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EN
In this paper, the mixed convective flow of an electrically conducting, viscous incompressible couple stress fluid through a vertical channel filled with a saturated porous medium has been investigated. The fluid is assumed to be driven by both buoyancy force and oscillatory pressure gradient parallel to the channel plates. A uniform magnetic field of strength 0B is imposed transverse to the channel boundaries. The temperature of the right channel plate is assumed to vary periodically, and the temperature difference between the plates is high enough to induce radiative heat transfer. Under these assumptions, the equations governing the two-dimensional couple stress fluid flow are formulated and exact solutions of the velocity and the temperature fields are obtained. The effects of radiation, Hall current, porous medium permeability and other various flow parameters on the flow and heat transfer are presented graphically and discussed extensively.
EN
In this paper, a theoretical analysis has been made to study the effect of mixed convection MHD oscillatory Couette flow in a vertical parallel channel walls embedded in a porous medium in the presence of thermal radiation, chemical reaction and viscous dissipation. The channel walls are subjected to a constant suction velocity and free stream velocity is oscillating with time. The channel walls are embedded vertically in a porous medium. A magnetic field of uniform strength is applied normal to the vertical channel walls. The nonlinear and coupled partial differential equations are solved using multi parameter perturbation techniques. The effects of physical parameters, viz., the radiation absorption parameter, Prandtl number, Eckert number, dynamic viscosity, kinematic viscosity, permeability of porous medium, suction velocity, Schmidt number and chemical reaction parameter on flow variables viz., temperature, concentration and velocity profile have been studied. MATLAB code is used to analyze theoretical facts. The important results show that an increment in the radiation absorption parameter and permeability of porous medium results in an increment of the temperature profile. Moreover, an increment in the Prandtl number, Eckert number and dynamic viscosity results in a decrement of the temperature profile. An increment in suction velocity results in a decrement of the velocity profile. An increment in the Schmidt number, chemical reaction parameter and kinematic viscosity results in a decrement of the concentration profile.
EN
This work investigates the mixed convection in a Magnetohydrodynamic (MHD) flow and heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the fourth order Runge-Kutta method with shooting technique. The influence of pertinent flow parameters on velocity, temperature, surface drag force and heat transfer rate are computed and analyzed. Graphical and tabular results are given to examine the nature of the problem. The heat transfer rate at the surface increases with the mixed convection.
EN
The objective of the present work is to investigate the influence of nanoparticles of copper within the base fluid (water) on magneto-hydrodynamic mixed-convection flow in a square cavity with internal generation. A control finite volume method and SIMPLER algorithm are used in the numerical calculations. The geometry is a lid-driven square cavity with four interior square adiabatic obstacles. A uniform heat source is located in a part of the left wall and a part of the right wall of the enclosure is maintained at cooler temperature while the remaining parts of the two walls are thermally insulated. Both the upper and bottom walls of the cavity are considered to be adiabatic. A comparison with previously published works shows a very good agreement. It is observed that the Richardson number, Ri, significantly alters the behavior of streamlines when increased from 0.1 to 100.0. Also, the heat source position parameter, D, significantly changes the pattern of isotherms and its strength shifted when D moves from 0.3 to 0.7.
EN
The problem of mixed convection flow of a heat generating/absorbing fluid in the presence existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface has been studied taking the first-order slip and jump effects into consideration. The research analysis is carried out by considering a fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations which arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. A parametric study of some of the physical parameters involved in the problem is conducted. The results of this research revealed that the magnetic field has a damping impact on the flow and results in decreases in fluid velocity for both air and water. Furthermore, the presence of the heat generation parameter is seen to enhance the temperature distribution and this is reflected as an increase in the magnitude of the oscillation dimensionless velocity, whereas in the presence of heat absorption a reversed trend occurs.
EN
In this paper, Buongiorno’s mathematical model is adopted to simulate both natural convection and mixed convection of a nanofluid in square porous cavities. The model takes into account the Brownian diffusion and thermophoresis effects. Both constant and variable temperatures are prescribed at the side walls while the remaining walls are maintained adiabatic. Moreover, all boundaries are assumed to be impermeable to the base fluid and the nanoparticles. The governing equations are transformed to a form of dimensionless equations and then solved numerically using the finite-volume method. Thereafter, effects of the Brownian diffusion parameter, the thermophoresis number, and the buoyancy ratio on the flow strength and the average Nusselt number as well as distributions of isocontours of the stream function, temperature, and nanoparticles fraction are presented and discussed.
EN
This article theoretically investigated mixed convection flow of heat generating/absorbing fluid in the presence of viscous dissipation and wall conduction effects. The flow is considered to be steady in a vertical channel with some boundary thickness. One of the plates is heated while the other is kept at ambient temperature. The governing flow equations were solved analytically using Homotopy Perturbation Method (HPM). The influences of the governing parameters were captured in graphs, tables and a table was constructed for validation of the work. It is worthwhile to stress that, both the velocity and temperature profiles decrease near the heated plate with an increase in boundary thickness (d) while the reverse cases were observed toward the cold plate. The velocity profile increases near the heated plate with increase in mixed convection parameter (Gre) and decreases towards the cold plate. Rate of heat transfer has been observed to decrease with increase in boundary plate thickness (d) while the critical value of (Gre) increases with growing boundary plate thickness. The study therefore established the importance of boundary plate thickness in mixed convection investigation.
EN
In this paper, we investigate the Dufour and Soret effects on MHD mixed convection of a chemically reacting fluid over a stretching surface in a porous medium with convective boundary condition. The similarity transformation is used to reduce the governing non-linear partial differential equations into ordinary differential equations. Then, they are solved analytically by using the homotopy analysis method (HAM) and are solved numerically by the Runge-Kutta fourth-order method. The analytical and numerical results for the velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are discussed.
EN
The aim of this work is to study the mixed convection boundary layer flow from a horizontal surface embedded in a porous medium with exponential decaying internal heat generation (IHG). Boundary layer equations are reduced to two ordinary differential equations for the dimensionless stream function and temperature with two parameters: ε, the mixed convection parameter, and λ, the exponent of x. This problem is numerically solved with a system of parameters using built-in codes in Maple. The influences of these parameters on velocity and temperature profiles, and the Nusselt number, are thoroughly compared and discussed.
EN
The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.
EN
We study the boundary layer characteristics of heat and mass transfer flow past a vertical wedge in the presence of thermal radiation. The surface temperature and the species concentration are assumed to be oscillating in the magnitude but not in the direction of oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the series solution for the low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions have been presented in terms of the amplitudes and phase angles of the skin friction, the rate of heat transfer and the mass transfer with the variations of Richardson’s number, the Prandtl number, the conduction–radiation parameter, the surface temperature parameter and the Schmidt number. Furthermore, the effects of these parameters are examined in terms of the transient skin friction, heat transfer and mass transfer.
EN
The unsteady laminar boundary layer characteristics of mixed convection flow past a vertical wedge have been investigated numerically. The free-stream velocity and surface temperature are assumed to be oscillating in the magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the extended series solution for low frequency range and the asymptotic series expansion method for high frequency range. The results demonstrate the effects of the Richardson number, Ri, introduced to quantify the influence of mixed convection and the Prandtl number, Pr, on the amplitudes and phase angles of the skin friction and heat transfer. In addition, the effects of these parameters are examined in terms of the transient skin friction and heat transfer.
EN
Laminar and turbulent convective heat transfer in a ventilated and non-ventilated cavity was analyzed by heatlines. Heatlines show that in non-ventilated cavities it is possible to estimate the energy path using the streamlines for turbulent flow regime. In ventilated cavities, heatlines allow to observe that thermal energy travels along the top, by the bottom or by both paths due to the inertial force, the buoyant force or a combination of both, respectively. In the laminar regime, these situations are well established for the Rayleigh number (Ra). Nevertheless, in the turbulent regime, it was found that the combined effect of the inertial and buoyant forces on the energy path is disrupted when Ra > 109. Furthermore, heatlines in conjunction with temperature and velocity profiles allow to see that natural convection is preferred when cooling is required, while the forced convection is a better choice if heating is needed.
EN
In this paper, the effect of radiation heat transfer on mixed convection in a lid-driven trapezoidal cavity is studied numerically. The governing equations of mixed convection are solved based on the SIMPLE algorithm and the solution of the radiative transfer equation inside the participating medium is carried out using the discrete ordinates method, simultaneously. To study the heat transfer and flow characteristics, sensitivity analysis is carried out based on the two parameters including the optical thickness and radiation-conduction parameter. Several interesting results are obtained such as sweep behavior on the isotherms, streamlines and convective Nusselt number with optical thicknesses.
EN
The meshless local Petrov-Galerkin (MLPG) method is extended to analyze the mixed convection and fluid flow in an inclined two-dimensional lid-driven cavity. The enclosure considered comprises two insulated vertical walls and a wavy bottom wall which is subjected to a higher constant temperature than its top counterpart, the sliding lid. For the proposed scheme, the stream function formulation with a weighting function of unity is employed. The simulation results reveal that the local Nusselt number increases with a clockwise increase in the inclination angle. Also, a decrease in the aspect ratio results in an increase in the hot wavy wall average Nusselt number.
EN
This article describes the influence of an inclined magnetic field on the mixed convective peristaltic transport of fluid in an inclined channel. Two types of non-Newtonian fluids are considered. The problem formulation is presented for the Eyring-Prandtl and Sutterby fluids. Viscous dissipation and Joule heating in the heat transfer process are retained. The presence of a heat source in the energy equation is ensured. The resulting problems are solved by the perturbation method. The plots for different parameters of interest are given and discussed. Numerical values of a heat transfer rate are given and analyzed.
EN
The laminar mixed convection in a two-dimensional rectangular inclined cavity with moving top lid is investigated using the double population thermal lattice Boltzmann method (LBM) at different values of the Richardson number, inclination angle and the Prandtl number. In this problem, velocity components are changed by both buoyancy forces and the inclination angle of the cavity. Comparison of the present results with other available data show good agreement. As the results, the velocity and temperature profiles, the Nusselt number, streamlines and isotherms are presented and discussed. It is shown that the increase of Prandtl number enhances the heat transfer rate, especially at higher values of inclination angle and Richardson number. Moreover, the average Nusselt number at the upper limit of the considered range of the Richardson and Prandtl numbers variability increases by a factor of 9.
PL
W pracy zajęto się problemem mieszanej konwekcji laminarnej w dwuwymiarowej, prostokątnej i ukośnie usytuowanej szczelinie domkniętej od góry ruchomą pokrywą. W badaniach zastosowano metodę siatki termicznej Boltzmanna (LBM) podwójnej populacji, uwzględniając rożne wartości liczby Richardsona, kąta pochylenia szczeliny oraz liczby Prandtla. W rozważanym zagadnieniu, składowe prędkości zostały poddane zmianom indukowanym siłami wyporu oraz kątem pochylenia szczeliny. Porównanie otrzymanych wynikow analizy z dostępnymi w literaturze danymi wykazało dobrą zgodność. Rezultatem badań w pracy są także profile rozkładu prędkości i temperatury, liczba Nusselta, linie prądu oraz izotermy, które szczegółowo przedyskutowano. Pokazano, że wzrost liczby Prandtla zwiększa transfer ciepła, zwłaszcza dla wyższych wartości kąta pochylenia szczelin i liczby Richardsona. Co więcej, średnia liczba Nusselta przy górnych wartościach przyjętego zakresu zmienności liczb Richardsona i Prandtla wzrasta 9-krotnie.
EN
Magnetohydrodynamic (MHD) mixed convection flow of a viscous, incompressible and electrically conducting fluid in a vertical channel is analyzed analytically. A magnetic field of uniform strength is applied perpendicular to the planes of the channel walls. The fluid is acted upon by a periodic variation of the pressure gradient in the vertically upward direction. The temperature of one of the plates is non-uniform and the temperature difference of the walls of the channel is high enough to induce heat transfer due to radiation. The fluid and the channel rotate in unison with an angular velocity about the axis normal to the plates of the channel. An exact analytical solution of the problem is obtained. Two cases of small and large rotation have been considered to assess the effects of different parameters involved in the flow problem. The velocity field, the amplitude and the phase angle of the shear stress are shown graphically and discussed in detail. During analysis it is found that the flow problem studied by Makinde and Mhone (2005) is incorrect physically and mathematically.
EN
This paper is focused on the study of heat and mass transfer in the unsteady MHD mixed convective flow of a viscous incompressible fluid bounded by a permeable vertical plate subject to the influence of buoyancy, viscous dissipation, ohmic heating and the Soret effect embedded with slip condition at the boundary layer. In order to obtain a better insight into this problem, we make use of the perturbation method. The results for velocity, temperature, concentration, skin friction, the Nusselt number as well as the Sherwood number are examined analytically and the effects of various significant parameters entering into this problem are displayed graphically.
EN
The theory of micro polar fluids due to Eringen is used to formulate a set of equations for the mixed convective flow and heat transfer in a vertical channel. The two boundaries of the channel are kept either at equal or at different temperatures. Through a proper choice of non-dimensional variables and parameters, the governing equations are developed and three types of thermal boundary conditions are prescribed. These thermal boundaries are isothermal-isothermal, isoflux-isothermal and isothermal-isoflux for the left-right walls of the channel. Exact analytical solutions are obtained for the velocity and temperature fields for heat generation/absorption conditions. It is found that the material and source/sink parameters have significant effects on the flow. A parametric study is conducted and the results are presented and discussed. By making the Newtonian solvent more and more micropolar, it is possible to obtain drag reduction.
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