parameters and mentioned in the tables. The velocity diminishes with escalating in the chemically reacting parameter as well as improves with an increment in temperature resource parameters. The temperature field reduces with an augment in the Prandtl number, whereas it enlarges with an augment in temperature absorption parameters. The concentrations field is enhanced by an amplifying in chemically reacting variable, whereas it lessens with an amplifying Schmidt number.

Finite element solution of mass transfer effects on unsteady hydromagnetic convective flow past a vertical porous plate in a porous medium with heat source

The objective of this chapter is to analyze the effect of mass transfer on unsteady hydromagnetic free convective flow of a viscous incompressible electrically conducting fluid past an infinite vertical porous plate in presence of constant suction and heat source. The governing equations of the flow field are solved using Galerkin finite element method and approximate solutions are obtained for velocity field, temperature field, concentration distribution, skin friction and the rate of heat and mass transfer. The numerical results for some special cases were compared with Das et al . [7] and were found to be in good agreement. The effects of the flow parameters such as Hartmann number ( M ), Grashof number for heat and mass transfer ( Gr , Gc) , Permeability parameter ( Kp ), Schmidt number ( Sc ), Heat source parameter ( S ), Prandtl number ( Pr ) and Eckert number ( Ec ) on the flow field are analyzed with the help of figures. The problem has some relevance in the geophysical and astrophysical studies.

Finite element solution of mass transfer effects on unsteady hydromagnetic convective flow past a vertical porous plate in a porous medium with heat source

The objective of this chapter is to analyze the effect of mass transfer on unsteady hydromagnetic free convective flow of a viscous incompressible electrically conducting fluid past an infinite vertical porous plate in presence of constant suction and heat source. The governing equations of the flow field are solved using Galerkin finite element method and approximate solutions are obtained for velocity field, temperature field, concentration distribution, skin friction and the rate of heat and mass transfer. The numerical results for some special cases were compared with Das et al . [7] and were found to be in good agreement. The effects of the flow parameters such as Hartmann number ( M ), Grashof number for heat and mass transfer ( Gr , Gc) , Permeability parameter ( Kp ), Schmidt number ( Sc ), Heat source parameter ( S ), Prandtl number ( Pr ) and Eckert number ( Ec ) on the flow field are analyzed with the help of figures. The problem has some relevance in the geophysical and astrophysical studies.

Transient free convective hydromagnetic flow in an infinite vertical cylinder with Hall current and heat source/sink

AbstractThe analysis of hydromagnetic flow has been a concern of consideration for research scientists and engineers. In this treatise, the unsteady hydromagnetic free convective flow of an incompressible, viscous, and electrically conducting fluid and heat transfer in a vertical cylinder with Hall effects and transverse magnetic field, in the presence of heat source and sink, is studied. Exact solutions of dimensionless unsteady governing equations are obtained by using the Laplace transform technique. Transient fluid velocity and temperature field are depicted by graphs, whereas heat transfer rate, mass flux, and skin‐friction are computed in a tabular form for different physical parametric values, such as the source/sink parameter, Hall current parameter, Prandtl number, and Hartmann number. The valuable result from the investigation is that the Hall parameter slightly accelerates the fluid velocity and it provides resistance to the skin friction at the cylindrical surface. Moreover, it is noticeable that temperature as well as velocity enhances and finally gets to its steady state with time. To be noted, the Hall effects have been widely applied in numerous experimental engineering applications, such as constrictions of turbines, Hall accelerators, Hall sensors.

Effect of heat source/sink on MHD start-up natural convective flow in an annulus with isothermal and isoflux boundaries

This article examines the influence of isothermal and isoflux heating/cooling with heat source/sink on unsteady hydromagnetic-free convective flow of a viscous incompressible fluid in an annulus. The flow is induced by buoyancy forces due to temperature differences as a result of the isothermal heating and constant heat flux applied on the outer surface of the inner cylinder. Our treatment of the governing energy and momentum equation is based on a two-step approach. First, the nonlinear partial differential equations are transformed to the Laplace domain using the Laplace transform method and solved analytically in the Laplace domain. The Laplace domain solution is then inverted back to time domain using a numerical scheme known as Riemann-Sum Approximation (RSA). The derived numerical values by the method of RSA exhibit an excellent conformity with PDEPE and steady-state solutions at large time. The influence of the various dimensionless controlling parameters on the flow formation is depicted graphically and in tabular form.

Magnetohydrodynamic Free Convection Flows with Thermal Memory over a Moving Vertical Plate in Porous Medium

The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux constitutive equation with a weakly memory. The exact solutions for the fractional governing differential equations for fluid temperature, Nusselt number, velocity field, and skin friction are obtained by using the Laplace transform method. The numerical calculations are carried out and the results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with the thermal memory and the ordinary fluid is made. It was observed that due to evolution in the time of the Caputo power-law kernel, the memory effects are stronger for the small values of the time t. Moreover, it is found that the fluid flow is accelerated / retarded by varying the inclination angle of the magnetic field direction.

Unsteady hydromagnetic-free convection flow with suction/injection

This article analyses the unsteady hydromagnetic free convection flow near impulsive as well as accelerated motion of the infinite vertical porous plate. The governing momentum and energy partial differential equations exhibiting the physics of the flow formation are presented. Using suitable dimensionless parameters, the equations are transformed to their corresponding dimensionless form and solved exactly in the Laplace domain using the well-known Laplace transform technique. However, the Riemann-sum approximation method is used to invert the solution from the Laplace domain to time domain due of the complexity of the solutions obtained in the Laplace domain. The effect of various pertinent parameters such as suction/injection, Hartmann number, Grashof number, and Prandtl number is discussed with the aid of line graphs.

Heat and Mass Transfer of Unsteady Hydromagnetic Free Convection Flow Through Porous Medium Past a Vertical Plate with Uniform Surface Heat Flux

AbstractSimultaneous effects of thermal and concentration diffusions in unsteady magnetohydrodynamic free convection flow past a moving plate maintained at constant heat flux and embedded in a viscous fluid saturated porous medium is presented. The transport model employed includes the effects of thermal radiation, heat sink, Soret and chemical reaction. The fluid is considered as a gray absorbing-emitting but non-scattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. The dimensionless coupled linear partial differential equations are solved by using Laplace transform technique. Numerical results for the velocity, temperature, concentration as well as the skin friction coefficient and the rates of heat and mass transfer are shown graphically for different values of physical parameters involved.

Unsteady MHD Free Convective Flow Past an Inclined Parabolic Accelerated Plate with Hall Current, Radiation Effects and Variable Temperature in a Porous Medium

We analyze the effects of hall current and radiation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an inclined parabolic accelerated plate in a porous medium by applying a transverse magnetic field which makes an angle α to the inclined plate.The fluid is assumed to be viscous, incompressible and electrically conducting with a strong magnetic field. Using the modified Ohm’s law and the Bossinesq approximation the governing equations of the problem are reduced to local non-similarity boundary layer equations using suitable transformation.The dimensionless governing equations of flow field are solved numerically by Crank-Nicolson finite difference method for different values of governing flow parameters. The velocity and temperature profiles are shown through graphs.

Effects of Hall current on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate with Newtonian heating

An investigation of unsteady hydromagnetic free convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively moving vertical plate with Newtonian surface heating embedded in a porous medium taking into account the effects of Hall current is carried out. The governing partial differential equations are first subjected to the Laplace transformation and then inverted numerically using INVLAP routine of Matlab. The governing partial differential equations are also solved numerically by the Crank-Nicolson implicit finite difference scheme and a comparison has been provided between the two solutions. The numerical solutions for velocity and temperature are plotted graphically whereas the numerical results of skin friction and the Nusselt number are presented in tabular form for various parameters of interest. The present solution in special case is compared with a previously obtained solution and is found to be in excellent agreement.

Unsteady MHD free convection flow with Hall effect of a radiating and heat absorbing fluid past a moving vertical plate with variable ramped temperature

Abstract Unsteady hydromagnetic free convection flow of a viscous, incompressible, electrically conducting, optically thick radiating and heat absorbing fluid past an accelerated moving vertical plate with variable ramped temperature is investigated. Exact solution of the governing equations for the fluid velocity and fluid temperature are obtained by Laplace transform technique. The numerical values of primary and secondary fluid velocities and fluid temperature are displayed graphically whereas those of shear stress and rate of heat transfer at the plate are presented in tabular form for various values of pertinent flow parameters.

Heat and Mass Transfer Effects on an Unsteady Hydromagnetic Free Convective Flow over an Infinite Vertical Plate Embedded in a Porous Medium with Heat Absorption

An unsteady, two dimensional, hydro magnetic, laminar mixed convective boundary layer flow of an incompressible and electrically conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effects of viscous dissipation and heat absorption. The dimensionless governing equations for this investigation are solved analytically using Galerkin finite element method. Numerical evaluation of the numerical results is performed and the results for velocity, temperature and concentration profiles within the boundary layer are discussed and shown through graphically.

Unsteady MHD Free Convective Flow Past a Moving Vertical Plate with Time Dependent Suction and Chemical Reaction in a Slip Flow Regime

The objective of the present paper is to investigate chemical reaction effect on unsteady hydromagnetic free convection flow of a viscous, incompressible, electrically conducting fluid with heat and mass transfer past a moving porous vertical plate of infinite length with time dependent suction in the presence of heat source in a slip flow regime. Slip flow conditions for the velocity, jump in temperature and jump in concentration are taken into account in the boundary conditions. The governing equations involved in the present analysis are solved by perturbation technique. The velocity, temperature and concentration are studied for different parameters like Prandtl number, velocity ratio parameter, magnetic field parameter, chemical reaction parameter and slip parameter due to jump in concentration. It is inferred from the graphs that the temperature of the plate decreases with increasing the values of the Prandtl number. The concentration is decreased in the presence of chemical reaction and slip parameter due to jump in concentration.

Aligned Magnetic Field, Radiation, and Rotation Effects on Unsteady Hydromagnetic Free Convection Flow Past an Impulsively Moving Vertical Plate in a Porous Medium

We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases.

Radiation and Inclined Magnetic Field Effects on Unsteady Hydromagnetic Free Convection Flow past an Impulsively Moving Vertical Plate in a Porous Medium

We analyse the effects of radiation and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium by applying inclined magnetic field, Under Boussinesq approximation, assuming that the temperature of the plate has a temporarily ramped profile. An exact solution of the governing equations, in dimensionless form is obtained by Laplace transform technique. To compare the results obtained in this case with that of isothermal plate and exact solution of the governing equations are also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases.

Hall effects on hydromagnetic free convection in a heated vertical channel in the presence of an inclined magnetic field and thermal radiation

An analytical study on unsteady hydromagnetic free convective flow of a viscous incompressible electrically conducting fluid in the presence of an inclined magnetic field taking Hall currents into account has been presented. The governing equations are solved analytically using the Laplace transform technique. The variations of the fluid velocity components and the fluid temperature are shown graphically and are discussed. The shear stresses and the rate of heat transfer at the channel plates are derived. The results are shown in figures and tables followed by a quantitative discussion.

Unsteady MHD free convective flow past a semi-infinite vertical wall with induced magnetic field

In this paper, the effect of an induced magnetic field on unsteady hydromagnetic free convective flow of an electrically conducting fluid past a semi-infinite vertical plate is considered. The coupled non-linear partial differential equations in non-dimensional form have been solved by implicit finite difference method of Crank–Nicolson type. The influence of magnetic parameter and magnetic Prandtl number on the velocity, temperature and induced magnetic field at a fixed cross-section, as well as on the skin-friction and Nusselt number on the heated surface, have been shown graphically. It is found that the effect of magnetic parameter is to decrease the velocity, temperature and induced magnetic fields while the effect of magnetic Prandtl number is to increase them.

Effects of Thermal Radiation and Rotation on Unsteady Hydromagnetic Free Convection Flow past an Impulsively Moving Vertical Plate with Ramped Temperature in a Porous Medium

The effects of radiation and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving infinite vertical plate with ramped temperature in a porous medium are investigated. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. To compare the results obtained in this case with that of isothermal plate, exact solution of the governing equations is also obtained for isothermal plate. The expressions for the primary and secondary skin frictions and Nusselt number are also derived. It is noticed that, for both ramped temperature and isothermal plates, rotation retards fluid flow in the primary flow direction whereas it accelerates fluid flow in the secondary flow direction in the boundary layer region while radiation exerts accelerating influence on the fluid flow in both the primary and secondary flow directions. For ramped temperature plate radiation reduces primary skin friction whereas it tends to increase secondary skin friction. For isothermal plate radiation has tendency to reduce secondary skin friction. Radiation tends to increase fluid temperature for both ramped temperature and isothermal plates. With the increase in time the rate of heat transfer at the plate is reduced for isothermal plate while it is increased for ramped temperature plate.