Unsteady MHD Free Convection Flow Research Articles

Unsteady MHD Free Convection Flow of Fluid in Micro Channel in the Presence of Viscous Dissipation Between Vertical Parallel Two Walls

Convection is a process by which heat is transferred by movement of a heated water. The phenomenon where heat transfer process is driven by natural fluid motion due to temperature and density gradients is called free convection. The effect of slip velocity on thermal behaviours of MHD free convection flow over a vertical parallel two walls is the focus of this research. The mathematical equations which described the phenomenom includes momentum, magnetic field and energy equations. Condition for the existence and uniqueness of solution of the model equations were established using the approach of Lipschitz continuity. The model equations in dimensionless form were solved using Olayiwola’s generalized polynomial approximation method (OGPAM). The results obtained which contains the dimensionless parameters were presented graphically and discussed. It was observed that increase in Reynolds number and Knudsen number both enhanced the velocity distribution at the two walls. Also, magnetic field and temperature field were enhanced by magnetic prandtl number and Eckert number respectively.

Unsteady MHD Free Convection Flow of a Second Grade Casson Fluid with Ramped Wall Temperature

The present study delves into the analysis of unsteady free convection flow involving a non-Newtonian Casson fluid adjacent to an infinitely tall vertical plate. The primary objective of this article is to examine the flow behaviour of a second-grade Casson fluid under varying critical parameters. The plate exhibits a gradual increase in wall temperature and is situated within a porous medium. The governing equations are transformed into a dimensionless form, using non dimensionless variables. The method of Laplace transform (MOLT) is employed to derive accurate solutions for the temperature and velocity within the flow field. To enhance comprehension of the issue, The impact of different physical parameters on the flow field has been examined through the utilization of graphs and tables. Outcome of the problem was compared with existing one which was in good agreement. The study revealed that the velocity magnitude was lower in the scenario with ramped temperature compared to the scenario with isothermal temperature. Finally, skin friction and Nusselt numbers of the present work are tabulated. The significant outcome of the present work is that the flow field for the present phenomena is same as that of the existing one in absence of radiation parameter and heat source parameter when, u(0,t)=0, β=∞.

Darcy-Forchheimer flow of MHD free convective CNTs Casson nanoliquid via a cosinusoidally fluctuating heated plate

ABSTRACT This study explores the influence of carbon nanotubes (CNTs), spanwise cosinusoidally fluctuating thermal and mass diffusion on unsteady MHD free convective flow of Casson nanoliquid via an infinite hot vertical porous plate in a Darcy-Forchheimer porous medium. The overlapping grid multi-domain trivariate spectral collocation method is used to solve the non-dimensional equations. The impact of varying physical estimators on profiles alongside skin friction factor, rate of heat, and mass transport is contemplated. It was disclosed that the velocity and skin friction factors can be maximized via strong buoyancy forces and porous permeability but minimized through strong magnetic field and the Darcy–Forchheimer relation. The temperature and rate of heat transport can be increased by higher levels of heat generation, viscous dissipation, diffusion-thermo, and radiation absorption. Conversely, these factors can be minimized with higher thermal radiation. The introduction of activation energy and nonlinear chemically reactive species is responsible for the increase in species concentration and the rate of mass transport. The velocity and temperature are enhanced with increasing CNTs volume fraction, which leads to an increment in skin friction factor and thermal transport rate. Therefore, the suspension of CNTs in conventional fluids to control the coolant level in industrial apparatuses is absolutely practical.

The Effect of Chemical Reaction on an Unsteady MHD Free Convective Flow Through Porous Medium with Hall Current

In this paper we investigate the effects of Chemical Reaction, Hall currents, Soret and Dufour on unsteady MHD free convective flow through porous medium in the presence of a magnetic field and first order chemical reaction. The similarity solutions were obtained using suitable transformations and the resulting similarity ordinary differential equations were solved by finite difference method. A parametric study illustrating the influence of different flow parameters on velocity, temperature and concentration fields are investigated. The skin frictions at the plate due to tangential and lateral velocity fields are obtained in non-dimensional form. The effects of the various physical parameters on these fields are discussed with help of tables and graphs.

The effects of thermal radiation, internal heat generation (absorption) on unsteady MHD free convection flow about a truncated cone in presence of pressure work

The aim of present paper is to analyse the effect of radiation, internal heat generation (absorption) on unsteady laminar natural convective boundary layer flow over a truncated cone considering pressure work and magnetic field due to the variation in fluid flow behavior in various physical conditions. Suitable transformation is used to form system of coupled non linear partial differential equations is to governing the flow and heat transfer. These equations have been solved numerically by using an implicit finite difference scheme along with quasilinearization technique. According to numerical findings, the pressure work, internal heat generation (absorption), radiation, and magnetic field have a significant impact on both skin friction and heat transfer. Further, skin friction is found to decrease 12.13%, 30.3% and 41.67% for various values (from 0.0 to 0.5) of pressure work, magnetic field and heat generation (absorption) alongside the cone surface whereas heat transfer rate rises 17.19%, 17.65% and 73.51% respectively due to unsteadiness in the flow. It is observed that the thickness of boundary layer enhances for various values (from 0.0 to 0.5) of heat generation and radiation parameter but diminishes for pressure work and Prandtl number.

Induced by heat source on unsteady MHD free convective flow of Casson fluid past a vertically oscillating plate through porous medium utilizing finite difference method

In this research, the unsteady MHD flow of a Casson fluid past a vertical plate that oscillates while maintaining a constant wall temperature and the heat source is the subject of this article. The fluid is electrically conductive and moves through a porous media. Partial differential equations with initial and boundary conditions are used to model this phenomenon. There are a few appropriate non-dimensional variables introduced. Using the finite difference method(FDM), the consistent dimensionless equations with circumstances are resolved. The energy and velocity equations are solved precisely. Expressions for Nusselt number and skin friction are also assessed. The outcomes of computations are analyzed for newly developing flow parameters. Additionally, skin friction and the Nusselt number effects are explained using table values. Furthermore, increasing the heat source parameter causes a rise in temperature and velocity.

Heat Transfer of Casson Fluid in Poiseuille Flow of Carbon Nanotubes: A Power Series Approach

Combination of Carbon Nanotubes (CNTs) with Human blood as base fluid indicates the enhancement of heat transport in Poiseuille flow and this physical phenomenon could not possible in normal liquids. Usually, when blood cells get touch with external surfaces, the platelets of blood become activated and form blood clots. Therefore, we have considered blood compatible CNT, so that chosen base fluid (blood) can easily pass through it. Due to the higher thermal conductivity, CNTs play an important role to enhance the heat transport in blood flow. These features lead to the novelty of this investigation to study the heat transport of Casson fluid through CNTs in unsteady MHD free convective Poiseuille flow with thermal radiation. Such study consigns practical applications in manufacturing of drugs, biomedical and Tissue engineering, biosensor and other applications in myocardial therapy, neuronal and muscle regeneration. The non-dimensional governing equations are formulated and solved analytically through classical Perturbation Technique and the analysis of results are drawn in smooth curves via MATLAB code. Significant results for different implanted parameters are compared between SWCNT and MWCNT and their significant behaviours are plotted graphically. The obtained results indicate that Casson parameter accelerates the flow velocity for MWCNT and SWCNT. Furthermore, interesting behavior on the outlines of velocity for SWCNT and MWCNT due to the presence of Schmidt number, Peclet number and Reynolds number are detected. Comparison with previously published work has been inspected and originated excellent agreement.

The effects of thermal radiation on unsteady MHD free convective flow through the porous medium between two vertical plates with Hall effects

AbstractThe effects of thermal radiation and Hall current on magnetohydrodynamic free convection three‐dimensional flow in a vertical channel filled with a porous medium have been studied. We consider an incompressible viscous and electrically conducting incompressible viscous fluid in a parallel plate channel bounded by a loosely packed porous medium. The fluid is driven by a uniform pressure gradient parallel to the channel plates, and the entire flow field is subjected to a uniform inclined magnetic field of strength inclined at an angle of inclination with the normal to the boundaries in the transverse xy‐plane. The temperature of one of the plates varies periodically, and the temperature difference between the plates is high enough to induce radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, the temperature field, and the rate of heat transfer in terms of their amplitude and phase angles are shown graphically.

Soret effect on an unsteady MHD free convective flow past an infinite vertical plate with constant suction

The present study aims to numerically investigate the impact of flow parameters on an unsteady MHD free convective flow past an infinite vertical plate with constant suction. Specifically, the study considers the Thermo diffusion (Soret effect) on a moving infinite vertical plate with variable temperature and mass diffusion. the thermal diffusion, isthe tendency of a convection-free mixture to separate under a temperature gradient.Given the significance of suction in fields such as aerodynamics and space science, this study is motivated by the need to investigate the problem of combined heat and mass transfer of an unsteady MHD flow past an infinite plate with suction. The finite element method is used to solve the dimensionless governing equations of the problem, and numerical solutions for velocity, temperature, and concentration are obtained for various parameters including Grashoff number, mass Grashoff number, Prandtl number, Schmidt number, and Soret number. The results are presented in graphical form to observe the effect of the parameters on the problem under investigation, and the stability and convergence of the finite element method is established.

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.

Viscous dissipation and radiation absorption effects on unsteady MHD free convective fluid flow past an inclined porous plate with chemical reaction

AbstractThe current scrutinization concentrated on the consequences of viscous dissipation and chemical reaction on unsteady MHD two‐dimensional free convective fluid flow past a semi‐infinite inclined permeable plate with radiation absorption and heat generation. The governing equations are determined analytically by employing the perturbation technique. The impact of various physical estimators on velocity, temperature, concentration, skin friction, and Nusselt number along with Sherwood number were exemplified quantitatively through graphs. It was concluded that velocity declined with the incremental values of Eckert number, but contradictory impact occurred in the case of skin friction. In addition temperature, Nusselt number, as well as velocity, declined with the progressive values of radiation absorption. However, skin friction was accelerated with the augmented values of radiation absorption. Velocity accelerated, with the progressive values of angle of inclination. Concentration declined with the various augmentation values of chemical reaction as well as Schmidt number.

Chemical reaction, heat absorption and Newtonian heating on MHD free convective Casson hybrid nanofluids past an infinite oscillating vertical porous plate

The numerical investigation of Newtonian heating effect on unsteady MHD free convective flow of radiating and chemically reacting Casson hybrid nanofluid past an infinite oscillating vertical plate embedded in a porous medium is conducted by considering the effects of heat sink and viscous dissipation. The fluid motion is persuaded due to the periodic oscillations of the plate along its length. First order consistent chemical reaction and heat absorption are also regarded. The Silver and Titania nano-particles are disseminated in base fluid water and ethylene glycol combination to be formed hybrid nanofluid. This phenomenon is represented as non-linear partial differential equations with initial and boundary conditions. By introducing suitable non-dimensional variable and parameters, the governing equation with initial and boundary conditions are converted into dimensionless form, which are then solved numerically using a finite difference method. It is considered as the values of Hartmann parameter 0 < M ≤ 2; the values of the penetrability parameter are 0 < K ≤ 3; Casson fluid parameter 0 < α < 4; thermal Grashof number 0 < Gr ≤ 20, mass Grashof number 0 < Gm ≤ 12; heat source parameter 0 < Q ≤ 8; the values of ϕ1 and ϕ2 volume fractions of Ag and TiO2 are 0.01, 0.05, 0.1 and 0.15; the Schmidt number as Sc = 0.22, 0.3, 0.6, 0.78 this analogous to hydrogen, helium, water vapours, as well as ammonia respectively; chemical reaction parameter 0 < Kc ≤ 4. The effects of several pertinent parameters on the velocity, temperature and concentration are displayed graphically whilst the effects of these parameters on the skin friction, Nusselt and Sherwood numbers are exhibited in tabular format and then discussed in detail. The velocity distribution is enhanced with increasing in permeability parameter, Newtonian heating parameter and thermal Grashof number whereas it is reduced with increasing Hartmann number, heat absorption parameter and Casson fluid parameter. Heat transport participates the significant role during the managing and dispensation of Casson fluids. This is of immense significance in numerous engineering applications, they are, transpiration cooling, termite welding, drag reduction as well as heat recovery of oils. In addition, this plays the enlargement of bio-convection prototypes produced by the populations of gravitactic microorganism in the porous media.

Significance of Casson dissipative fluid and spanwise cosinusoidally fluctuating temperature on unsteady MHD free convective flow past a hot vertical permeable plate with radiation absorption and chemical reaction

AbstractThe current analysis concentrated on the consequence of Casson dissipative fluid and spanwise consinusoidally fluctuation temperature on unsteady magnetohydrodynamics free convective flow past a moving hot vertical permeable plate with heat generation, radiation absorption, and chemical reaction. It has imperative practical applications in plentiful fields like physiological processes, biomedical science, food processing, pharmaceutical, chemical material processing engineering, manufacturing systems, and so on. The governing partial differential equations are evaluated analytically by employing a multiple regular perturbation method. The influence of assortment physical estimators on fluid velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number was illustrated quantitatively through graphs. Eventually, it was revealed that velocity, concentration, and Sherwood number declined with the progressive values of the chemical reaction parameter. Velocity and temperature were enhanced with incremental values of Prandtl number, while the contradictory impact occurred in Nusselt number and skin friction. Meanwhile, velocity and skin friction lessened with the incremental values of the magnetic parameter and Casson fluid parameter.

Unsteady MHD free convection flow of an exothermic fluid in a convectively heated vertical channel filled with porous medium

Utilizing porous media in a new mathematical model to improve convective heat transfer characteristics in a variety of applications, such as radiation nuclear disposal storing, evaporation cooling, sieving, geological extraction, crude petroleum refining, and building heating and cooling, is becoming increasingly important. This study proposed a numerical analysis of the unsteady magnetohydrodynamic free convection flow of an exothermic fluid with Newtonian heating. This discovery reveals two types of solutions: steady state and unsteady state. After transforming the governing equation from dimensional form to dimensionless form, the steady state governing equation was solved by the Homotopy Perturbation Method. However, the implicit finite difference approach is used to solve the time-dependent governing equations numerically. The impact of various emerging parameters, namely the Hartmann number, Boit number, Darcy number, Navier slip parameter, and the Frank-Kamenetskii parameter, was discussed and graphically analyzed. During the computations and analysis, it was discovered that a minor rise in the Hartman number results in the Lorentz force, which streamlines the momentum barrier layer and hence slows the fluid flow. The fluid velocity, on the other hand, rose as the porous medium, thermal Biot number, slip parameter, and temperature field increased as the viscous reactive fluid parameter and Newtonian heating increased. The skin friction and Nusselt number were also examined and reported. By comparing the finding to an existing work, a great agreement was revealed.

Unsteady MHD free convective flow past a moving vertical plate in a porous medium with radiation and chemical reaction including arbitrary thermal and solutal ramped condition

AbstractThe motive behind this investigation is to examine the unsteady magnetohydrodynamics free convective fluid flow with heat and mass transfer of a viscous, incompressible flow past a moving upright plate in a porous medium with radiation, chemical reaction, arbitrary thermal, and solutal ramped condition. An analytical solution for momentum, energy, and concentration equations is accomplished by implementing the Laplace transformation technique. The influence of different nondimensional parameters on fluid velocity, temperature, and concentration along with skin friction and rate of heat transfer as well as mass transfer at the plate are exhibited graphically. It can be spotted that both the concentration and temperature field decrease for rising values of the ramped parameter, radiation parameter, chemical reaction parameter, and Schmidt number. Moreover, it is detected that the fluid velocity drops in the case of the isothermal plate, and velocity upsurges for the ramped plate temperature. Investigation simulates that the rate of heat transfer, as well as rate of mass transfer, is escalated on hiking radiation parameter.

Thermal diffusion effect on unsteady MHD free convective flow past a semi-infinite exponentially accelerated vertical plate in a porous medium

The objective of the present work was to obtain an exact solution to the problem of a free convective, radiative, viscous, chemically reacting, heat-absorbing, incompressible, and unsteady magnetohydrodynamic flow past an exponentially accelerated moving vertical plate embedded in a porous medium. The fluid was assumed to be optically thick and nongray. A magnetic field was applied in the transverse direction of the flow. Effects of arbitrary ramped temperature and thermal diffusion were also considered. The Rosseland approximation method was used to describe the radiative heat flux that appears in the energy equation. Analytical solutions of the nondimensional governing equations were obtained by adopting a closed form of the Laplace transformation technique. The influence of various physical parameters on flow and transport characteristics was analyzed with suitable graphs. From the investigation, it was observed that increasing the Soret number increased both the concentration and velocity fields. Increasing the radiation parameter caused an upsurge in the Nusselt number but reduced the Soret number.

Slip Effects on Unsteady MHD Free Convective Flow of Rivlin-Ericksen Fluid in the Presence of Heat Source/Sink

In the present work, an investigation on MHD flow of viscoelastic fluid of Rivlin-Ericksen type across a semi-infinite plate in the presence of heat source/sink under free convection is conducted. The plate is moving with constant velocity subjected to periodic suction along with slip conditions. Further, the free stream velocity is taken of oscillatory in nature. The transport equations governing the flow are solved using perturbation analysis. The solutions obtained for the required fields viz. velocity, temperature, and concentration which characterizes the flow are discussed graphically for varying situational parameters appeared in the flow. The presence of heat source/sink in the vicinity of considered fluid has significant effect on the velocity near the plate. Further, the drag at the plate, Nusselt and Sherwood number, are evaluated for varying situational parameters which are compiled in the tabular format.

Effectiveness of magnetize flow on nanofluid via unsteady natural convection inside an inclined U-shaped cavity with discrete heating

This analysis investigates the unsteady MHD free convection flow and heat transfer in an inclined U-shaped cavity filled with Cu-water nanofluid. Both the right and left walls of the cavity and the internal walls of the cavity are supposed to be adiabatic, while the upper horizontal walls of the cavity are kept at a lower temperature. A heat source is located on the bottom horizontal wall with its position that alters the left vertical wall. The dimensionless governing equations are solved using the Successive Under-Relaxation technique. The investigation is achieved by controlling the impact of a set of pertinent parameters, namely; the size and position of the heat element (B = 0.3–0.6, D = 0.3–0.6), Hartman number (Ha = 0–50), nanoparticle volume fraction (ϕ = 0.0–0.07), heat source generation/ absorption (Q = −4.0–2.0), and aspect ratio (AR = 0.2–0.6). The results show that the mean Nu declines with heat source length and Hartmann number, whereas it augments with dimensionless heat source location. Furthermore, the mean Nu rises in parallel with the solid volume fraction of nanoparticles and decreases with aspect ratio. In addition, the increasing of aspect ratio reduces the convection mode compared to conduction heat transfer.

Quadratic regression analysis of unsteady MHD free convective and radiative–dissipative stagnation flow of hybrid nanofluid over an exponentially stretching surface under porous medium

In this research article, we have analyzed the unsteady MHD free convective stagnation point flow of hybrid nanofluid towards an exponentially stretching surface placed in a uniform porous medium with velocity slip, thermal radiation, Ohmic and viscous dissipations. A convective heating type condition at the surface boundary is incorporated into the system. The base fluid water (H2O) along with alumina (Al2O3) and copper (Cu) nanoparticles is chosen to stimulate the fluid flow. Such flow problem arises in several industrial and engineering processes including aerodynamic heating, polymer processing, etc. By utilizing appropriate similarity transformations, the resulting governing equations along with the boundary conditions are converted into dimensionless forms for numerical computations. For the simulation of transformed highly nonlinear ordinary differential equations, Runge–Kutta–Fehlberg method-based shooting technique is applied. The consequences of physical parameters on velocity and temperature distributions are explored via pictorial representations. The values of the local surface drag coefficient and local Nusselt number for all the implanted parameters are calculated at the boundary and presented through the tables. Further, a regression analysis is performed to estimate the local surface drag coefficient and local Nusselt number and the numerical data are presented in tabular form. Moreover, under some limiting conditions, a comparison of the present results with the available results has also been made and an excellent correlation is observed among the results.

Unsteady MHD free convective flow past a vertical plate: An automated solution approach

The case of unsteady two-dimensional laminar free convection flow over a vertical plate by an incompressible viscous fluid is analysed in the presence of uniform magnetic field perpendicular to the flow. The governing equations in a vector form are transformed into non- dimensional form. Then, the dimensionless equations are solved using automated solution technique which is FEniCS. The effects of magnetic parameter on the velocity and temperature profiles are obtained and discussed in this paper