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In this paper, we present a numerical study of turbulent natural convection in a square cavity differentially heated and filled with nanofluid and subjected to an inclined magnetic field. The standard k-e model was used as the turbulence model. The transport equations were discretized by the finite volume method using the SIMPLE algorithm. The influence of the Rayleigh number, the Hartmann number, the orientation angle of the applied magnetic field, the type of nanoparticles as well as the volume fraction of nanoparticles, on the hydrodynamic and thermal characteristics of the nanofluid was illustrated and discussed in terms of streamlines, isotherms and mean Nusselt number. The results obtained show that the heat transfer rate increases with increasing Rayleigh number and orientation angle of the magnetic field but it decreases with increasing Hartmann number. In addition, heat transfer improves with increasing volume fraction and with the use of Al2O3 nanoparticles.

This paper presents a numerical study of a double diffusive convection in an inclined square porous cavity filled with an electrically conducting binary mixture. The upper and bottom walls are maintained at a constant temperatures and concentrations whereas the left and right walls are assumed to be adiabatic and impermeable. A uniform and tilted magnetic field is applied at an angle, γ, about the horizontal, it is obvious that this is related to the orientation of the magnetic force that can help or oppose the buoyant force. The Dupuit-Darcy flow model, which includes effects of the inertial parameter, with the Boussinesq approximation, energy and species transport equations are solved numerically using the classical finite difference method. Governing parameters of the problem under study are the thermal Rayleigh number, Rt, Hartmann number, Ha, Lewis number, Le, the buoyancy ratio, φ,inclination angle, Φ and tilting angle of the magnetic field, γ,. The numerical results are reported on the contours of streamline, temperature, and concentration and for the average Nusselt and Sherwood numbers for various parametric conditions. It is demonstrated that both the inertial effect parameter and the magnetic field, have a strong influence on the strength of the natural convection heat and mass transfer within the porous layer.

This paper presents numerical simulations for a MHD convective process in curved channels. The worked suspension consists of water as a based hybrid nanofluid and two types of the nanoparticles, namely, Cu and Al2O3. Two systems of the governing equations are formulated for the hybrid nanofluid and dusty phases. The hybrid nanofluid system is modeled in view of lubrication approach. The governing equations are mapped to a regular computational domain then they solved numerically using the fourth order Runge-Kutta method. The obtained findings revealed that the growing in the Hartmann number causes a reduction in both of the hybrid nanofluid and dusty velocities while the mixture temperature is enhanced. Also, the temperature distributions are supported when either the Grashof number or the amplitude ratio is altered.

In this paper, we introduced a numerical analysis for the effect of a magnetic field on the mixed convection and heat transfer inside a two-sided lid-driven cavity with convective boundary conditions on its adjacent walls under the effects of the presence of thermal dispersion and partial slip. A single-phase model in which the water is the base fluid and a copper is nanoparticles is assumed to represent the nanofluid. The bottom and top walls of the cavity move in the horizontal direction with constant speed, while the vertical walls of the cavity are stationary. The right wall is mentioned at relatively low temperature and the top wall is thermally insulated. Convective boundary conditions are imposed to the left and bottom walls of the cavity and the thermal dispersion effects are considered. The finite volume method is used to solve the governing equations and comparisons with previously published results are performed. It is observed that the increase in the Hartmann number causes that the shear friction near the moving walls is enhanced and consequently the horizontal velocity component decreases.

This study reveals the entropy analysis of hydromagnetic pumping flow of Williamson fluid through a two-dimensional symmetric channel carrying cilia. Propulsive metachronal waves are mobilized by whipping and beating of uniformly distributed cilia which follow elliptic trajectory movements in the parallel direction of flow. The flow is resisted by a uniform transverse magnetic field. The entire study is carried out in wave frame of reference. After implying lubrication approximations, the governing equations of the present flow problem are solved by perturbation method. Effects of physical parameters of interest on various flow quantities, the total entropy generation number and the Bejan number are plotted and discussed. It is observed that fluid velocity and temperature is enhanced in the core channel region for small values of Hartmann number and cilia length. It is also noticed that the entropy generation and the Bejan number are decreasing function of magnetic field. Near the channel center, irreversibility due to fluid friction is dominant but at the channel wall heat transfer irreversibility effects are observed to be substantial. The confined bolus reduces in size for small values of cilia length parameter and large values of Hartmann number.

Thermal radiation analysis in MHD Casson nanofluid-flow over an exponentially stretching sheet is investigated. A chemical reaction is also considered. A non-uniform magnetic field of strength is imposed in a transverse direction. The governing boundary-layer equations are reduced into ODE by using suitable similarity transformations. The coupled non-linear equations are solved numerically using an implicit finite difference scheme by means of the Keller-box method. A comparison of the obtained results is performed with the published results. It is found that velocity profiles are suppressed with the increasing values of Hartmann number and Casson fluid parameter.

The motion of a non-Newtonian nanofluid over a semi-infinite moving vertical plate through porous medium stressed by an external uniform magnetic field with heat and mass transfer is investigated. The fluid under consideration obeys Eyring-Powell model. The effects of the physical parameters of the problem such as, permeability, chemical reaction as well as the fluid material parameters such as Hartmann number, Eckert number, and Reynolds number are discussed. The effects of external cooling (Gr > 0) of the plate by the free convection are considered. Graphical results are presented to highlight effects of various emerging parameters on velocity, temperature and concentration profiles.

The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

This paper studies the effect of a constant magnetic field on the mixed convection heat transfer and the entropy generation of CuO-water nanofluid in an open C-shaped cavity with a numerical method. The governing equations are presented by control volume method and they are solved simultaneously by the SIMPLE algorithm. This study examines the effect of the Hartman number, aspect ratio, Reynolds number, and Richardson number parameters for different solid volume fraction of nanoparticles. Also Nusselt number, entropy generation, thermal performance criteria and coefficient of performance is studied in this research. The calculated parameters are the Hartman number, aspect ratio, Reynolds number, Richardson number, nanofluid solid volume fraction, Nusselt number, and coefficient of performance. The results show that increasing the Hartmann number reduces the entropy generation. However, the thermal performance increases. Increasing the aspect ratio raises heat transfer and thermal performance. The effects of nanofluid solid volume fraction on mixed convection heat transfer and entropy generation are also investigated and discussed.

In this article, the influence of heat transfer on solid particle motion in MHD Ree-Eyring fluid due to peristaltic wave has been investigated. The governing flow problem is modelled for fluid phase and particle phase with the help of continuity, momentum, and energy equations under the assumption of long wave-length and creeping flow regime. The obtained coupled ODE have been solved analytically and exact solutions have been presented. The influence of all the physical parameters are discussed for Newtonian and non-Newtonian fluid with the help of graphs. In the present analysis, it is observed that due to influence of Hartmann number, the magnitude of the velocity diminishes.

This present numerical study explores the MHD mixed convective flow and heat transfer analysis in a square porous enclosure filled with nanofluid having center thin heater. The left and right walls of the enclosure are maintained at temperature T . The bottom wall is c considered with a constant heat source whereas the remaining part of bottom wall and top wall are kept adiabatic. The finite volume method based on SIMPLE algorithm is used to solve the governing equations in order to investigate the effect of heater length, Hartmann, Richardson, and Darcy numbers on the fluid-flow and heat transfer characteristics inside the enclosure. A set of graphical results are presented in terms of streamlines, isotherms, mid height velocity profiles and average Nusselt numbers. The results reveal that heat transfer rate increases as heater length increases for increasing Darcy and Richardson numbers. Among the two positions of heaters, larger enhancement of heat transfer is obtained for horizontal heater of maximum length. It is observed that, Hartmann number is a good control parameter for heat transfer in fluid-flow through porous medium in enclosure. Moreover, Ag-water nanofluid has greater merit to be used for heat transfer enhancement. This problem may be occurred in designing cooling system for electronic equipment to maximize the efficiency with active and secured operational conditions.

A numerical study of unsteady hydromagnetic flow of Casson liquid passed through the oscillatory moving surface is presented. The interaction of radiation term is reported in the energy equation. The flow is generated by the rapid move?ment of elastic surface that stretched back and forth periodically. The number of variables is reduced by introducing dimensionless variables. An implicit technique developed on finite difference algorithm is implemented to the system of PDE. The impact of various parameters like Casson liquid parameter, the oscillation frequency and stretching rate ratio, Hartmann number and effective Prandtl number are shown through various graphs. The observation indicates that the amplitude of the velocity declines by enhancing Casson liquid parameter, oscillation frequency and stretching rate ratio and Hartmann number. The temperature declines by increasing Casson fluid parameter and effective Prandtl number. The results also indicate that the time-series of local Nusselt number increases by enhancing effective Prandtl number.

This article describes the steady magnetohydrodynamic mixed thermo-bioconvection in a square enclosure filled with a homogeneous and isotropic porous medium in the presences of oxytactic microorganisms. The model used for the oxytactic microorganisms is based on a continuum model of a suspension of oxytactic microorganisms. The mixed convection is resulting for the interaction between the buoyancy force and the moving of the top wall of the cavity with constant speed. The horizontal walls of the cavity are considered to be adiabatic while the vertical walls are differentially heated. The governing equations are solved using the finite volume method with SIMPLE technique. Comparisons with previously published works are performed and found to be in excellent agreements. It is found that the increase in both Richardson number and Hartmann number reduces the average Nusselt and Sherwood numbers.

The MHD flow of three immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied electric and inclined magnetic field has been investigated in the paper. All three fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ODE and closed-form solutions are obtained in three fluid regions of the channel. Separate solutions with appropriate boundary and interface conditions for each fluid have been determined. The analytical results for various values of the Hartmann number, magnetic field inclination angle, ratio of fluid viscosities, and electrical conductivities have been presented graphically to show their effect on the flow and heat transfer characteristics. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR 35016: Research of MHD flow in the channels, around the bodies and application in the development of the MHD pump]

In the present study, numerical simulation of magnetohydrodynamic (MHD) mixed convection heat transfer and fluid flow has been analyzed in a lid-driven enclosure provided with a constant flux heater. Governing equations were solved via differential quadrature (DQ) method. Moving wall of the enclosure has constant temperature and speed. The calculations were performed for different Richardson number ranging from 0.1 to 10, constant heat flux heater length from 0.2 to 0.8, location of heater center from 0.1 to 0.9, Hartmann number from 0 to 100 and aspect ratio from 0.5 to 2. Two different magnetic field directions were tested as vertical and horizontal. It was found that results of DQ method show good agreement with the results of literature. The magnetic field was more effective when it applied horizontally than that of vertical way. In both direction of magnetic field, it reduced the flow strength and heat transfer. Thus, it can be used as an important control parameter for heat and fluid flow.

In this study, heat and mass transfer characteristic of unsteady nanofluid flow between parallel plates is investigated. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via Differential Transformation Method. The validity of this method was verified by comparison previous work which is done for viscous fluid. The analytical investigation is carried out for different governing parameters namely; the squeeze number, Hartmann number, Schmidt number, Brownian motion parameter, thermophoretic parameter and Eckert number. The results indicate that skin friction coefficient has direct relationship with Hartmann number and squeeze number. Also it can be found that Nusselt number increases with increase of Hartmann number, Eckert number and Schmidt number but it is decreases with augment of squeeze number.

The aim of this paper is to investigate the velocity and thermal slip effects in MHD flow and heat transfer of two-phase viscous fluid. It is assumed that both the phases have different densities, viscosities and electrical conductivities. The fully developed flow governed by a constant pressure gradient is passing through an inclined channel having inclination f with horizontal axis. The electrical conductivity in phase I is assumed to be zero so that the constant applied magnetic field of strength B0 in the transverse direction only effect the fluid in phase II. The method of successive approximation is used to develop the analytic solution of order 1 for the developed dimensionless coupled ordinary differential equations. The main focus is to discuss the influence of velocity and thermal slip parameters and Hartmann number on the velocity and temperature profiles.

This paper presents an investigation on the MHD thin film flow and heat transfer of a power law fluid over an unsteady stretching sheet. The effects of power law viscosity on a temperature field are taken into account with a modified Fourier?s law Proposed by Zheng by assuming that the temperature field is similar to the velocity field. The governing equations are reduced to a system of nonlinear ordinary differential equations. The numerical solutions are obtained by using the shooting method coupled with the Runge-Kutta method. The influence of the Hartmann number, the power law exponent, the unsteadiness parameter, the thickness parameter and the generalized Prandtl number on the velocity and temperature fields are presented graphically and analyzed. Moreover, the critical formula for parameters are derived which indicated that the magnetic field has no effect on the critical value.

In this paper, the steady flow and heat transfer of an incompressible electrically conducting micropolar fluid through a parallel plate channel is investigated. The upper and lower plates have been kept at the two constant different temperatures and the plates are electrically insulated. Applied magnetic field is perpendicular to the flow, while the Reynolds number is significantly lower than one i.e. considered problem is in induction-less approximation. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and three closed-form solutions are obtained. The velocity, micro-rotation and temperature fields in function of Hartmann number, the coupling parameter and the spin-gradient viscosity parameter are graphically shown and discussed.

The present paper is concerned with the magnetohydrodynamic unsteady rotating flows of generalized Burgers' fluid with a porous medium. The flows are created by the plate oscillations. Modified Darcy's law has been employed to model the governing problem. Closed-form solutions corresponding to cosine and sine oscillations are obtained by the Laplace transform method. The performed calculations disclose that Hartmann number, porosity of the medium, angular frequency, and oscillating frequency have strong influence on the velocity. The graphs are presented for such influence and examined carefully.

The magnetohydrodynamic flow of three immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied magnetic field has been investigated. All three fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and closed-form solutions are obtained in three fluid regions of the channel. Separate solutions with appropriate boundary conditions for each fluid have been obtained and these solutions have been matched at the interface using suitable boundary conditions. The analytical results for various values of the Hartmann number, the ratio of fluid heights and thermal conductivities have been presented graphically to show their effect on the flow and heat transfer characteristics. [Projekat Ministarstva nauke Republike Srbije, br. TR 35016]

An investigation of unsteady MHD free convective flow and mass transfer during the motion of a viscous incompressible fluid through a porous medium, bounded by an infinite vertical porous surface, in a rotating system is presented. The porous plane surface and the porous medium are assumed to rotate in a solid body rotation. The vertical surface is subjected to uniform constant suction perpendicular to it and the temperature at this surface fluctuates in time about a non-zero constant mean. Analytical expressions for the velocity, temperature and concentration fields are obtained using the perturbation technique. The effects of R (rotation parameter), k0 (permeability parameter), M (Hartmann number) and w (frequency parameter) on the flow characteristics are discussed. It is observed that the primary velocity component decreases with the increase in either of the rotation parameter R, the permeability parameter k0, or the Hartmann number M. It is also noted that the primary skin friction increases whenever there is an increase in the Grashof number Gr or the modified Grashof number Gm. It is clear that the heat transfer coefficient in terms of the Nusselt number decreases in the case of both air and water when there is an increase in the Hartmann number M. It is observed that the magnitude of the secondary velocity profiles increases whenever there is an increase in either of the Grashof number or the modified Grashof number for mass transfer or the permeability of the porous media. Concentration profiles decreases with an increase in the Schmidt number.

This paper deals with the problem of thermal radiation effects on magneto hydro dynamic flow and heat transfer in a channel with porous walls of different permeability. The equations governing the flow are coupled non-linear partial differential equations. By introducing the stream function, the governing partial differential equations are reduced to ordinary differential equations. The governing equations which are coupled and highly non-linear are first linearized by quasilinearization technique and obtained numerical solution by using implicit finite difference scheme. The effects of various parameters, namely, Reynolds number R, Permeability parameter K, Hartmann number S2, Prandtl number Pr, and Thermal radiation parameter F, entering into the problem on the velocity field and temperature distribution are shown graphically.

Optimal design of a heat exchanger is one of the concerns of energy conversion engineers. In the present work, the mixed convection flow between two vertical concentric pipes with constant heat flux at the boundaries and MHD flow effects is considered. To determine the optimal design for such a heat exchanger, at first, the momentum and energy equations are simplified and solved analytically. Next, using entropy generation analysis and cost analysis, the operational costs due to entropy generation are estimated. It is concluded that with an increase in the Hartmann number, the energy costs increase. In addition, for two small deviations from the base radius ratio )2(=P including 9.1=P and 1.2=P , the changes in the energy cost are calculated. It is found that for 9.1=P the energy cost increases by 17.5% while for P = 2.1 the energy cost is reduced by 13.6 %.

The paper investigates the magnetohydrodynamic flow of two immiscible, electrically conducting fluids between isothermal and insulated moving plates in the presence of an applied electric and inclined magnetic field with the effects of induced magnetic field. Partial differential equations governing the flow and heat transfer and magnetic field conservation are transformed to ordinary differential equations and solved exactly in both fluid regions, under physically appropriate boundary and interface conditions. Closed-form expressions are obtained for the non-dimensional velocity, non-dimensional induced magnetic field and nondimensional temperature. The analytical results for various values of the Hartmann number, the angle of magnetic field inclination, loading parameter and the ratio of plates’ velocities are presented graphically to show their effect on the flow and heat transfer characteristics. [Projekat Ministarstva nauke Republike Srbije, br. TR 35016]

The aim of the present numerical study is to investigate the effect of thermally active zones and direction of the external magnetic field on hydromagnetic convection in an enclosure. Nine different relative positions of the thermally active zones are considered. Top and bottom of the enclosure are adiabatic. The governing equations are solved by the finite volume method. The results are obtained for different directions of the external magnetic field, thermally active locations, Hartmann numbers, Grashof numbers and aspect ratios. It is observed that the heat transfer is enhanced for heating location is either at middle or at bottom of the hot wall while the cooling location is either at top or at middle of the cold wall. The flow field is altered when changing the direction of the magnetic field in the presence of strong magnetic field. The average Nusselt number decreases with an increase of the Hartmann number and increases with increase of the Grashof number and aspect ratio.