Unsteady MHD Natural Convection Flow Research Articles

Impacts of chemical reaction, thermal radiation, and heat source/sink on unsteady MHD natural convective flow through an oscillatory infinite vertical plate in porous medium

The main objective of this exploration is to analyze the effects of heat source/sink, chemical reactions, and radiation on the unsteady free convective flow through a porous medium using an infinitely oscillating vertical plate. The Laplace transformation tactics is utilized to solve the governing equations for concentration, energy, and momentum. The simulation results demonstrate that the chemical reaction parameter dwindles both primary and secondary velocities. It has been noted that an upsurge in heat generation (heat source) enhances the temperature field, while a decrease in heat absorption (heat sink) leads to a reduction in the temperature field. Furthermore, the radiation parameter causes a drop in both temperature and velocity patterns. The equation for skin friction is derived and presented graphically, and 3-dimensional surface plots are provided to depict the Nusselt number and Sherwood number. Additionally, graphical illustrations are employed to showcase the influence of various non-dimensional variables on concentration, temperature, and velocity patterns.

Effects of Injection/Suction on Unsteady MHD Natural Convective Radiative Flow of Heat Mass Transfer in a Plumb Frequency

This paper explores the effects of injection/suction on MHD unsteady natural convective radiative flow of heat mass transfer in a plumb frequency. The governing partial differential equations are converted to non- dimensional forms and solved numerically by an efficient, implicit, iterative method of Crank Nicolson. Suction/injection is used to control the fluid flow in the channel, and an exothermic chemical reaction of Arrhenius kinetic is considered. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the velocity, temperature, ad concentration as well as the skin friction factor, surface heat and mass transfer rates have been presented for parametric variations of injection/suction, Grashof number, MHD, Prandtl number and Schmidt number. It is reported that the velocity profile increase as thermal grashof number increases. The temperature profile rises by the influence in increasing values of injection and decreases by increasing values of suction parameter. While concentration profile decreases by the increasing values of chemical reaction in the case of suction and injection. The dependence of the skin friction coefficient, rate of heat transfer and mass transfer on these parameters has been discussed.

Radiative effects on unsteady MHD natural convection flow in an inclined wavy porous cavity using hybrid nanofluid containing a square obstacle

The introduction of hybrid nanofluids is a significant notion in several engineering and industrial applications. It is utilized prominently in diverse engineering applications, such as low-pressure drop, wider absorption range, generator cooling, good thermal conductivity, nuclear system cooling, heat exchangers. The present model describes the unsteady MHD free convection flow in an inclined wavy permeable enclosure using hybrid nanofluid (Aluminum oxide/Copper-water) containing a square obstacle with the effects of radiation and heat generation/ absorption. The flow is buoyancy-driven and is subjected to heat radiation (Rd) and an angled magnetic field that is constant (B0). The left wall of the cavity is partially heated and cooled by the wavy-right wall, while the remaining sides are adiabatic and contain a square solid block. A numerical Finite difference technique is utilized to resolve the governing PDEs formulated in stream function, temperature and nanoparticle volume fraction. The acquired results are validated with previous numerical studies. The parameters number in this study are discussed as the inclination angle 0°⩽α⩽π/2, Dimensionless heat source length (0.2 ≤ B ≤ 0.8), porosity of the porous medium 0.1⩽ε⩽0.9 dimensionless location of the left heater (0.3 ≤ D ≤ 0.7), Heat generation -2⩽Q⩽2, nanoparticles volume fraction (0.01 ≤ φ ≤ 0.02), thermal radiation 0⩽Rd⩽10 and the Hartmann number (0 ≤ Ha ≤ 100). The results show that improving the porosity raises the average Nusselt number; however, the rate of increase is greater at higher heat flux locations. The average Nusselt number grows when the nanoparticle volume fraction raises in Rd. The distribution of isothermal lines is slightly reduced for the higher value of the Hartman number. Natural convective hybrid nanofluid flow in a wavy porous square cavity combined with heat source/sink has a vital role in various engineering and industrial processes such as solar collector electric machinery, creation of constructing shelters and attics.

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.

General Solution for Unsteady MHD Natural Convection Flow with Arbitrary Motion of the Infinite Vertical Plate Embedded in Porous Medium

This article has concentrated on heat transfer analysis in the unsteady MHD natural convection flow of viscous fluid under radiation and uniform heat flux over an infinite vertical plate embedded in a porous medium. Overall solutions are found for temperature as well as velocity by the Laplace transform techniques. In the literature, the solutions that have been achieved are rare, meet with all the initial and boundary conditions imposed, and can make general solutions for any problem with motion with this form’s methodological relevance. Also, few different cases of engineering applications are discussed. Solutions are plotted graphically through the use of the Mathcad software to analyze how the variation is taking place in the physical behavior of the viscous fluid flow with respect to the change in a distinct physical parameter.

Special function form exact solutions for Jeffery fluid: an application of power law kernel

This research note’s objective is to elaborate on the study of the unsteady MHD natural convective flow of the Jeffery fluid with the fractional derivative model. The fluid flow phenomenon happens between two vertical parallel plates immersed in a porous medium. The one plate is moving with the time-dependent velocity U_{0} f(t), while the other is fixed. The mathematical model is presented with the system of the partial differential equation along with physical conditions. Appropriate dimensionless variables are employed in the system of equations, and then this dimensionless model is transformed into the Caputo fractional-order model and solved analytically by the Laplace transform. The exact expressions for velocity and temperature, which satisfy the imposed initial and boundary conditions, are obtained. Memory effects in the fluid are observed which the classical model fails to elaborate. Interesting results are revealed from the investigation of emerging parameters as Grashof number, Prandtl number, relaxation time parameter, Jeffery fluid parameter, Hartmann number, porosity, and fractional parameter. The results are elucidated with the detailed discussion and the assistance of the graphs. For the sake of validation of results, the corresponding solutions for viscous fluids are also obtained and compared with the solutions already existing in the literature.

Unsteady MHD natural convection flow of Casson fluid incorporating thermal radiative flux and heat injection/suction mechanism under variable wall conditions

Unsteady magnetohydrodynamic flow of Casson fluid over an infinite vertical plate is examined under ramped temperature and velocity conditions at the wall. Thermal radiation flux and heat injection/suction terms are also incorporated in the energy equation. The electrically conducting fluid is flowing through a porous material and these phenomena are governed by partial differential equations. After employing some adequate dimensionless variables, the solutions are evaluated by dint of Laplace transform. In addition, the physical contribution of substantial parameters such as Grashof number, radiation parameter, heat injection/suction parameter, porosity parameter, Prandtl number, and magnetic parameter is appropriately elucidated with the aid of graphical and tabular illustrations. The expressions for skin friction and Nusselt number are also derived to observe wall shear stress and rate of heat transfer. A graphical comparison between solutions corresponding to ramped and constant conditions at the wall is also provided. It is observed that graphs of the solutions computed under constant conditions are always superior with respect to graphs of ramped conditions. The magnetic field decelerates the flow, whereas the radiative flux leads to an upsurge in the flow. Furthermore, the shear stress is a decreasing function of the magnetic parameter.

Convection heat mass transfer and MHD flow over a vertical plate with chemical reaction, arbitrary shear stress and exponential heating

The present research article is directed to study the heat and mass transference analysis of an incompressible Newtonian viscous fluid. The unsteady MHD natural convection flow over an infinite vertical plate with time dependent arbitrary shear stresses has been investigated. In heat and mass transfer analysis the chemical molecular diffusivity effects have been studied. Moreover, the infinite vertical plate is subjected to the phenomenon of exponential heating. For this study, we formulated the problem into three governing equations along with their corresponding initial and boundary conditions. The Laplace transform method has been used to gain the exact analytical solutions to the problem. Special cases of the obtained solutions are investigated. It is noticed that some well-known results from the published literature are achieved from these special cases. Finally, different physical parameters’ responses are investigated graphically through Mathcad software.

Soret and Dufour Effects on Unsteady Free Convection Fluid Flow in the Presence of Hall Current and Heat Flux

Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.

Effects of soret, dufour, hall current and rotation on MHD natural convective heat and mass transfer flow past an accelerated vertical plate through a porous medium

This article concentrates on the impact of Hall current, Radiation, Soret, and Dufour on an unsteady MHD Natural convective flow over an infinite vertical plate fixed in a porous media. The entire system is supposed to revolve with an unvarying angular velocity Ω′around the perpendicular to the plate and an unvarying transverse magnetic field is enforced along the normal to the plate which is coordinated in the fluid area. The solution of the non-deimensional governing equations along with the boundary conditions are solved by using effeicient Galerkin Method. The effect of different pertinent flow parameters on velocity, temperature, and concentration distributions and the numerical outcomes are examined and revealed graphically. With the increase of Sorent number the concentration profile increases and reverse trend is observed in the case of Dufour numbers. Comparision done with the recent work on exceptional instances of the problem is acquired and is seen to be in accord.

Unsteady MHD natural convective boundary layer flow and heat transfer over a truncated cone in the presence of pressure work

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Unsteady oscillatory MHD boundary layer flow past a moving plate with mass transfer and binary chemical reaction

In this work, we have studied analytically the heat and mass transfer of unsteady MHD natural convective flow past a motioning plate with binary chemical reaction. The flow surface spontaneously moves with unvaried velocity in the flow direction or opposite under the influence of magnetic field. We studied both frequency-dependent effects and “long-time” effects that would require non-practically long channels to be observed in steady flow. We also explored mathematically the important aspects of reactive fluid flow, especially the residence time flow behaviour, scale-up and scale-down procedures. From the present study, it is seen amongst others that temperature is enhanced as the fluid angular velocity rises which leads to maximum temperature in the body of the liquid. It is discovered that mean velocity decrease with a rise in the species reaction and reaction order. The graphical results representing the governing flow parameters effect were presented and discussed. The flow conditions at the wall were also investigated, presented and described.

Unsteady MHD Natural Convection Flow of Nanofluid in a Cavity Containing Adiabatic Obstacle with Heat Corners

Unsteady natural convection heat transfer of nanofluid within cavities with local heaters occurs in several engineering applications. Therefore, investigation of nanofluid flow and heat transfer processes in such systems has a considerable value for evolution of industry. In the current investigation, unsteady MHD natural convection flow of Cu-water nanofluid and heat transfer behavior in square cavity containing a centered adiabatic square block. The mathematical formulation part for present problem is presented in succeeding section. It has been found the size of the adiabatic obstacle influences the behavior of the nanofluid and conduction becomes dominant when size aspect ratio increases to 0.5. It is also noticed that angle of the applied magnetic field can maximize(minimum)the rate of heat transfer if applied in the stream-wise (normal) direction. The novelty of the present work is to consider cavity containing a centered adiabatic square block as well as unsteady effects in the natural convection of nanofluids.

Unsteady MHD natural convection flow of heat generating/absorbing fluid near a vertical plate with ramped temperature and motion

This work investigates the unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid near an infinite vertical plate with ramped temperature and ramped motion. A unified closed form solution is obtained for the velocity field and skin friction coefficient corresponding to the case when the magnetic field fixed relative to the fluid or the moving boundary. It is assumed that the boundary plate has a ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the supposition of negligible induced magnetic field. Exact solutions of energy and momentum equations are obtained using the Laplace transform techniques. Graphical representations are attained for different values of the Prandtl number, magnetic field and heat sink parameter. Results show that wall ramped temperature and ramped motion tend to decrease fluid temperature, velocity, Nusselt number and skin friction.

Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

Thermal radiation and inclined magnetic field effects on MHD flow past a linearly accelerated inclined plate in a porous medium with variable temperature

AbstractAn analysis of unsteady MHD natural convective flow, transfer of mass, and radiation past linearly accelerated slanted plate inserted in an immersed permeable medium with uniform permeability, variable temperature, and concentration within the sight of a slanted magnetic field has been done. The novelty of the current examination is to analyze the effect of a slanted magnetic field on the flow phenomena with heat source/sink and destructive reaction for linearly accelerated slanted plate. The governing equations have been solved by using Laplace transform strategy. The estimations of flow velocity, concentration, and temperature are exhibited graphically, while local skin friction, mass, and heat transfer rates are put on view in tabular form for different values of relevant stream parameters. It is fascinating to observe that the raise of inclination angle of an applied magnetic field diminishes both velocity profiles and local skin friction.

Unsteady MHD Natural Convective Flow of a Rotating Fluid over an Infinite Vertical Plate due to Oscillatory Movement of the Free-Stream with Hall and Ion-Slip Currents

In the present research study a mathematical analysis has been presented for unsteady MHD natural convective flow of a rotating fluid over an infinite vertical plate immersed in a fluid saturated porous medium with oscillating free-stream. The effects of Hall and ion-slip currents also considered on the fluid flow. The unsteady MHD flow over the vertical plate is induced due to thermal and concentration buoyancy forces and oscillatory movement of the free-stream. The partial differential equations governing the motion for the fluid flow are solved analytically. The effects of various pertinent flow parameters on the fluid velocity, fluid temperature and species concentration are presented in graphical form whereas that on skin friction and rate of heat and mass transfer at the plate are presented in tabular form. An interesting observation recorded from the present analysis that there appears reversal flow in the secondary flow direction due to presence of thermal and/or concentration buoyancy forces. However, in the absence of both reversals flow does not exist in the secondary flow direction. It is also noted that the thickness of momentum boundary layer decreases with rise in frequency of oscillations of the free-stream.

Unsteady MHD Natural Convective Flow of a Rotating Walters’-B Fluid Over an Oscillating Plate with Fluctuating Wall Temperature and Concentration

AbstractIn the present study, unsteady MHD boundary layer flow of a rotating Walters’-B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration taking Hall and ion-slip effects into consideration is discussed. The MHD flow in the rotating fluid system is induced due to the non-torsional oscillations of the plate in its own plane and the buoyancy forces arises from temperature and concentration differences in field of gravity. The partial differential equations governing the fluid motion are solved analytically by using regular perturbation and variable separable methods by assuming very small viscoelastic parameter. Solution for velocity field in the case when natural frequency due to rotation and Hall current is equals to the frequency of oscillations i.e. in the case of resonance is also obtained. In order to note the influences of various system parameters and to discuss the important flow characteristics, the numerical results for fluid velocity in the non-resonance case, temperature and species concentration are computed and depicted graphically versus boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form. An interesting observation recorded that there arises flow reversal in the primary flow direction due to high rotation. When natural frequency is greater than the frequency of oscillations the fluid velocity in the primary flow direction is maximum at the plate whereas incase when natural frequency is smaller than the frequency of oscillations, it is maximum in the neighborhood of the plate.

Influence of viscous dissipation on unsteady MHD natural convective flow of Casson fluid over an oscillating vertical plate via FEM

Abstract In this paper, an unsteady magnetohydrodynamic natural convection, heat transfer, electrically conductive non-Newtonian Casson fluid over an oscillating vertical porous plate taken in to the account with an influence of viscous dissipation. An efficient computational Finite Element Method (FEM) employed to solve non-dimensional boundary layer partial differential equations for velocity and temperature distribution with the influence of emerging dimensionless parameters. Also, the local Skin-friction and local Nusselt number coefficients are obtained and analyzed through graphical and tabular forms. The results shows that increasing of Eckert number leads to increase in the velocity and temperature distribution while decrease in the local Skin-friction and Nusselt number coefficients. An increasing of Casson parameter leads to decrease in the velocity distribution and the local Skin-friction coefficient. Compared the present results with earlier reported studies of analytical solutions of Newtonian and non-Newtonian fluid flow problems. The current results are in excellent agreement with earlier existed results. The velocity and temperature distributions are closure for various mesh (grid) size. Therefore, these computational results are stable and converge. FEM is flexible and simplest method to solve this type of problems in various cases like Newtonian and non-Newtonian fluid flow problems.

Unsteady MHD natural convection flow with exponentially accelerated free-stream past a vertical plate in the presence of hall current and rotation

Investigation of unsteady MHD natural convection flow of an electrically conducting, viscous, incompressible and heat absorbing fluid past an infinite vertical plate through a fluid saturated porous medium with exponentially accelerated free-stream in a rotating system with Hall effects is carried out. Exact solution for fluid temperature and fluid velocity are obtained using Laplace transform technique. Expressions for the shear stresses at the plate due to primary and secondary flows and rate of heat transfer at the plate are also derived. In order to get some physical insight into the flow pattern, asymptotic behavior of the solution for fluid temperature and fluid velocity are analyzed for small as well as large values of time. It is interesting to note that there exists reverse flow in the secondary flow direction due to presence of thermal buoyancy force.