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.     

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.     

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.     

Effect of Heat Transfer on Natural Convection in a Square Cavity With Two Source Pairs

In this paper, the influence of a small heating source, positioned in the lateral walls of a square cavity, is investigated. Numerical and experimental analyses are performed to investigate natural convection heat transfer in a square cavity heated by hot strips in the side walls. The H side square cavity is filled with air and heated by two hot strips with heights of H/4. The effect of placing the hot strips at two different positions is evaluated. The temperature distribution and the Nusselt numbers at different Rayleigh numbers are experimentally measured using both real-time and double-exposure holographic interferometry. The isothermal patterns obtained through the holographic interferometry are compared with the temperature and velocity fields from a numerical study performed using the finite-volume code Fluent.     

MHD Mixed Convection with Joule Heating Effect in a Lid-Driven Cavity with a Heated Semi-Circular Source Using the Finite Element Technique

A computational fluid dynamics simulation of heat transfer characteristics on the conjugate effect of Joule heating and magnetic field acting normal to the lid-driven cavity with a heated semi-circular source on one wall under constant temperature is investigated. The left wall of the cavity moves in an upward (case I) or downward (case II) direction, and buoyancy forces are also effective. Horizontal walls are adiabatic. The governing mass, momentum, and energy equations along with boundary conditions are expressed in a normalized primitive variables formulation. The finite element method is used in the solution of the normalized governing equations. The study is performed for pertinent parameters such as the Rayleigh number, Hartmann number, and Joule heating parameter. It is found that the average Nusselt number can be decreased with the increasing of the Rayleigh number in the presence of Joule effect. The magnetic field can be a good control parameter for heat transfer and fluid flow.     

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.     

Wind Effect on Combined Convection and Surface Radiation Heat Losses of a Fully Open Cylindrical Cavity With Insulation

Wind effect, of both the wind incidence angle and the wind speed, on convection and surface radiation heat losses of a fully open cylindrical cavity with constant bottom wall temperature was numerically investigated. The impacts of cavity tilt angle and wall temperature were also considered. Temperature contours, velocity contours, and vectors inside and around the cavity were presented. The variations of average convection and radiation heat loss Nusselt numbers Nu_c and Nu_r and percentages of heat losses with related parameters (wind speed, wind incidence angle, tilt angle, and bottom wall temperature) were also shown. In the end, correlations about Nu_c and Nu_r for practical applications were proposed. Results show that compared with no-wind condition, Nu_c under a wind condition is almost always higher except for head-on wind with velocity of 1.5 m/s, while Nu_r is always lower. Nu_c varies slightly, while Nu_r increases rapidly as the bottom wall temperature increases. With the existence of wind, the effect of tilt angle on heat transfer becomes more complex. A critical wind direction close to 30° is detected, which maximizes Nu_c and percentage of convective heat loss. The results also demonstrate that wind speed, wind incidence angle, and tilt angle should be considered simultaneously when analyzing heat transfer inside the cavity under a wind condition.     

Comparison of Mixed Convection in a Square Cavity with an Oscillating versus a Constant Velocity Wall

This article presents a numerical investigation of unsteady laminar mixed convection heat transfer in a two-dimensional square cavity. The cavity is configured such that one of the vertical walls is cooled and slides either with a constant speed or with a sinusoidal oscillation. A portion of the opposite stationery wall is heated by a constant temperature heat source while, the remaining walls of the cavity are thermally insulated. Different configurations of sliding wall movement and a series of Richardson numbers and Strouhal numbers are tested. The results indicate that the direction and magnitude of the sliding wall velocity affect the heat transfer rate. At low Richardson numbers, the average heat transfer rate for the cavity with an oscillating wall is found to be lower compared to that for the cavity with a constant velocity wall. In addition, at a fixed Richardson number, as the Strouhal number decreases the oscillation frequency of average Nusselt number on the vertical walls decreases; however, the oscillation amplitude of average Nusselt number increases.     

封闭方腔自然对流换热的研究

论述和分析了封闭方腔自然对流换热的研究进展,研究了采用商业软件FLUENT对此模拟的方法以及换热规律研究的可行性,所获得的数值模拟结果与研究文献做了对比分析,其模拟结果是正确的,由此表明:采用FLUENT软件通过数值模拟方法不仅能获得封闭腔自然对流换热的结果,还能研究其换热规律,是解决封闭腔自然对流换热的有效工具。     

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.     

Effect of Heat-Generating Solid Body on Mixed Convection Flow in a Ventilated Cavity

The mixed convection flow and heat transfer characteristics inside a square ventilated cavity with a heat-generating solid circular body located at the center have been investigated numerically. The inlet opening is at the bottom of the left wall, while the outlet one is at the top of the right wall, and all the walls of the cavity are considered to be adiabatic. A Galerkin weighted residual finite element method is used to solve the governing equations of mass, momentum, and energy. The behavior of the fluid in the ranges of dimensionless cylinder diameter from 0.1 to 0.6 of the heat generating body, thermal conductivity ratio range from 0.2 to 50 between solid and fluid, and heat generating parameter range from 1 to 5 is described in detail. The medium considered is air with a Prandtl number of 0.71. It is found that the flow and temperature field is strongly dependent on the already-mentioned parameters for the ranges considered. The variation of the mean Nusselt number, the dimensionless average drag force, and the average temperature of the fluid versus Richardson number are presented for these parameters.     

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.     

Mixed Convection Heat Transfer from Tandem Square Cylinders in a Vertical Channel at Low Reynolds Numbers

The fluid flow and heat transfer characteristics around two isothermal square cylinders arranged in a tandem configuration with respect to the incoming flow within an insulated vertical channel at low Reynolds number range (1 ≤ Re ≤ 30) are estimated in this article. Spacing between the cylinders (S) is fixed at four widths of the cylinder dimension (d) and, the blockage parameter (B) is set to 0.25. The buoyancy-aided/opposed convection is examined for the Richardson number (Ri) ranges from ?1 to 1 with a fixed Prandtl number (Pr) of 0.7. The transient numerical simulation for this two-dimensional, incompressible, laminar flow and heat transfer problem is carried out by a finite volume code based on the PISO algorithm in a collocated grid system. The results suggest that the flow remains steady for the entire range of parameters chosen in this study. The representative streamlines, vorticity, and isotherm patterns are presented to interpret the flow and thermal transport visualization. Additionally, the time average drag coefficient (C _D ) as well as time and surface average Nusselt number (Nu) for the upstream and downstream cylinders are determined to elucidate the effects of Re and Ri on flow and heat transfer phenomena.     

Simulation of Thermal Radiation Effects on MHD Free Convection in a Square Cavity Using the Chebyshev Collocation Spectral Method

This article deals with the application of the Chebyshev collocation spectral method (CSM) to the analysis of thermal radiation effects on magnetohydrodynamics free convection in a square cavity. The improved projection scheme, which is based on the spectral methods, is applied to treat the coupling of the velocity and the pressure. The radiative transfer equation is angularly discretized by discrete ordinates method with an SRAP_N quadrature scheme, and then solved by CSM using the same grid system as in solving the flow field. Streamlines, isotherms, and Nusselt number are analyzed for the effects of various parameters, such as inclination angle of the magnetic field, Hartmann number, optical thickness, and scatter albedo.     

Simulation Studies on Buoyancy-Aided Conjugate Mixed Convection With Radiation From a Vertical Plate With Multiple Nonidentical Heat Sources

This paper documents certain salient results of the simulation studies performed on conjugate mixed convection with surface radiation from a vertical electronic board equipped with multiple nonidentical flush-mounted discrete heat sources. Air that is assumed to be radiatively transparent with constant thermophysical properties subjected to the Boussinesq approximation is considered to be the cooling agent. The governing fluid flow and heat transfer equations without the boundary-layer approximations are initially transformed into vorticity-stream function form and are later appropriately normalized. The resulting equations, along with pertinent boundary conditions, are subsequently solved using a finite-volume-based finite-difference method coupled with Gauss–Seidel iterative technique. An extended computational domain has been used to capture the fluid flow and heat transfer adequately employing optimum combination of finer and coarser grids. A computer code is specifically written for the job. Effects of modified Richardson number, surface emissivity, and thermal conductivity on local temperature distribution, peak board temperature, and contributions of mixed convection and radiation in heat dissipation have been clearly elucidated. Two correlations that help in calculation of maximum and average nondimensional plate temperatures have also been developed.     

Mixed Convection and Non-Gray Radiation in a Horizontal Rectangular Duct

Numerical studies for fluid flow and heat transfer in a horizontal rectangular duct are carried out. The flow is considered to be laminar, hydrodynamically and thermally developing. Heat transfer by both forced and natural convection is taken into account. The radiation from the gas is modeled with weighted sum of gray gases (WSGG) model. While considering non-gray radiation with WSGG, the fluid is considered to be a mixture of CO₂ and H₂O. Simulations are carried out with lower wall temperature than the inlet temperature of the gas. The effect of buoyancy and radiation on bulk mean temperature and Nusselt number are studied. The effects of temperature dependent properties are discussed. Comparative studies are carried out among forced convection, mixed convection, gray and non-gray gas radiation. It is found from the simulations that the assumption of gray gas can produce an error of ±10% over a non-gray model with WSGG for the cases studied.     

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.