Unsteady Free Convection Research Articles

SORET AND DUFOUR EFFECTS ON UNSTEADY MHD FREE CONVECTIVE FLOW OF MICROPOLAR FLUID WITH OSCILLATORY PLATE VELOCITY CONSIDERING VISCOUS DISSIPATION EFFECTS

The present paper deals with the study of micropolar fluid flow of an unsteady incompressible free convection heat and mass transfer flow past a semi-infinite vertical plate fixed firmly in porous medium with the influence of heat absorption, viscous dissipation, Soret, Dufour and chemical reaction has been analyzed. The governing partial differential equations are transformed into a set of coupled partial differential equations using suitable dimensionless quantities. The resulting non-dimensional boundary value problem is solved by the Galerkin finite element method. The effects of different pertinent parameters on translation velocity, microrotation, temperature and concentration distributions along boundary layer have been represented with the help of graphs. Under special case, comparison of the Skin friction, Wall couple stress, Nusselt number and Sherwood number are made with the Numerical results available from the literature obtained through analytical approach and found to be in good agreement.

Perturbation analysis of unsteady boundary layer slip flow and heat transfer of Casson fluid past a vertical permeable plate with Hall current

The current study focuses on the effect of Hall current on an unsteady free convection slip flow of a Casson fluid past an infinite vertical permeable plate in presence of variable suction. The non-linear coupled partial differential equations of the momentum and energy, which control the flow field, are converted into a system of ordinary differential equations using perturbation technique. The resulting equations are solved analytically with the objective of getting non-dimensional velocity and temperature fields. The study has also presented graphically the velocity and temperature profiles for different values of the parameters entering into the problem. Skin friction coefficient and Nusselt number which are of physical interest are sorted out and presented in the form of graphics.

Exact and numerical solutions for unsteady heat and mass transfer problem of Jeffrey fluid with MHD and Newtonian heating effects

The combined heat and mass transfer of unsteady magnetohydrodynamic free convection flow of Jeffrey fluid past an oscillating vertical plate generated by thermal radiation and Newtonian heating is investigated. The incompressible fluid is electrically conducting in the presence of a uniform magnetic field which acts in a direction perpendicular to the flow. Mathematical formulation of the problem is modeled in terms of partial differential equations with some physical conditions. Some suitable non-dimensional variables are introduced to transform the system of equations. The dimensionless governing equations are solved analytically for exact solutions using the Laplace transform technique. Numerical solutions of velocity are obtained via finite difference scheme. Graphical results for velocity, temperature and concentration fields for various pertinent parameters such as material parameter of Jeffrey fluid \(\lambda_{1}\), dimensionless parameter of Jeffrey fluid \(\lambda\), Newtonian heating parameter \(\xi\), phase angle \(\omega t\), Grashof number \(Gr\), modified Grashof number \(Gm\), Hartmann number or magnetic parameter \(Ha\), Prandtl number \(Pr\), radiation parameter \(Rd\), Schimdt number \(Sc\) and dimensionless time \(t\) are displayed and discussed in detail. This study showed that the magnetic field resists the fluid flow due to the Lorentz force, whereas the thermal radiation and Newtonian heating parameters lead to the enhancement of velocity and temperature fields. Present results are also compared with the existing published work, and an excellent agreement is found.

Exact Solution of Unsteady MHD Free Convective Chemically Reacting Visco-Elastic Fluid Flow Past a Moving Vertical Plate Through Porous Medium

The influence of radiation on the unsteady MHD free convection Viscoelastic fluid flow past an exponentially accelerated moving vertical plate through porous medium with chemical reaction is investigated theoretically. The fluid considered here is a gray, absorbing-emitting radiation but non-scattering medium, and the Boussinesq’s approximation is considered for pressure gradient in momentum equation and Taylor’s series expansion to describe the radiative heat flux in the energy equation. The dimensionless governing partial differential equations are solved using Laplace transform technique. They satisfy all imposed initial and boundary conditions and for $$S\rightarrow 0$$ can be reduce to the similar solutions for Newtonian fluids. The corresponding expressions for skin friction, Nusselt number and Sherwood number also evaluated. Numerical results for velocity, temperature and concentration are shown graphically. This study is of fundamental importance and frequently arises in many practical situations such as chemical engineering and polymer extrusion processes. The effect of different parameters like thermal radiation parameter, visco-elastic parameter, chemical reaction parameter, magnetic field parameter, permeability parameter, Schmidt number and Prandtl number are discussed. It is observed that the momentum and thermal boundary layer thickness decreases owing to an increase in the value of the radiation parameter. An increase in the Prandtl number is found to decrease the velocity and temperature but increasing in Nusselt number for air and water.

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

This paper presents an analytical solution of unsteady one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless coupled linear governing partial differential equations are solved by Laplace transform technique for unit Prandtl number and Schmidt number. Effects of various physical parameters are presented with graphs. Numerical values of boundary layer thickness for different parameters are presented in table. Due to the effects of thermal and mass stratifications, the velocity, temperature, and skin friction, Nusselt number shows oscillatory behaviour at smaller times and then reaches steady state at larger times.

Unsteady Hydromagnetic Natural Convection Flow Past an Oscillating Vertical Surface with Hall Effect and Convective Boundary Condition

The aim of this paper is to analyze the effect of Hall current on unsteady MHD free convection flow of a viscous, incompressible and electrically conducting fluid past an oscillating vertical plate with convective boundary condition. The fluid flow is due to both the oscillation and the convective heating of the plate. The resulting governing equations are nondimensionalized and solved analytically using the Laplace transform technique. Numerical results for axial and transverse velocities and temperature as well as the skin-friction coefficient and Nusselt number are shown graphically for various values of pertinent flow parameters.

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 arbitrary shear stress on unsteady free convection flow of Casson fluid past a vertical plate

This article studies the unsteady free flow of a Casson fluid over an infinite vertical plate with constant wall temperature. The Problem is modelled by employing equations of continuity, momentum and energy. Exact solutions for the dimensionless velocity and temperature are established by the Laplace transform technique. The solutions that have been obtained, uncommon in the literature, satisfy all imposed initial and boundary conditions and can generate huge number of solutions for any motion problem with technical relevance of this type. For illustration, some special cases are considered. The velocity solutions are presented as a sum of convective and mechanical parts. Pertinent results are discussed and displayed graphically.

Effects of Soret, Dufour, Variable Viscosity and Variable Thermal Conductivity on Unsteady Free Convective Flow Past a Vertical Cone

Effects of Soret, Dufour, Variable Viscosity and Variable Thermal Conductivity on Unsteady Free Convective Flow Past a Vertical Cone

Magneto-hydrodynamic free convection flows of a viscoelastic fluid in porous medium with variable permeability heat source and chemical reaction

Abstract The unsteady free convection flow, with heat and mass transfer, of an electrically conducting viscoelastic fluid, through a porous medium of variable permeability is investigated. The flow domain is a half space, bounded by a vertical porous plate, with the constant heat flux, constant concentration and a rectilinear translation in its plane with constant velocity. The applied magnetic field of uniform strength is perpendicular to the plate and the magnetic lines of force are fixed relative to plate or, to fluid. Permeability of the porous medium decreases exponentially, with respect to time t, relative to a constant mean value. The closed forms of the temperature, concentration and velocity fields are determined by means of the Laplace transform and method of separation of variables. Numerical calculations are carried out and graphically displayed in order to study the effects of several parameters such as Hartmann number, permeability of porous medium, Prandtl number, heat source/sink parameter, Schmidt number, chemical reaction parameter. The numerical results show that, if the applied magnetic field is fixed to the plate the fluid flows more slowly than if the magnetic field is fixed to fluid. If the magnetic field strength is high, the fluid moves more slowly than into weak magnetic fields.

Unsteady free convection flow of a micropolar fluid with Newtonian heating: Closed form solution

This article investigates the unsteady free convection flow of a micropolar fluid over a vertical plate oscillating in its own plane with Newtonian heating condition. The problem is modelled in terms of partial differential equations with some physical conditions. Closed form solutions in terms of exponential and complementary error functions of Gauss are obtained by using the Laplace transform technique. They satisfy the governing equations and impose boundary and initial conditions. The present solution in the absence of microrotation reduces to well-known solutions of Newtonian fluid. Graphs are plotted to study the effects of various physical parameters on velocity and microrotation. Numerical results for skin friction and wall couple stress is computed in tables. Apart from the engineering point of view, the present article has strong advantage over the published literature as the exact solutions obtained here can be used as a benchmark for comparison with numerical/ approximate solutions and experimental data.

Analysis of heat transfer for unsteady MHD free convection flow of rotating Jeffrey nanofluid saturated in a porous medium

In this article, the influence of thermal radiation on unsteady magnetohydrodynamics (MHD) free convection flow of rotating Jeffrey nanofluid passing through a porous medium is studied. The silver nanoparticles (AgNPs) are dispersed in the Kerosene Oil (KO) which is chosen as conventional base fluid. Appropriate dimensionless variables are used and the system of equations is transformed into dimensionless form. The resulting problem is solved using the Laplace transform technique. The impact of pertinent parameters including volume fraction φ, material parameters of Jeffrey fluid λ1, λ, rotation parameter r, Hartmann number Ha, permeability parameter K, Grashof number Gr, Prandtl number Pr, radiation parameter Rd and dimensionless time t on velocity and temperature profiles are presented graphically with comprehensive discussions. It is observed that, the rotation parameter, due to the Coriolis force, tends to decrease the primary velocity but reverse effect is observed in the secondary velocity. It is also observed that, the Lorentz force retards the fluid flow for both primary and secondary velocities. The expressions for skin friction and Nusselt number are also evaluated for different values of emerging parameters. A comparative study with the existing published work is provided in order to verify the present results. An excellent agreement is found.

Numerical Treatment of Casson Fluid Free Convective Flow Past An Infinite Vertical Plate Filled in Magnetic Field in Presence Of Thermal Radiation: A Finite Element Technique

The combined effects of hall current, thermal radiation on an unsteady MHD free convection casson fluid flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical plate are investigated in presence of heat transfer. Numerical solutions of the non-linear coupled governing equations is obtained by finite element technique. The expressions for primary fluid velocity, secondary fluid velocity and fluid temperature, skin friction due to primary and secondary velocity fields and rate of heat transfer coefficient due to temperature at the plate are obtained and discussed with the help of different material parameters like Grashof number for heat transfer, Casson fluid parameter, Magnetic field parameter, hall parameter, thermal radiation parameter, Prandtl number. Finally, it is seen that the numerical results of the present study conform very well to those of previous studies reported in available scientific literatures.

Time-dependent hydromagnetic free convection nanofluid flows within a wavy trapezoidal enclosure

This paper considers unsteady MHD free convection flows of alumina (Al2O3)-water and single-walled carbon nanotube (SWCNT)-water nanofluids within a symmetrical wavy trapezoidal enclosure. Initially, the fluid within the enclosure has a constant cold temperature and is at rest. The temperature of the wavy bottom wall is suddenly raised to a constant hot temperature, while the top wall is thermally insulated. The temperature of the side walls is maintained at the initial cold temperature. The dimensionless governing equations with the corresponding initial and boundary conditions are solved using the mixed finite element method with polynomial pressure projection stabilization. The effects of Rayleigh number Ra and Hartmann number Ha on the nanofluid flow and heat transfer are investigated.

Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil

The basic idea of nanofluid was to enhance the thermal conductivity of base fluid. However, the classical nanofluid models have some drastic limitations, i.e. they cannot describe a class of fluids that have certain microscopic characters arising from the microrotation and local structure of the fluid elements. Therefore, the present work is one of the infrequent contributions that describes the microrotation and microinertia characteristics of nanofluids. More exactly, in this work, the unsteady free convection flow of micropolar nanofluids is investigated over a vertical plate. Five types of oxide nanoparticles namely copper oxide, titanium oxide, alumina oxide, iron oxide and graphene oxide are suspended in three different types of fluids such as water, kerosene and engine oil. Exact solutions of the governing problem are obtained by the Laplace transform method. Solutions for conventional or regular nanofluid is also recovered as a special case. Temperature of graphene oxide suspended micropolar nanofluid is higher than other oxide nanoparticles based nanofluids.

Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation.

BackgroundNon-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature.MethodsThe governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t ), the Grashof number (Gr), the Prandtl number (Pr ), and the phase angle (omega t). Skin friction and the Nusselt number are also evaluated.ResultsThe exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver–Stehfest algorithm.ConclusionThe interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number (Pr ), and the phase angle (omega t).

Unsteady free convection flow past a periodically accelerated vertical plate with Newtonian heating

Purpose The purpose of this paper is to present an analytical study for a problem of unsteady free convection boundary layer flow past a periodically accelerated vertical plate with Newtonian heating (NH). Design/methodology/approach The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expressions for skin friction, Nusselt number and Sherwood number are also derived and discussed numerically. Findings It is observed that velocity, concentration and skin friction decrease with the increasing values of Sc whereas temperature distribution decreases in the increase in Pr in the presence of NH. Research limitations/implications This study is limited to a Newtonian fluid. This can be extended for non-Newtonian fluids. Practical implications Heat and mass transfer frequently occurs in chemically processed industries, distribution of temperature and moisture over agricultural fields, dispersion of fog and environment pollution and polymer production. Social implications Free convection flow of coupled heat and mass transfer occurs due to the temperature and concentration differences in the fluid as a result of driving forces. For example, in atmospheric flows, thermal convection resulting from heating of the earth by sunlight is affected differences in water vapor concentration. Originality/value The authors have studied heat and mass transfer effects on unsteady free convection boundary layer flow past a periodically accelerated vertical surface with NH, where the heat transfer rate from the bounding surface with a finite heat capacity is proportional to the local surface temperature, and which is usually termed as conjugate convective flow. The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expression for skin friction also derived and discussed.

English

English

Unsteady MHD Free Convection and Mass Transfer Flow Through a Vertical Oscillatory Porous Plate in a Rotating Porous Medium with Hall, Ion-slip Currents and Heat Source

The analytical solution is made on the unsteady flow of an electrically conducting viscous incompressible fluid bounded by an infinite vertical porous plate. The plate executes harmonic oscillation at a frequency n in its own plane. The governing equations of the problem contain coupled partial differential equations. The dimensionless equations are solved analytically using perturbation technique. The effect of various parameters of the problem on the velocity, temperature and concentration field within the boundary layer are discussed and shown graphically.
 Dhaka Univ. J. Sci. 64(2): 91-98, 2016 (July)

Heat and Mass Transfer in Unsteady MHD Casson Fluid Flow with Convective Boundary Conditions

Through this paper, we investigated the unsteady free convection flow of a Casson fluid bounded by a moving vertical flat plate in a rotating system with convective boundary conditions. The governing equations of the flow have been solved analytically using perturbation technique. The effects of various non-dimensional governing parameters like Casson parameter, magnetic field parameter, thermal diffusion parameter, chemical reaction parameter and thermal radiation parameter on velocity, temperature and concentration profiles are discussed and presented through graphs. We also evaluated the friction factor, Nusselt and Sherwood numbers and presented numerically. Through this study it is found that the Casson parameter controls the velocity profiles and Soret number have tendency to enhance the both velocity and concentration fields.