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.     

Natural convection heat transfer in partially open inclined square cavities

A numerical study has been carried out on inclined partially open square cavities, which are formed by adiabatic walls and a partial opening. The surface of the wall inside the cavity facing the partial opening is isothermal. Steady-state heat transfer by laminar natural convection in a two dimensional partially open cavity is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10³ to 10⁶, dimensionless aperture size from 0.25 to 0.75, aperture position at high, center and low, and inclination of the opening from 0° (facing upward) to 120° (facing 30° downward). It is found that the volume flow rate and Nusselt number are an increasing function of Rayleigh number, aperture size and generally aperture position. Other parameters being constant, Nusselt number is a non-linear function of the inclination angle. Depending on the application, heat transfer can be maximized or minimized by selecting appropriate parameters, namely aperture size, aperture position and inclination angle at a given operation Rayleigh number.     

Natural convection in an open square cavity with slots

In this paper, we investigate heat transfer by natural convection in an open cavity in which a uniform heat flux is applied to the inside active wall facing the opening with slots. Conservation equations are solved by finite difference–control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to 10⁶, the Prandtl number, Pr = 0.7, constant for air, the cavity aspect ratio, A = L/H = 1. Number of slots N is varied from 2 to 8 and the dimensionless opening ratio OR from 0.1 to 0.6. We found that the Nusselt number and the volume flow rate are both increasing functions of the Rayleigh number; they are a decreasing function of the number of slots and increasing function of the opening ratio, though there is an optimum opening ratio at high Rayleigh numbers.     

Natural convection heat transfer in a partially opened cavity filled with porous media

This paper examines the steady natural convection in a partially opened enclosure filled with porous media using the Brinkman–Forchheimer model. Whilst the part of the left vertical wall of the cavity is heated, the other walls are adiabatic or thermally insulated Based upon numerical predictions, the effects of pertinent parameters such as Grashof number, Darcy number, porosity, length of the heated wall and the location center of the opened cavity are examined. It is found that as the Grashof number increases, due to strengthening buoyancy driven flows, the local Nusselt number from partially heated vertical wall, at a given position on this wall increases. This, in turn, increases the temperature of the heated wall. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Transient natural convection with temperature-dependent viscosity in a square partially porous cavity having a heat-generating source

A numerical study is performed on the transient natural convection with a temperature-dependent viscosity inside a square partially porous cavity with a local heat-generating and heat-conducting source. The vertical walls of the cavity are kept at constant cooling temperature while the horizontal walls are adiabatic. The discrete heat-conducting and heat-generating source is located on the bottom wall. A porous layer is located under the clear fluid layer. Governing equations formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions are solved using implicit finite difference schemes of the second order. The control parameters are the Darcy number, Ostrogradsky number, viscosity variation parameter, height of the porous layer, and dimensionless time. The effects of these parameters on the average Nusselt number along the heat source surface, average temperature of the heater, fluid flow rate inside the cavity, as well as on the streamlines and isotherms are analyzed. The results show that porous layer thickness and viscosity of the working fluid are very good control parameters for optimization of the passive cooling system.     

Natural convection in a square enclosure with a hot source

The aim of this paper is to analyse the convective heat transfer generated by a source with three different heights (ζ). This strip is located in the middle of a square enclosure. In detail the experimental analysis was carried out using holographic interferometry, to study the effect of the heat transfer, and a 2D-PIV system, to analyse the dynamic behaviour of the phenomenon. The comparison is based both on the evaluation of the Nusselt numbers at different Rayleigh numbers and on the study of the velocity fields at the same Rayleigh numbers in different configurations. During the experimental analysis we can see how the height of the strip influences the distribution of the velocity fields and consequently the heat transfer efficiency. Three different heights are analysed: ζ = 0, ζ = 0.25 and ζ = 0.5. The study shows how the natural convective heat transfer worsens with the increase in the source height. This can clearly be seen by analysing the upper side of the strip, which was studied for each geometrical configuration, and is also confirmed by the results on the lateral sides, analysed only for ζ = 0.25 and ζ = 0.5.Finally the experimental data are compared with the results obtained through a numerical simulation performed using the volume finite software, Fluent 6.3.26. The aim of this comparison is to validate the numerical procedure, which is useful for enlarging the Rayleigh number range.     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

Natural convection flow due to a heat source in a vertical channel

An analysis is presented of the laminar natural convection flow due to a localized heat source on the centerline of a long vertical channel or pipe whose walls are kept at a constant temperature. Stationary solutions are obtained for infinitely long and finite length channels, the asymptotic limit of infinite Rayleigh numbers is discussed, and an optimal height of the channel is found leading to maximum mass flux and minimum temperature for a given heat release rate.     

Natural convection in a rectangular cavity with partially active side walls

A numerical study is performed to investigate the effect of aspect ratio on the natural convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature than that of the right side wall. The top and bottom of the cavity and inactive part of the side walls are thermally insulated. Nine different relative positions of the active zones are considered. The equations are discretized by the control volume method with power law scheme and are solved numerically by iterative method together with a successive over relaxation (SOR) technique. The results are obtained for Grashof numbers between 10³ and 10⁵ and the effects of the aspect ratio on the flow and temperature fields and the rate of heat transfer from the walls of the enclosure are presented. The heat transfer rate is high for the bottom–top thermally active location while the heat transfer rate is poor in the top–bottom thermally active location. The heat transfer rate is found to increase with an increase in the aspect ratio.     

Natural convection in a partially porous cavity: Roads to chaos

Abstract

A numerical study of a periodic and chaotic behavior of natural convection in a square cavity, with a porous layer is presented. The cavity under study consists of two opposite vertical walls of which the lower half walls are hot (hold high temperature) and the upper half walls are cold (hold low temperature), whereas the horizontal walls are adiabatic. The porous medium is located in the lower part of the cavity. The natural heat transfer and the Darcy Brinkman equations are solved by using the finite volume method and the TDMA. The results show that thermal natural convection evolves towards a deterministic chaos by following Curry York scenario.     

Natural convection effects on heat and mass transfer in a curvilinear triangular cavity

Finite element method is used in this study to analyze the effects of buoyancy ratio and Lewis number on heat and mass transfer in a triangular cavity with zig-zag shaped bottom wall. Buoyancy ratio is defined as the ratio of Grashof number of solutal and thermal. Inclined walls of the cavity have lower temperature and concentration according to zig-zag shaped bottom wall. Enclosed space consists mostly of an absorber plate and two inclined glass covers that form a cavity. Both high temperature and high concentrations are applied to bottom corrugated wall. Computations were done for different values of buoyancy ratio (?10 ? Br ? 10), Lewis number (0.1 ? Le ? 20) and thermal Rayleigh number (10⁴ ? Ra_T ? 10⁶). Streamlines, isotherms, iso-concentration, average Nusselt and Sherwood numbers are obtained. It is found that average Nusselt and Sherwood numbers increase by 89.18% and 101.91% respectively as Br increases from ?10 to 20 at Ra_T = 10⁶. Also, average Nusselt decreases by 16.22% and Sherwood numbers increases by 144.84% as Le increases from 0.1 to 20 at this Rayleigh number.     

Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid

This paper presents a numerical study of natural convection cooling of a heat source horizontally attached to the left vertical wall of a cavity filled with copper-water nanofluid. The left vertical wall is kept at the constant temperature, while the other ones are kept adiabatic. The numerical approach is based on the finite volume method with a collocated grid arrangement. The SIMPLE algorithm is used for handling the pressure velocity coupling. In this study, the influence of some effective parameters such as: Rayleigh number, location and geometry of heat source and solid concentration are studied and discussed. Results are presented in the form of streamlines, isotherms, and average Nusselt number. The results show that dimension of the heat source is an important parameter affecting the flow pattern and temperature field, so that the average Nusselt number decreases with an increase in the length of the heater. It is also observed that at a given Rayleigh number and definite heat source geometry, the average Nusselt number increases linearly with the increase in the solid volume fraction of nanofluid. The increase of Rayleigh numbers strengthens the natural convection flows which leads to the decrease in heat source temperature. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model.     

Natural convection investigation in square cavity filled with nanofluid using dispersion model

A cooling achieved with compact and efficient device is one of the major challenges encountered in the promising technique of fuel cell stacks. The safe and reliable use of such a system is highly dependent on the efficiency of the assured heat transfer and consequently on the quality of the coolant used. To test the possible improvement of the coolant performances, laminar natural convection in square cavity filled with copper-water nanofluid is numerically carried out taking into account the thermal dispersion effect on the heat transfer intensity. The finite element method is used to solve the governing equations. The hydrodynamic structure of the flow and its thermal behavior are studied for a wide range of Rayleigh numbers. The obtained results showed an enhancement of heat transfer with an increase in nanoparticle volume fraction for all examined Rayleigh numbers. However, it is found that an increase in nanoparticle diameter enhances heat transfer only when thermal dispersion is significant. Correlation with 99.94% confidence coefficient is proposed to quantify the heat transfer intensity according to the Rayleigh number and particle diameter and concentration.     

Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: An experimental study

An experimental study has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosures of different sizes, whose dimensions, width × height × length (mm), are 25 × 25 × 60, 40 × 40 × 90, and 80 × 80 × 180, respectively. The nanofluid formulated in the present experiment is water dispersed with various volumetric fractions of the alumina (Al₂O₃) nanoparticles ranging from 0.1 vol.% to 4 vol.%. The Rayleigh number varies in the range of 6.21 × 10⁵–2.56 × 10⁸. A correlation analysis based on the thermophysical properties of the nanofluid formulated shows that efficacy of applying the nanofluid for natural convection heat transfer enhancement in enclosure is inferred to be generally infeasible. The experimental results for the average heat transfer rate across the three enclosures appear generally consistent with the assessment based on the changes in thermophysical properties of the nanofluid formulated, showing systematic heat transfer degradation for the nanofluids containing nanoparticles of c_v ≥ 2 vol.% over the entire range of the Rayleigh number considered. However, for the nanofluid containing much lower particle fraction of 0.1 vol.%, a heat transfer enhancement of around 18% compared with that of water was found to arise in the largest enclosure at sufficiently high Rayleigh number. Such enhancement cannot be explained simply based on the net influence due to relative changes in thermophysical properties of the nanofluid containing such low particle fraction, thus strongly suggesting other factors may come into play.     

Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation

The effects of an inclined magnetic field and heat generation on unsteady free convection within a square cavity filled with a fluid-saturated porous medium have been investigated numerically. The top and bottom horizontal walls of the enclosure are adiabatic whereas the vertical walls are kept at constant but different temperatures. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite-difference scheme, namely the ADI method (Alternative Direction Implicit), the non-dimensional governing equations are numerically solved. The influential parameters are the Rayleigh number Ra, the inclination angle γ of the magnetic field relative to the gravity vector g, the Hartmann number Ha and the heat generation parameter Q. In the present study, the obtained results are presented in terms of streamlines, isotherms and average Nusselt number along the hot wall. The result shows that with increasing Ha, the diffusive heat transfer become prominent even though the Rayleigh number increases.     

Projection- and characteristic-based operator-splitting simulation of mixed convection flow coupling heat transfer and fluid flow in a lid-driven square cavity

ABSTRACT

Mixed convection flow in a 2D rectangular cavity is simulated by a novel finite element method, namely the projection- and characteristic-based operator-splitting algorithm. In each time step, the Navier–Stokes equations are split as follows: the diffusion part, the convection part by applying operator-splitting method, and the Poisson’s equation by adopting projection method. The implicit diffusion part is solved by the preconditioned conjugate gradient (PCG) method, whereas characteristic method is applied for the convection part in a multistep explicit scheme. The characteristic Galerkin approach is used to solve the energy equation. To validate the model, lid-driven cavity flow and natural convection flow are simulated.