Lattice Boltzmann Method Based Simulation of Natural Convection in Partially Open Enclosure

A thermal lattice Boltzmann method‐based analysis was performed to numerically investigate the heat transfer by natural convection from an enclosure with a large vertical side opening. The height of the opening was less than the enclosure height and the vertical wall opposite to the opening was maintained at constant temperature. A parametric study was carried out for different values of Rayleigh number (Ra) ranging from 10³ to 10⁵ with air as the working fluid for three opening sizes and three opening locations. The Prandtl number was fixed at 0.71 and the enclosure aspect ratio was also fixed at 2 in all calculations. With Boussinesq approximation, the temperature distribution and stream functions in the enclosure were predicted. The profile of the normal velocity component at the opening location was determined. The opening size affects the stratification and recirculation pattern within the enclosure. The average Nusselt number at the heated wall was determined for all cases. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21110     

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.     

Finite element simulation of magnetoconvection inside a sinusoidal corrugated enclosure with discrete isoflux heating from below

A numerical investigation of the steady magnetoconvection in a sinusoidal corrugated enclosure has been performed. In this analysis, two vertical sinusoidal corrugated walls are maintained at a constant low temperature whereas a constant heat flux source whose length is varied from 20 to 80% of the reference length of the enclosure is discretely embedded at the bottom wall. The Penalty finite element method has been used to solve the governing Navier–Stokes and energy conservation equation of the fluid medium in the enclosure in order to investigate the effect of discrete heat source sizes on heat transfer for different values of Grashof number and Hartmann number. The values of the governing parameters are the Grashof number Gr (10³ to 10⁶), Hartmann number Ha (0 to 100) and Prandtl number Pr (0.71). The present numerical approach is found to be consistent and the solution is obtained in terms of stream functions and isotherm contours.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Mixed convection in a square vented enclosure filled with a porous medium

Steady mixed convection flow in a vented enclosure with an isothermal vertical wall and filled with a fluid-saturated porous medium is investigated numerically. The forced flow conditions are imposed by providing an inlet at the bottom surface, and a vent at the top, facing the inlet. 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, and the width of the inlet as a fraction of the height of the square enclosure. These parameters are varied over wide ranges and their effect on the heat transfer characteristics is studied in detail.     

Combination technique for improving natural convection cooling in electronics

The combination of an appropriately placed cross-flow opening and a strategically positioned transversely vibrating plate is proposed as a means of augmenting pure natural convection in a vertical channel. This method is intended to provide a more efficient, reliable, and consumer conscious alternative to conventional techniques for lower power dissipating devices where standard natural convection cooling proves insufficient. Two-dimensional numerical simulations are employed to investigate this combination method using models consisting of a vertical channel containing two rectangular heat sources which are attached to a vertical mounting board, as well as a transversely oscillating plate and a cross-flow opening in the mounting board area between the two heat sources. Varied parameters and geometric configurations are studied. The results indicate the combined effects of the vibrating plate and the opening flow have the potential to cause significant improvement in the thermal conditions over pure natural convection. As much as a 70% improvement in the local heat transfer coefficient from that for a system with a board opening but without a vibrating plate was attained.     

Control of buoyancy-induced temperature and flow fields with an embedded adiabatic thin plate in porous triangular cavities

Natural convection has been performed in an insulated horizontally thin plate embedded in a triangular enclosure filled with fluid saturated porous medium, numerically. Bottom and inclined wall of triangular enclosure are isothermally heated and cooled, respectively. Vertical wall of enclosure is adiabatic. Steady, two-dimensional, laminar governing equations, which are written with Darcy model, were solved with finite-difference method. Calculations are conducted for different lengths and locations of thin plate, different aspect ratios, and Darcy-modified Rayleigh number. Prandtl number was chosen as 0.71. It is observed that the change on plate location in vertical and horizontal axes makes small effect on heat transfer; however flow field and temperature distribution strongly affected from these parameters.     

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.     

Magnetohydrodynamic Natural Convection in a Square Enclosure with Four Circular Cylinders Positioned at Different Rectangular Locations

We deploy a finite volume numerical computation to investigate the two-dimensional hydromagnetic natural convection in a cooled square enclosure in the presence of four inner heated circular cylinders with identical shape. The inner circular cylinders are placed in a rectangular array with equal distance away from each other within the enclosure and moving along the diagonals of the enclosure. All the walls of the enclosure are kept isothermal with temperatures less than that of the cylinders. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. All solid walls are assumed electrically insulated. Simulations are performed for a range of the controlling parameters such as the Rayleigh number 10³ to 10⁶, Hartmann number 0 to 50, and the dimensionless horizontal and vertical distance from the center of a cylinder to center of another cylinder 0.3 to 0.7. The study specifically aims to understand the effects of the location of the cylinders in the enclosure on the magnetoconvective transport, when they moved along the diagonals of the enclosure. It is observed that the unsteady behavior of the flow and thermal fields at relatively larger Rayleigh numbers and for some cylinder position are suppressed by imposition of the magnetic field. The heat transfer strongly depends on the position of the cylinders and the strength of the magnetic field. Hence, by controlling the position of the objects and the magnetic field strength, a significant control on the hydrodynamic and thermal transport can be achieved.     

Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses

Entropy generation due to conjugate natural convection heat transfer and fluid flow has been studied inside an enclosure with bounded by two solid massive walls from vertical sides at different thicknesses. Enclosure is differentially heated from vertical walls and horizontal walls are adiabatic. Governing equations which are written in streamfunction-vorticity form solved by finite difference technique for the governing parameters as Rayleigh number, 10³ ≤ Ra ≤ 10⁶, length ratio of solid walls as ₁ (for left vertical wall) and ₂ (for right vertical wall) and thermal conductivity ratio of solid to fluid (k), 1 ≤ k ≤ 10. Entropy generation contours due to fluid friction and heat transfer irreversibility, isotherms, streamlines, Nusselt numbers and velocity profiles were obtained. It is found that entropy generation increases with increasing of thermal conductivity ratio and thicknesses of the walls. Entropy generation due to heat transfer is more significant than that of fluid flow irreversibility for all values of thickness of the solid vertical walls.     

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.     

Conjugate natural convection in an enclosure with a heat source of constant heat transfer rate

A numerical study of two-dimensional transient natural convection in a rectangular enclosure having finite thickness heat-conducting walls with a heat source of constant heat transfer rate located on the inner side of the left wall in conditions of convection–radiation heat exchange with an environment on one of the external boundaries has been performed. Mathematical simulation has been carried out in terms of the dimensionless variables such as stream function – vorticity – temperature. Stream function, vorticity and energy equations have been solved by finite difference numerical method. The relevant governing parameters were: the Grashof number from 10⁶ to 10⁸, the Prandtl number, Pr = 0.7 and the conductivity ratio. Detailed results including streamlines and temperature profiles have been obtained.     

An experimental study of the generation and characteristics of a two-layer thermally stable environment

An experimental system has been developed to generate a thermally stratified, two-layer, environment in an enclosure, with air as the fluid. Such a stably stratified circumstance, in which an essentially isothermal heated layer overlies a relatively cooler isothermal layer, frequently arises in several practical problems such as those related to heat rejection, heat transfer from isolated thermal sources in confined regions, and enclosure fires. A detailed study of the thermal field is carried out to determine the basic characteristics of the stratified environment and the dependence of the physical parameters such as interface location and temperature level on the governing variables. The location of the interface, between the two layers can be controlled by varying the temperature and the velocity of the heated fluid discharged at the top of the enclosure for stratifying the enclosed region. It is found that the interface moves down as the Richardson number Ri, based on the conditions of the heated air entering at the top of enclosure, is increased. The stratification can be maintained essentially constant with time. Also, the temperature levels in the two zones can be varied over fairly wide ranges to simulate practical circumstances. The nature of such a stably stratified region is studied, particularly the effect of the inflow and outlet conditions.     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure

In this paper, numerical simulations of laminar, steady, two-dimensional natural convection flows in a square enclosure with discrete heat sources on the left and bottom walls are presented using a finite-volume method. Two different orientated wall boundary conditions are designed to investigate the natural convection features. The computational results are expressed in the form of streamlines and isothermal lines for Rayleigh numbers ranging from 10² to 10⁷ in the cavity. In the course of study, a combination of third-order and exponential interpolating profile based on the convective boundedness criterion is proposed and tested against the partially heated cavity flow up to the highest Rayleigh number 10⁷. The effects of thermal strength and heating length on the hydrodynamic and thermal fields inside the enclosure are also presented. Numerical results indicate that the average Nusselt number increases as Rayleigh number increases for both cases. Moreover, it is seen that the effect of the heat transfer rate due to the heating strength on the left wall is different from the one on the bottom. For the heater size effect, it is observed that by increasing the length of heat source segment, the heat transfer rate is gradually increased for both cases.     

Brownian motion of nanoparticles in a triangular enclosure with natural convection

This paper presents the results of a numerical study on the natural convection in a right triangular enclosure, with a heat source on its vertical wall and filled with a water–CuO nanofluid. The effects of parameters such as Rayleigh number, solid volume fraction, heat source location, enclosure aspect ratio and Brownian motion on the flow and temperature fields as well as the heat transfer rate, are examined. The results show that when Brownian motion is considered in the analysis, the solid volume fraction, the heat source location and the enclosure aspect ratio affect the heat transfer performance differently at low and high Rayleigh numbers. At high Rayleigh numbers, an optimum value for the solid volume fraction is found which results in the maximum heat transfer rate. This is in contradiction to the results of the analysis in which Brownian motion is neglected.     

Effects of Heating Location and Size on Natural Convection in Partially Heated Open-Ended Enclosure by Using Lattice Boltzmann Method

Natural convection heat transfer in an square enclosure, consisting of a partially heated west wall with east end open to ambient, is investigated numerically by using an in-house computational fluid dynamics solver based on thermal lattice Boltzmann method. In particular, the influences of Rayleigh number (10³–10⁶), heating location (bottom, middle, and top) on west wall, and dimensionless heating length (0.25–0.75) on momentum and heat transfer characteristics of air are presented and discussed. The streamline patterns show bifurcation at the lowest Rayleigh number for bottom and middle heating, whereas at the highest Rayleigh number, all heating positions yield bifurcation and elongation of flow patterns with a secondary vortex near the lower side of open end. The middle and bottom heating locations show a linear increase in Nusselt number with heater size, whereas inverse dependence is seen for top heating. The maximum heat transfer is observed in the case of middle heating. As expected, average Nusselt number increased with increasing Rayleigh number. Finally, the functional dependence of the average Nusselt number on flow governing parameters (Rayleigh number and heating length) for different heating locations is presented as a simple predictive empirical relationship.     

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.     

A Study of Free Convection Induced by a Vertical Wavy Surface with Heat Flux in a Porous Enclosure

Free convection induced by a vertical wavy surface with uniform heat flux in a porous enclosure has been analyzed numerically using the finite element method (FEM). The flow and the convection process in the cavity is found to be sensitive to the flow parameter Rayleigh number (Ra), and geometrical parameters like wave amplitude (a), wave phase (φ), and number of waves (N) in the vertical dimension of the cavity. The study reveals that small sinusoidal drifts from the smoothness of a vertical wall with a phase angle of 60^o and high frequency enhances the free convection from a vertical wall with uniform heat flux.