MHD Mixed Convection in a Lid-Driven Cavity Including Heat Conducting Solid Object and Corner Heaters with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a top sided lid-driven square enclosure is numerically simulated in this paper following a finite volume approach based on the SIMPLEC algorithm. The enclosure is heated by corner heaters which are under isothermal boundary conditions with different lengths in bottom and right vertical walls. The lid is having lower temperature than heaters. The other boundaries of the enclosure are insulated. A uniform magnetic field is applied along the horizontal direction. A heat conducting horizontal solid object (a square cylinder) is placed centrally within the outer enclosure. Shear forces through lid motion, buoyancy forces due to differential heating and magnetic forces within the electrically conducting fluid inside the enclosure act simultaneously. Heat transfer due to forced flow, thermal buoyancy, Joule dissipation and conduction within the solid object are taken into account. Simulations are conducted for various controlling parameters such as the Richardson number (0.1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50) and Joule heating parameter (0 ≤ J ≤ 5) keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number and bulk fluid temperature are also plotted to show the effects of Ha, J and Ri on them.     

MHD Mixed Convection in a Channel with a Triangular Cavity

A numerical study has been carried out in an open channel, which have a heated triangular cavity at the bottom wall. The remaining walls of the channel are adiabatic. Flow inlets to the channel with uniform velocity and fully developed flow are accepted at the exit of the channel. Steady state mixed convection by laminar flow has been studied by numerically solving governing equations to obtain flow field and temperature distribution under the magnetic field and Joule effect. Equations are solved via the Galerkin weighted residual finite element technique. Calculations are performed for different governing parameters such as Hartmann number (10 ≤ Ha ≤ 100), Reynolds number (100 ≤ Re ≤ 2,000), Rayleigh number (10³ ≤Ra ≤ 10⁵), Joule parameter (0 ≤ J ≤ 5), and Prandtl number (1 ≤ Pr ≤ 10). It is found that heat transfer decreases with an increasing of the Hartmann number especially at higher values of Rayleigh number. Fluid temperature at the exit of the channel also decreases with increasing of Hartmann number. Fluid temperature at the outlet of the channel becomes higher at low Reynolds number and higher Rayleigh number. However, it decreases with the decreasing of the Reynolds number.     

Numerical Study on Double Diffusive Mixed Convection with a Soret Effect in a Two-Sided Lid-Driven Cavity

In the present study, a numerical analysis is performed to understand the mixed convection flow, and heat and mass transfer with Soret effect in a two-sided lid-driven square cavity. The horizontal walls of the cavity are adiabatic and impermeable, while vertical walls are kept at constant but different temperatures and concentrations. The vertical walls move in a constant velocity. According to the direction of the movement of walls, three cases have been studied for different combinations of parameters involved in the study. The governing unsteady equations are solved numerically by the finite volume method with the SIMPLE algorithm. The results are presented graphically in the form of streamlines, isotherms, and velocity profiles. Heat and mass transfer rates are reduced if both walls are moving the in same direction, while heat and mass transfer rates are enhanced if the walls are moving in the opposite direction.     

Mixed Convection of Nanofluid Flows in a Square Lid-Driven Cavity Heated Partially From Both the Bottom and Side Walls

This article presents the results of a numerical study on mixed convection within a square lid-driven which was heated simultaneously by two finite heat sources on the bottom and side walls, and also filled with nanofluids. The results were presented for different nanofluids. The governing equations were solved using a finite volume approach by the SIMPLE algorithm. The effects of the Rayleigh number, Reynolds number, the solid volume fraction, the dimensions of heaters, and their locations on the streamlines and isotherms contours were investigated accurately. Also, the effects of the above parameters on the average Nusselt number along two heat sources were precisely presented. Moreover, variations of the average Nusselt number of two heaters were considered whenever one heater was fixed and the location of the other heater was varied along the wall. In addition, variations of the length of one heater on the average Nusselt number were also studied whenever the length of the other heater was fixed.     

Numerical Simulation of Double Diffusive Mixed Convection in a Lid-Driven Square Cavity Using Velocity-Vorticity Formulation

In this article, convection driven by combined thermal and solutal concentration buoyancy effects in a lid-driven square cavity is examined using velocity-vorticity form of Navier-Stokes equations. The governing equations consist of vorticity transport equation, velocity Poisson equations, energy equation, and concentration equation. Validation results are discussed for convection due to heat and mass transfer in a lid-driven square cavity at Re = 500, Le = 2, and G_RT  = G_RS  = 100. These results indicate that the present velocity-vorticity formulation could predict the characteristic parameters of flow, temperature, and solutal concentration fields using a much coarser mesh compared to the mesh used in a stream function-vorticity formulation. The capability of the proposed algorithm to handle complex geometry is demonstrated by application to mixed convection in a lid-driven square cavity with a square blockage. The effect of buoyancy ratio on the convection phenomenon is discussed for buoyancy ratio varying from ? 100 to 100 at Re = 100. Under opposing temperature and concentration gradients along the vertical direction, the negative buoyancy ratios give rise to aiding flows.     

Magnetoconvective Transport in a Vertical Lid-Driven Cavity Including a Heat Conducting Square Cylinder with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a vertical lid-driven square enclosure is numerically simulated following a finite volume approach based on the SIMPLEC algorithm. Both the top and bottom horizontal walls of the enclosure are insulated, and the left and right vertical walls are kept isothermal with different temperatures. The left vertical wall is translating in its own plane at a uniform speed, while all other walls are stationary. Two cases of translational lid motion, viz. vertically upward and downward, are considered. A uniform magnetic field is applied along the horizontal direction normal to the translating wall. A heat conducting horizontal solid square cylinder is placed centrally within the outer enclosure. Simulations are conducted for various controlling parameters, such as the Richardson number (1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), and Joule heating parameter (0 ≤ J ≤ 5), keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J, and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number, and bulk fluid temperature are also plotted to show the effects of Ha, J, and Ri on them.     

Effect of Nanoparticles on the Hysteresis Loop in Mixed Convection within a Two-Sided Lid-Driven Inclined Cavity Filled with a Nanofluid

The present work deals with numerical modeling of mixed convection flow in a two-sided lid driven inclined square enclosure filled with water-Al₂O₃ nanofluid. The limiting cases of a cavity heated from below and cooled from above and the one differentially heated are recovered respectively for inclination angles 0° and 90°. The moving walls of the cavity are pulled in opposite directions with the same velocity and maintained at constant but different temperatures while the remaining walls are kept insulated. The numerical resolution of the studied problem is based on the lattice Boltzmann method. A parametric study is conducted and a set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles and enclosure inclination angle on fluid flow and heat transfer characteristics. The governing parameters of this problem are the Richardson number (varied from 0.1 to 10⁶), the nanoparticles volume fraction (varied from 0 to 0.04) and the inclination angle (varied from 0° to 180°). The critical conditions leading to the transition from monocellular flow to multicellular flow and vice versa are determined. In the common ranges of Richardson number and inclination angle where both monocellular and tri-cellular patterns coexist, the heat transfer is seen to be strongly reduced by the latter.     

Influences of Physical Parameters on Mixed Convection in a Horizontal Lid-Driven Cavity with an Undulating Base Surface

The problem of steady, laminar, and incompressible mixed convection flow in a horizontal lid-driven cavity is studied. In this investigation, two vertical walls of the cavity are perfectly insulated and the wavy bottom wall is considered at an identical temperature higher than the top lid. The enclosure is assumed to be filled with a Bousinessq fluid. The study includes computations for different physical parameters, such as cavity aspect ratio (AR) from 0.5 to 2, amplitude of undulating wall (A) from 0 to 0.075, and number of undulations (λ) from 0 to 3. The pressure-velocity form of Navier-Stokes and energy equations are used to represent the mass, momentum, and energy conservations of the fluid medium in the cavity. The governing equations and boundary conditions are converted to dimensionless form and solved numerically by the penalty finite element method with discretization by triangular mesh elements. Flow and heat transfer characteristics are presented in terms of streamlines, isotherms, average Nusselt number (Nu), and maximum temperature (θ _max ) of the fluid. Results show that the wavy lid-driven cavity can be considered an effective heat transfer mechanism at larger wavy surface amplitude, as well as the number of waves and cavity aspect ratio.     

Laminar Mixed-Convection Heat Transfer in a Lid-Driven Cavity with Modified Heated Wall

In this numerical study, steady laminar mixed-convection heat transfer in a two-dimensional square lid-driven cavity with a modified heated wall is investigated over a range of Richardson numbers, including 0.01, 1, and 10. The heated bottom wall of the cavity is characterized by rectangular, triangular, and sinusoidal wave shapes. The cooled top wall of the cavity is sliding with constant velocity, while the vertical walls are kept stationary and adiabatic. The governing equations are solved using a finite-volume technique. The results are presented in the form of streamlines, isotherms, and Nusselt number plots. The effects of the number of undulations and the amplitude on the flow field and heat transfer are also investigated. The predicted results demonstrate that the heat transfer enhancement is generally observed with the modification of the heated wall, while the improvement is found to be more profound for the case of rectangular wave and at low Richardson number.     

Effect of Radiation on Mixed Convection Inside a Lid-Driven Square Cavity With Various Optical Thicknesses and Richardson Numbers

This work studies numerically the effect of the radiative heat transfer on the flow and thermal behaviors of the mixed convection in a lid-driven square cavity in the presence of radiatively emitting, absorbing, and isotropically scattering gray medium. The Boussinesq approximation has been used in modeling the governing equations, and the SIMPLE (semi-implicit method for pressure-linked equations) algorithm is used in coupling the velocity and pressure fields. The radiative transfer equation and the governing equations have been solved respectively by the discrete ordinates method and the finite-volume method in order to obtain the temperature, velocity, and heat flux distributions in the participating medium. The present numerical simulations are validated by comparison with several earlier studies. Then, the temperature and velocity distributions and Nusselt numbers have been analyzed in a broad range of optical thicknesses from 0 to 100 and Richardson numbers from 0.01 to 100. The results show that the radiation has a significant role on the flow and thermal behaviors in the lid-driven square cavity. As an example, we can refer to a sweep behavior that is detected in the velocity distributions of the lid-driven cavity.     

Varying Heating Effect on Mixed Convection of Nanofluids in a Vented Horizontal Cavity with Injection or Suction

The problem of mixed convection heat transfer inside a horizontal vented enclosure through the lower and upper parts, respectively, of its left and right vertical walls is studied numerically using Al₂O₃-water nanofluid as working fluid. The bottom wall is subjected to a linearly varying (increasing or decreasing) heating temperature profiles, while the other boundaries are considered thermally insulated. The fresh fluid is admitted from the bottom part of the left vertical wall by injection or by the suction imposed on the opening of the right vertical wall. Based on numerical predictions, the conjugate effect of the Reynolds number and the nanoparticle concentration on fluid flow and heat transfer characteristics is studied. The obtained results demonstrate clearly the positive role of the nanoparticles addition on the improvement of the heat transfer rate and the mean temperature within the cavity. In addition, the flow structure and the temperature distribution inside the cavity are seen to be very sensitive to the variations of the Reynolds number, the imposed external flow mode, and the heating type. Results presented show that, in general, the decreasing heating mode is more favorable to the heat transfer in comparison with the case of the increasing heating mode. The cooling efficiency is found to be more pronounced by the injection/suction mode by applying the increasing/decreasing heating type.     

Natural Convection in a Differentially Heated Cavity with Parallel Heat-Generating Baffles

Natural convection in a horizontal differentially heated square cavity containing two vertical heat generating baffles is studied numerically. The baffles are assumed to generate heat uniformly at the same or different rates. Asymptotic steady-state results for the vorticity–stream function formulation are presented in the form of streamline and isotherm plots. The fluid flow, heat transfer, and average Nusselt number are investigated for different heat generation ratios and spacing between the baffles. Convection within the cavity gets augmented for increasing values of heat generation ratio. When the two baffles are located very near the cavity walls, an increase in heat generation ratio induces a strong buoyancy convective flow. When they are very close to each other an increase in heat generation ratio strengthens the innermost cell around the baffles, which in turn drives the global flow at a faster rate through a pair of intermediate inner cells. It is found that the blocking effect of the baffles strongly depends on heat generation ratio and spacing between the baffles. The heat transfer rate varies nonlinearly against spacing between the baffles, and the possible physical reason is given.     

Optimization of Mixed Convection in a Lid-Driven Enclosure with a Heat Generating Circular Body

The physical model considered here is a lid-driven enclosure with bottom heating and top cooling conditions, and a heat generating circular body is placed at the center. The vertical walls of the cavity are kept thermally insulated, and the top lid moves at a constant speed. The steady two-dimensional governing equations for the physical problem are transformed in a dimensionless form with dimensionless governing parameters that decide the fluid flow and heat transfer characteristics in the system. The solution of these transport equations is obtained numerically with the finite element approach using the Galerkin method of weighted residuals. The parametric study has been carried out for variation of the heat generation parameters, the Reynolds numbers, solid-fluid thermal conductivity ratios as well as the Richardson numbers. The working fluid is assigned as air with a Prandtl number of 0.71 throughout the simulation. Results are presented in the form of streamlines, isotherms, average Nusselt number, bulk temperature, and drag force for the afore mentioned parameters. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as average Nusselt number, average bulk temperature, and drag force. An optimum combination of the governing parameters would result in higher heat transfer and lower drag force.     

Numerical Investigation of Transient Magnetohydrodynamic Mixed Convection in a Ventilated Cavity Containing Two Heated Circular Cylinders

A two-dimensional finite volume computation is performed to analyze the transient magnetoconvective transport in a ventilated cavity containing two inner heated circular cylinders with identical shape. An electrically conducting fluid (Prandtl number 0.01) enters the cavity through an opening at the middle of the left wall and is taken away by a similar opening at the middle of the right wall. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. Simulations are performed for the parameters, Richardson number (0, 0.25, 0.5, and 1), Reynolds number (380–550), Hartmann number (0, 10, 20, and 50) and dimensionless gap between the cylinders 0.1, 0.2, and 0.3. The analysis indicates that the transport process is a complex function of the magnetic field strength, mixed convective strength and the cylinder distance. Some typical combinations of these controlling parameters may produce three different transport characteristics such as the steady state, periodic oscillatory, and chaotic. With a lower cylinder distance and higher mixed convective strength, the flow instability increases causing periodic and even chaotic oscillations, whereas the magnetic field due to its damping nature imparts stability to the flow resulting in a steady state flow condition.     

Mixed Convection in Lid-Driven Trapezoidal Cavities with an Aiding or Opposing Side Wall

Mixed convection heat transfer and fluid flow fields inside a lid-driven trapezoidal cavity were studied numerically. The cavity horizontal walls were thermally insulated while the inclined side walls were maintained isothermally at different temperatures. Forced convection was induced by moving the hotter right inclined side wall. The problem is formulated using the stream function–vorticity procedure. Together with the established boundary conditions on the right moving wall, the problem is solved by the finite difference method. The Richardson number Ri (0.01–10) and inclination angle of the side walls Φ (66–80°) were considered as pertinent parameters and investigated in two lid-driven cases: aiding and opposing directions. The results show that the behavior of Nusselt number is different from Richardson number depending on the direction of the lid. The inclination angle of the side walls was found to have a significant effect on Nusselt number when Ri was relatively low (≤1); otherwise, a negligible effect of Φ on Nusselt number was recorded.     

Mixed Convection from a Heated Sphere in Bingham Plastic Fluids

In this work, the steady and laminar mixed-convection heat transfer from an isothermal sphere immersed in Bingham plastic fluids has been investigated in the aiding-buoyancy configuration. The pertinent coupled equations of motion and thermal energy have been solved numerically over the following ranges of conditions: Richardson number, 0 ≤ Ri ≤ 2, Bingham number, 0 ≤ Bn ≤ 10, Reynolds number, 0.1 ≤ Re ≤ 100 and Prandtl number, 10 ≤ Pr ≤ 100. Flow characteristics like streamlines, pressure coefficient, morphology of yielded/unyielded regions and drag coefficient are discussed extensively. Similarly, isotherms, local Nusselt number and average Nusselt number are thoroughly examined to develop an overall understanding of the corresponding heat transfer characteristics. All else being equal, in contrast to the positive role of the aiding-buoyancy free convection in Newtonian and power-law fluids, due to the fluid yield stress, heat transfer is impeded in viscoplastic fluids. While the average value of the Nusselt number is influenced by four dimensionless groups, namely, Reynolds number, Bingham number, Prandtl number and Richardson number, by using novel scaling, it has been possible to consolidate the present results via the use of the Colburn j-factor in a simple form. This is particularly suitable for predicting the value of the Nusselt number in a new application.     

Soret Effect on Double-Diffusive Convection in a Square Porous Cavity Heated and Salted from Below

This article presents a numerical study of the Soret effect on double diffusion in a two-dimensional square cavity filled with a saturated Darcy porous medium. The horizontal walls of the cavity are subject to different but uniform temperatures and concentrations such that the medium is heated and salted from below. The left and right vertical walls are adiabatic and impermeable. Combined effects of the buoyancy ratio N (?1.5 < N < 4.4) and the Soret parameter M (?60.5 < M < 155) on the fluid flow and heat and mass transfer characteristics corresponding to monocellular, bicellular, and tricellular modes are studied for R _T  = 200 and Le = 10. It is found that the thresholds of N marking the transitions towards the oscillatory regime strongly depend on the Soret parameter M. The thermodiffusion phenomenon considerably affects the heat transfer; the Nusselt number increases with M in the case of the tricellular flow, but it goes through a maximum in the case of monocellular and bicellular flows.     

Natural Convection in a Porous Cavity with Sinusoidal Heating on Both Sidewalls

A numerical study has been performed on buoyancy-induced convection in a square porous cavity. The vertical sidewalls of the cavity are maintained with sinusoidal temperature distribution. The finite volume method is used to numerically solve the nondimensional governing equations. The Brinkman Forchheimer extended Darcy model is used in the present study. The results are analyzed over a range of the amplitude ratio, phase deviation, porosity, and Grashof and Darcy numbers. It is found that the heat transfer rate is increased when increasing the amplitude ratio, porosity, and Darcy number. The nonuniform heating on both sidewalls provides higher heat transfer rate than the nonuniform heating of one wall.     

Analysis of Non-Darcy Models for Mixed Convection in a Porous Cavity Using a Multigrid Approach

This article investigates the performance of two models; namely the Brinkman-Forchheimer Darcy model (BFDM) and the Brinkman-extended Darcy model (BDM), in a problem involving mixed convection in a square cavity filled with a porous medium using the multigrid method. The left and right walls, moving in opposite directions, are maintained at different constant temperatures, while the top and bottom walls are thermally insulated. The transport equations were solved numerically by the finite-volume method on a colocated grid arrangement using a quadratic upwind interpolation for convective kinematics (QUICK) scheme. The influence of the key parameters, namely the Darcy number (Da) and Grashof number (Gr) on the flow and heat transfer pattern is examined. Further, the issue of reliability of the results is addressed. The results demonstrate that BDM over-predicts the momentum and heat transfer rates compared with BFDM, which is in conformity with the fact that the additional term present in the BFDM hinders convective effects. The full approximation storage (FAS) multigrid method achieves considerable acceleration of convergence for the present relatively unexplored problem.     

Steady Mixed Convection in Power-Law Fluids from a Heated Triangular Cylinder

The steady mixed convective transport from a heated triangular cylinder immersed in power-law fluids in an unconfined vertical domain is investigated numerically. Two different configurations of the cylinder are chosen; one when the base of the cylinder is facing the flow and the other when the apex of the triangle is facing the flow. The simulation is performed for: Reynolds number (1 to 35), Richardson number (0 to 2), power law index (0.4 to 1.8) and Prandtl number, 50. The flow and thermal fields are visualized through the streamlines and isotherm contours at the close proximity of the heated object for various Reynolds numbers, Richardson numbers and power law indices. The distributions of the surface pressure coefficient and local Nusselt number provide further insight of the hydrodynamic and thermal characteristics. Finally, the total drag coefficient and average Nusselt numbers on the surface of the cylinder are computed to explore the overall macroscopic behavior of the involved thermo-hydrodynamics. The flow separation is observed to be more when the apex of the cylinder is facing the flow. The average heat transfer, measured in terms of the Nusselt number, and the total drag on the cylinder are also found higher for that configuration.