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EN
This computational work explores the heat and mass transfer of copper water nanofluid flowing along an inclined plate with varying surface temperature and concentration in the presence of a magnetic field and radiation through a permeable medium. The dimensionless governing equations are solved numerically using an efficient finite-difference technique, which is fast convergent and unconditionally stable. The findings are reviewed and illustrated through graphs for pertinent parameters.
EN
An analysis is made of heat and mass transfer in a three dimensional flow between two vertical porous plates through a porous medium. Analytical solutions have been obtained using the perturbation technique. The effect of non-dimensional parameters on velocity, temperature and concentration field are shown graphically. It is seen that the main flow velocity decreases with an increase in both the radiation parameter and Schmidt number but increases with an increase in the thermal Grashoff number, mass Grashoff number as well as the permeability parameter. Variations of the shear stress at the left plate are given in a tabular form. It is seen that the shear stress due to the primary flow at the left plate increases with an increase in the Reynolds number but decrease with an increase in the Schmidt number. With the increase of both the radiation parameter and Reynolds number the temperature decreases. The concentration field also decreases with an increase of the Schmidt number. Variations of mass flux at the left plate are given in tabular form. It is seen that the mass flux at the left plate increases with increase in both Schmidt number or Reynolds number.
EN
This work studies the simultaneous effects of helical force, rotation and porosity on the appearance of stationary convection in a binary mixture of a ferrofluid and on the size of convection cells. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. The effect of each parameter on the system is studied. The consideration of the simultaneous effect of the basic characteristics made it possible to determine the evolution of the convection threshold in the ferrofluid and then the size of convection cells. The analyzes of the various results obtained allowed us to deduce whether the convection sets in quickly or with a delay when the various effects taken into account in the study are considered simultaneously.
EN
The onset of stationary convection in thermal instability of porous layer saturating a Jeffrey nanofluid is studied. The behaviour of nanofluid is described by a Jeffrey fluid model and the porous layer is assumed to follow Darcy’s law. Due to the presence of the Jeffrey parameter and nanoparticles, the momentum-balance equation of fluid is modified. The linear stability analysis and normal modes analysis method are utilised to derive the dispersion relation for the Rayleigh number in terms of various parameters for free-free boundaries. The effects of the Jeffrey parameter, Lewis number, modified diffusivity ratio, nanoparticles’ Rayleigh number and medium porosity on the physical system are discussed analytically and graphically.
EN
The mathematical model of heat generation and dissipation during thermal energy transmission employing nanoparticles in a Newtonian medium is investigated. Dimensionless boundary layer equations with correlations for titanium dioxide, copper oxide, and aluminium oxide are solved by the finite element method. Parameters are varied to analyze their impact on the flow fields. Various numerical experiments are performed consecutively to explore the phenomenon of thermal performance of the combination fluid. A remarkable enhancement in thermal performance is noticed when solid structures are dispersed in the working fluid. The Biot number determines the convective nature of the boundary. When the Biot number is increased, the fluid temperature decreases significantly. Among copper oxide, aluminium oxide, and titanium oxide nanoparticles, copper oxide nanoparticles are found to be the most effective thermal enhancers.
EN
In this paper, the effects of rotation on a Jeffery nanofluid flow in a porous medium which is heated from below is studied. Darcy model is employed for porous medium and the Jeffrey fluid model is used as a base fluid. The Navier-Stokes equations of motion of fluid are modified under the influence of the Jeffrey parameter, naoparticles and rotation. The basic perturbation technique based on normal modes is applied to derive the dispersion relation for a Rayleigh number. The effects of the Taylor number, Jeffrey parameter, Lewis number, modified diffusivity ratio, nanoparticles Rayleigh number and medium porosity on the stationary convection of the physical system have been analyzed analytically and graphically. It is observed that the rotation parameter has a stabilising influence for both bottom/top-heavy configurations.
EN
The effect of magnetic dependent (MFD) viscosity on Soret driven ferrothermohaline convection in a densely packed anisotropic porous medium has been studied. The Soret effect is focused on the system. A linear stability analysis is carried out using a normal mode technique and a perturbation method is applied. It is found that a stationary mode is favorable for the Darcy model. Vertical anisotropy tends to destabilize the system and the magnetization effect is found to stabilize the system. It is also found that the MFD viscosity delays the onset of convection. Numerical computations are made and illustrated graphically.
EN
This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order 𝛼 are described using Caputo's definition with 01<α≤ or 12<α≤. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.
EN
The free convective magnetohydrodynamics (MHD) flow of a non-Newtonian fluid due to a semi-infinite vertical plate under the influence of radiation and viscous dissipation is investigated. The system of partial differential equations is derived and solved for the solutions of velocity and temperature profiles along with the Nusselt number and skin friction by using the perturbation technique. The related important dimensionless parameters of Eckert, Grashof, and Prandtl numbers, magnetic field, radiation and heat source are discussed and shown in graphs. Also, the Nusselt number and skin friction at the plate are obtained and presented in the tabular forms. Finally, the corresponding result of Newtonian fluid is obtained by setting viscoelastic parameter k1 = 0. It is worth mentioning that the obtained results coincide with the previously published results.
EN
The effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferrofluid layer saturating a sparsely distributed porous medium has been investigated by using the Darcy-Brinkman model in the simultaneous presence of a uniform vertical magnetic field and a uniform vertical rotation. A correction is applied to the study of Vaidyanathan et al. [11] which is very important in order to predict the correct behavior of MFD viscosity. A linear stability analysis has been carried out for stationary modes and oscillatory modes separately. The critical wave number and critical Rayleigh number for the onset of instability, for the case of free boundaries, are determined numerically for sufficiently large values of the magnetic parameterM1 . Numerical results are obtained and are illustrated graphically. It is shown that magnetic field dependent viscosity has a destabilizing effect on the system for the case of stationary mode and a stabilizing effect for the case of oscillatory mode, whereas magnetization has a destabilizing effect.
EN
The aim of the paper is to investigate an oscillatory fluid flow and heat transfer through a porous medium between parallel plates in the presence of an inclined magnetic field, radiative heat flux and heat source. It is assumed that electrical conductivity of the fluid is small and the electromagnetic force produced is very small. The governing coupled equations of motion and energy are solved analytically. Numerical results for the velocity and temperature profiles, local skin friction coefficient and local Nusselt number for various values of physical parameters are discussed numerically and presented graphically.
EN
The impact of heat and mass transfer effects on an MHD flow past an inclined porous plate in the presence of a chemical reaction is investigated in this study. An effort has been made to explain the Soret effect and the influence of an angle of inclination on the flow field, in the presence of the heat source, chemical reaction and thermal radiation. The momentum, energy and concentration equations are derived as coupled second order partial differential equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless partial differential equations can be solved by using a closed analytical method. Numerical results for pertaining parameters, such as the Soret number (Sr), Grashof number (Gr) for heat and mass transfer, the Schmidt number (Sc), Prandtl number (Pr), chemical reaction parameter (Kr), permeability parameter (K), magnetic parameter (M), skin friction (τ), Nusselt number (Nu) and Sherwood number (Sh) on the velocity, temperature and concentration profiles are presented graphically and discussed qualitatively.
EN
The governing equations of an electrohydrodynamic oscillatory flow were simplified, using appropriate nondimensional quantities and the conversion relationships between fixed and moving frame coordinates. The obtained system of equations is solved analytically by using the regular perturbation method with a small wave number. In this study, modified non-dimensional quantities were used that made fluid pressure in the resulting equations dependent on both axial and vertical coordinates. The current study is more realistic and general than the previous studies in which the fluid pressure is considered functional only in the axial coordinate. A new approach enabled the author to find an analytical form of fluid pressure while previous studies have not been able to find it but have found only the pressure gradient. Analytical expressions for the stream function, electrical potential function and temperature distribution are obtained. The results show that the electrical potential function decreases by the increase of the Prandtl number, secondary wave amplitude ratio and width of the channel.
EN
In the present work, a numerical study on the free-convective heat transfer in a porous media cavity with a wavy boundary was carried out. The validation was done by comparing the results with the experimental data. The cavity inclination angle, material of nanofluid, nanoparticles volume fraction, the Rayleigh number, and porosity of the medium are the parameters which are investigated in this study. Results suggested that, due to the thermophysical properties of Cu particles in water, the heat transfer rate was increased for Cu-Water nanofluid in comparison to Al2O3-Water nanofluid, while the heat transfer rate decreased by increasing the volume fraction of nanoparticles. Numerical results showed that the Rayleigh number has significant effect on the heat transfer rate so that increase in the Rayleigh number from 100 to 10 000 increased the averaged Nusselt number between 2 to 3 times. The effect of porosity on heat transfer proved that the convective heat transfer rate increased with increasing the porosity of the porous medium. The effect of inclination angle of cavity on the heat transfer rate suggested that the optimum angle of cavity causing the highest heat transfer rate from wavy wall is 45°.
15
Content available Exact solution of flow in a composite porous channel
EN
This article concerns fully developed laminar flow of a viscous incompressible fluid in a long composite cylindrical channel. Channel consist of three regions. Outer and inner regions are of uniform permeability and mid region is a clear region. Brinkman equation is used as a governing equation of motion in the porous region and Stokes equation is used for the clear fluid region. Analytical expressions for velocity profiles, rate of volume flow and shear stress on the boundaries surface are obtained and exhibited graphically. Effect of permeability variation parameter on the flow characteristics has been discussed.
EN
In this study, the instability of Walters’ (model B’) viscoelastic fluid in a Darcy-Brinkman-Boussinesq system heated from below saturating a porous medium in electrohydrodynamics is considered. By applying the linear stability analysis and normal modes, the dispersion relations accounting for the effect of Prandtl number, electric Rayleigh number, Darcy number, Brinkman-Darcy number, Taylor number and kinematic viscoelasticity parameter is derived. The effects of electric Rayleigh number, Darcy number, Brinkman-Darcy number and Taylor number on the onset of stationary convection have been investigated both analytically and graphically.
EN
In this paper, triple diffusive convection in a Rivlin-Ericksen fluid layer, which is permeated with suspended particles in the porous medium under the effect of compressibility and variable gravity, is investigated. Linear stability theory and normal mode analysis have been used to study the problem under consideration. It is observed that, for stationary convection, suspended particles, compressibility and medium permeability have destabilizing/stabilizing effects under certain conditions. The variable gravity parameter destabilizes the system whereas stable solute gradients have a stabilizing effect.
EN
An analysis is presented to study the effects of thermal radiation, chemical reaction, viscous and Joule dissipation on MHD free convection flow between a pair of infinite vertical Couette channel walls embedded in a porous medium. The fluid flows by a strong transverse magnetic field imposed perpendicularly to the channel wall on the assumption of a small magnetic Reynolds number. The governing non linear partial differentia equations are transformed in to ordinary differential equations and are solved analytically. The effect of various parameters viz., Eckert number, electric conductivity, dynamic viscosity and strength of magnetic field on temperature profile has been discussed and presented graphically.
EN
The numerical investigation of the effects of radiation and chemical reaction on an unsteady MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical porous plate taking into account the viscous dissipation effect has been carried out. The fluid is considered a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing equations for this investigation are solved numerically by applying the Ritz finite element method. Numerical results for the velocity profiles, temperature profiles and concentration profiles as well as the skin-friction are presented through graphs and tables for different values of the physical parameters involved. Results obtained show a decrease in the temperature and velocity in the boundary layer as the radiation parameter increased. The velocity increases with an increase in the thermal and mass Grashof numbers and decreases with an increase in the magnetic parameter. Further, the concentration and velocity decreases with increasing the Schmidt number and chemical reaction parameter. These findings are in very good agreement with the studies reported earlier.
EN
An investigation has been carried out for the MHD 3-dimensional flow of nanofluid over a shrinking sweet saturating a porous media in the presence of thermal radiation and heat generation. Convective boundary conditions for the flow phenomena are used in the present analysis. The governing equations are reduced to ODEs employing suitable similarity transformations. The solutions of formulated differential equations have been attained mathematically by fourth order R-K technique along with the shooting method. The impact of the governing constraints on momentum, heat, and local Nusselt number, are explored. It is noticed that the momentum and heat decrease with raise in the porosity variable, temperature reduces with an enhance in the thermal radiation variable, and temperature enhances with an enhance in the heat source/sink parameter.
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