Numerical simulation of double diffusive mixed convection in an open enclosure with different cylinder locations

This article reports numerical simulation of the double diffusive mixed convection around a cylinder in an open enclosure with an inlet and exit ports. The temperature and mass concentration of the cylinder are higher than those of the inlet flow and the cylinder can be at three different locations (lower, middle and upper) in the enclosure. The inlet flow with low temperature and mass concentration is located at the lower-left wall of the enclosure and the exit is at the upper-right wall. Other walls are assumed to be adiabatic. Effects of Lewis number Le, buoyancy ratio Br, and cylinder locations on the double diffusive mixed convection are investigated at Richardson number Ri = 1.0 and 0.01 while Prandtl number Pr is kept at 0.7. Streamlines, isotherms, isoconcentrations, and the average and local Sherwood number at different parameters are reported to characterize the double diffusive mixed convection phenomena in the open enclosure.     

Numerical Simulation of Steady Mixed Convection Around Two Heated Circular Cylinders in a Square Enclosure

In this paper, a numerical study has been carried out to investigate the steady-state mixed convection around two heated horizontal cylinders in a square two-dimensional enclosure. The cylinders are located at the middle of the enclosure height and the walls of the cavity are adiabatic. Streamlines and isotherms are produced and the effects of cylinder diameter, Reynolds number, and Richardson number on the heat transfer characteristics are numerically analyzed. The average Nusselt number over the surface of cylinders and average nondimensional temperature in the enclosure are also presented. The results show that both heat transfer rates from the heated cylinders and the dimensionless fluid temperature in the enclosure increase with increasing Richardson number and cylinder diameter. However, the trend of average Nusselt number and nondimensional temperature variation is completely opposite when Reynolds number increases. In addition, by increasing the cylinders diameter and Richardson number, the left cylinder is less affected by the inlet flow than right one.     

Finite element simulation of mixed convection heat and mass transfer in a right triangular enclosure

A simulation of mixed convection heat and mass transfer in a right triangular enclosure is investigated numerically. The bottom surface of the enclosure is maintained at uniform temperature and concentration that are higher than that of the inclined surface. Moreover, the left wall of cavity moves upward (case 1) and downward (case 2) directions, which have constant flow speed, and is kept adiabatic. The enclosure represents the most common technology utilizing solar energy for desalination or waste-water treatment. A simple transformation is employed to transfer the governing equations into a dimensionless form. A finite-element scheme is used for present analysis. Comparison with the previously published work is made and found to be an excellent agreement. The study is performed for pertinent parameters such as buoyancy ratio, Richardson number and the direction of the sliding wall motion. The effect of aforesaid parameters on the flow and temperature fields as well as the heat and mass transfer rate examined. The results show that the increase of buoyancy ratio enhances the heat and mass transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the direction of the sliding wall motion can be a good control parameter for the flow and temperature fields.     

Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations

In this investigation, a numerical simulation using a finite volume scheme is carried out for a laminar steady mixed convection problem in a two-dimensional square enclosure of width and height (L), with a rotating circular cylinder of radius (R = 0.2 L) enclosed inside it. The solution is performed to analyze mixed convection in this enclosure where the left side wall is subjected to an isothermal temperature higher than the opposite right side wall. The upper and lower enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. Fluid flow and thermal fields and the average Nusselt number are presented for the Richardson numbers ranging as 0, 1, 5 and 10, while Reynolds number ranging as 50, 100, 200 and 300. The effects of various locations and solid-fluid thermal conductivity ratios on the heat transport process are studied in the present work. The results of the present investigation explain that increase in the Richardson and Reynolds numbers has a significant role on the flow and temperature fields and the rotating cylinder locations have an important effect in enhancing convection heat transfer in the square enclosure. The results explain also, that the average Nusselt number value increases as the Reynolds and Richardson numbers increase and the convection phenomenon is strongly affected by these parameters. The results showed a good agreement with further published works.     

Three-Dimensional Numerical Study of Natural Convective Heat Transfer of Liquid in a Cubic Enclosure

ABSTRACT

Steady-state laminar natural convection in a cubic enclosure with a cold vertical wall and two hot square heaters with constant temperature on the opposite wall is studied numerically. The enclosure is filled with various liquids. Three-dimensional Navier–Stokes Equations are solved by employing the SIMPLE algorithm. Computations are performed for a range of Rayleigh number from 10³ to 10⁷ while enclosure aspect ratio varies from 0.05 to 1.6. The effects of Rayleigh number, enclosure aspect ratio, and Prandtl number on heat transfer characteristics are studied in detail. The results show that the flow field is very complex and heat transfer from the two heaters is not the same. The effects of Prandtl number are negligible in the range from 5 to 140 with other parameters kept constant. This allows the use of liquids such as water for studying other dielectric liquids, provided the flow geometry and other nondimensional parameters are similar. The overall Nusselt number increases markedly with Rayleigh number. It is also affected by enclosure aspect ratio. It attains the maximum value when aspect ratio is in the range of 0.1–0.2 and decreases as enclosure aspect ratio varies from 0.2 to 1.6. Also, various settings of cooling face and arrangement of heaters are investigated, and the results show that they have considerable effects on heat transfer of both heaters.     

Finite element simulation of MHD combined convection through a triangular wavy channel

The present paper implements the analysis of magnetohydrodynamic (MHD) combined convective flow and heat transfer characteristics through a triangular wavy vertical channel using the Galerkin weighted residual finite element method. The flow enters at the bottom and exits from the top surface. The wavy vertical walls are at constant temperature and the cold flow enters the channel from the inlet. The numerical model is based on a 2D Navier–Stokes incompressible flow and energy equation. The effects of Grashof number, Reynolds number and Prandtl number on flow and thermal fields are investigated. The variation of local Nusselt number along the vertical walls for the mentioned parameters is also presented. The study reveals that the flow as well as thermal field strongly depends on the aforesaid parameters.     

Numerical Investigation on Natural Convection Inside the Side Ventilated Square Enclosure with Vertical Mid-Partition

A finite volume-based computational study of steady laminar natural convection inside the square enclosure with cold partition wall centrally placed on top and bottom is presented. The fluid considered is air with Prandtl number 0.71. Except the partition walls, all other walls were assumed as hot. The heights of inlet and outlet ports are constantly fixed as 20% of height of the enclosure. The height of the opening in the partition walls were 10%, 20%, and 30% of height of enclosure. The buoyancy-driven heat transfer mechanism inside the domain is influenced by the percentage of opening in the partition, Rayleigh number, and geometrical position of inlet and outlet. The cold partition walls attract the flow that subsequently influences the thermal modifications around the partition. The fluid flow and heat transfer were investigated for 81 cases with different positions of inlet and outlet and varying height of openings for Ra = 10³, 10⁴, and 10⁵. The cross flow between the vertical walls through the opening in the central partition wall was considered in this study. The formation of vortices and their sizes depends on the configuration of inlet and outlet ports. The higher temperature gradient occurs near the inlet and outlet port of vertical walls. Local Nusselt number is maximum just below the inlet for all cases. Due to the dominance of buoyancy forces, heat transfer rate increases when Rayleigh number increases for all the cases. The hydrodynamic block effect by the openings on the partition wall has significant effect on the velocity profile than on the heat transfer.     

Influences of a confined elliptic cylinder at different aspect ratios and inclinations on the laminar natural and mixed convection flows

Numerical investigations were carried out for natural and mixed convection within domains with stationary and rotating complex geometry by using an immersed-boundary method. The method was first validated with flows induced by natural convection in the annulus between concentric circular cylinder and square enclosure, and the grid-function convergence tests were also examined. Natural convection induced by isothermally elliptic cylinder was further investigated for different Rayleigh numbers within the range of 10⁴–10⁶ and the influence of the outer enclosure was also considered. The parameters investigated in the study included Rayleigh number, axis ratio and inclination angle of the elliptic cross-section. Local and average heat transfer characteristics were fully studied around the surfaces of both inner cylinder and outer enclosure. Finally, mixed convection in a square enclosure with an active rotating elliptic cylinder was considered and the heat transfer quantities of the system were obtained for different rotating speeds.     

Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity

The development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom heated open enclosure has been numerically studied. The enclosure considered has rectangular horizontal lower surface and vertical side surfaces. The lower surface is at a uniform temperature T_h while other sides of the cavity along with the channel walls are adiabatic. The governing two-dimensional flow equations have been solved by using Galarkin weighted residual finite element technique. The investigations are conducted for different values of Rayleigh number (Ra), Reynolds number (Re) and Hartmann number (Ha). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt number (Nu), the Drag force (D) and average bulk temperature (θ_av) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity whereas in the channel these effects are less significant.     

Laminar combined magnetoconvection in a wavy enclosure with the effect of heat conducting cylinder

In the current work, a numerical study of the flow characteristics on combined magnetoconvection in a lid-driven square enclosure, differentially heated, is carried out. This problem is solved by using finite element method of the partial differential equations, which are the heat transfer and stream function in Cartesian coordinates. The tests are performed for different solid–fluid thermal conductivity ratio, cylinder location and Richardson number while the Prandtl number, Reynolds number, magnetic and Joule heating parameters are kept constant. One geometrical configuration is used namely two undulations. The outcome obtained shows that the heat conducting inner square cylinder affects the flow and the heat transfer rate in the enclosure. The trend of the local heat transfer is found to follow a wavy pattern. Results are presented in terms of streamlines, isotherms, average Nusselt number at the heated wavy wall, average temperature of the fluid in the enclosure and dimensionless temperature at the cylinder center for different combinations of the governing parameters.     

Hydromagnetic effect on mixed convection in a lid-driven cavity with sinusoidal corrugated bottom surface

The present numerical simulation is conducted to analyze the mixed convection flow and heat transfer in a lid-driven cavity with sinusoidal wavy bottom surface in presence of transverse magnetic field. The enclosure is saturated with electrically conducting fluid. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. In addition, the transport equations are solved by using the finite element formulation based on the Galerkin method of weighted residuals. The implications of Reynolds number (Re), Hartmann number (Ha) and number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail while, Prandtl number (Pr) and Rayleigh number (Ra) are considered fixed. The trend of the local heat transfer is found to follow a wavy pattern. The results of this investigation illustrate that the average Nusselt number (Nu) at the heated surface increases with an increase of the number of waves as well as the Reynolds number, while decreases with increasing Hartmann number.     

Mixed convection from two thermal sources in a vertical porous layer

In this paper the steady mixed convection flow adjacent to a vertical surface embedded in a fluid-saturated porous medium, on which two isolated thermal sources are located is investigated theoretically. The thermal sources are taken as long planar sources of finite height and the resulting two-dimensional flow is numerically studied using the finite volume method. The nature and the basic characteristics of the mixed aiding as well as mixed opposing flows that arise are investigated using the Darcy law model. The governing parameters are the Rayleigh number, Péclet number, separation distance between heated elements, their lengths and heat flux ratio in additional to the external flow direction. These parameters are varied over wide ranges and their effect on the heat transfer characteristics is studied in detail.     

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.     

Acknowledgment

An experimental and numerical study has been carried out in order to investigate mixed and natural convection heat transfer in a two-dimensional enclosure. A discrete isothermal heat source is located at one of the vertical walls. Also, two ventilation ports are at the bottom and on top of the opposite wall. A forced flow condition was imposed by providing an inlet of air at the bottom port. A Mach–Zehnder interferometer was used to visualize the temperature field within the enclosure and to determine the local and average heat transfer characteristics of the heat source. Five heater positions on the vertical wall and different Rayleigh numbers (4.5 × 10⁵ to 1.15 × 10⁶) and Reynolds numbers (120 to 1600) were considered in the experiments. A finite volume code has been developed based on the SIMPLE algorithm and hybrid discretization scheme for the numerical study. It is observed that the interaction of natural convection with the forced flow leads to various flow fields depending on the Richardson number, Reynolds number and the heater position. Also, results show different trends for variation of the average Nusselt number with the heater position at low and high Reynolds numbers. An optimum position for the heat source, at which the maximum heat transfer is achieved, exists for high Reynolds numbers and has been found to be at the middle of the vertical wall.     

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.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

Natural convection between a circular enclosure and an elliptic cylinder using Control Volume based Finite Element Method

In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner elliptic cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both of the circular enclosure and the inner cylinder are maintained at constant temperatures with air filled inside the enclosure. The governing equations are used in their vorticity stream function form to simulate the fluid flow and heat transfer. The numerical calculations are performed for various Rayleigh numbers, the inclination angle of the enclosure and different sizes of inner cylinder. The results show that streamlines, isotherms, and the number, size and formation of the cells inside the enclosure are strongly depend on these parameters which considerably enhance the heat transfer rate.     

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.     

Natural convection in an enclosure with non-uniform wall temperature

A numerical study of natural convection in an enclosure was investigated. The heated wall of the enclosure is divided into two of the higher and lower temperature regions and the temperature of the cold wall is maintained at a constant. The parameters of Rayleigh number and length ratio are mainly considered. The results show that the local Nusselt number distribution varies drastically at the intersection of the higher and lower temperature regions, and the flow is strongly affected by the above two parameters.     

Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure

A computational work has been done to investigate the effects of mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure. Finite difference method is used to solve governing equations of mixed convection for different parameters as Hartmann number, Richardson number, nanoparticle volume rate in partially heated and wavy walled enclosure. It is found that the rate of heat transfer decreases with increasing the Hartmann number. The rate of heat transfer can be enhanced or reduced by increasing the volume fraction of nanoparticles based on Hartmann and Richardson numbers.