Convection In Rectangular Enclosure Research Articles

Complex transition of double-diffusive convection in a rectangular enclosure with height-to-length ratio equal to 4: Part II

The paper investigates numerical results of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. The case with the thermal Rayleigh number, RaT=105, the Prandtl number, Pr=1, the Lewis number, Le=2 and height-to-width aspect ratio, A=4 is considered. Effects of the buoyancy ratio of composition to temperature, N, on dynamical behavior, flow structure and heat and mass transfer efficiency are investigated carefully. The present results suggest that with the buoyancy ratio N increasing from 1 to 2, the flow of transition is a complex series of changes from the periodic to quasi-periodic, chaotic, periodic, and finally to laminar with concentration dominated. There are three types of periodic flows, the first one is simple periodic flow with single fundamental frequency (FF), the second one is periodic flow with FF and its integer multiple of frequencies (INTMF), the last one is the more complex periodic flow with FF, INTMF and its sub-harmonic frequency multiple (SFM). A new type periodical solution with reverse central symmetrical structure is captured in the present paper. Multi cells structures traversing between two vertical walls will produce salt figure phenomenon and benefit to enhance heat and mass transfer efficiency.

Rayleigh–Bénard Power-Law Fluid Convection in Rectangular Enclosures

The influences of the aspect ratio (ratio of height to length) on the laminar Rayleigh–Bénard convection of power-law fluids in rectangular enclosures have been numerically investigated for the constant wall heat flux boundary condition for horizontal walls. The steady-state simulations have been conducted for a range of aspect ratios of 0.25 to 4, a nominal Rayleigh number range of to , and a power-law index of 0.6 to 1.8 for a representative single value of the nominal Prandtl number (). It has been found that convective transport weakens with an increasing aspect ratio and thermal conduction dominates thermal transport for tall enclosures. Moreover, the critical Rayleigh number for the onset of convection increases with increasing values of the power-law index and aspect ratio for both shear-thinning and Newtonian fluids. Thermal convection, irrespective of the value of the aspect ratio, has been found to augment with an increasing (decreasing) Rayleigh number (power-law index) due to strengthening of the buoyancy force in comparison to viscous resistance with an increasing Rayleigh number (shear-thinning behavior with decreasing power-law index). The simulations revealed that the flow patterns and mean Nusselt number are dependent on the initial condition, and it is possible to obtain different steady-state solutions for different initial conditions. The numerical findings have been explained with the help of scaling arguments and, in turn, have been used to propose a correlation for the mean Nusselt number.

Hybrid LBM-MRT model coupled with finite difference method for double-diffusive mixed convection in rectangular enclosure with insulated moving lid

This paper presents a numerical study of thermosolutal mixed convection in rectangular enclosure with sliding top lid. The fluid flow is solved by the multiple relaxation time (MRT) lattice Boltzmann method (LBM), whereas the temperature and concentration fields are computed by finite difference method (FDM). The main objective of this study is to investigate the accuracy and the effectiveness of such model to predict thermodynamics for heat and mass transfer in a driven cavity. This model is validated with different numerical methods in the current literature. A good agreement is obtained between our results and previous works. The different comparisons demonstrate the robustness and the accuracy of the proposed approach.

Optical constants effect on laminar natural convection and radiation in rectangular enclosure with one vertical semitransparent wall

Optical constants effect on conjugate laminar natural convection and radiative heat transfer in an air filled rectangular enclosure with one vertical isothermal wall and one vertical semitransparent wall was numerically investigated. The steady-state continuity, Navier–Stokes and energy equations were carried out by the finite volume method, and the Discrete Ordinates Method (DOM) was used to solve the radiative heat transfer equation. Semitransparent radiation effect of vertical wall on laminar natural convection in rectangular enclosure was compared with non-semitransparent for Ra=107 and Pr=0.71. Detailed results including flow profiles, temperature fields, and Nusselt numbers were presented. The influence of optical constants of semitransparent wall on natural convection and radiation heat transfer in enclosure were also solved, considering different refractive indexes and absorption coefficients of semitransparent wall. It is found that optical constants effect of semitransparent wall on laminar natural convection in rectangular enclosure is marked.

Heatfunction Formulation of Thermal Convection in Rectangular Enclosures Filled with Porous Media

Numerical investigations were conducted to study the effects of Rayleigh, Ra, Prandtl, Pr, Darcy, Da, numbers, and the temperature difference ratio, J, on the fluid flow, isotherms, heat transfer, and distributions in a square cavity filled with porous medium. The range of parameters used is 5 × 102 ≤ Ra ≤ 106, 10−3 ≤ Pr ≤ 103, 10−3 ≤ Da ≤ 103, and 0 ≤ J ≤ 2. The flow governing equations including the Brinkman-extended Darcy equations of motion, energy, and heatfunction equations were thereby solved using the finite-difference method. The results show that all the problem governing parameters have strong effect on the convection vigour, isotherms, and heatfunction fields and profiles. An increase in the value of the Darcy number above unity has no more influence on the heatfunction profiles.

Unified Treatment of Natural Convection in Tall Narrow and Flat Wide Rectangular Enclosures

Numerical simulation was used to investigate natural convection in rectangular enclosures ranging in aspect ratio from tall, narrow shapes to flat, wide shapes. For each of the selected aspect ratios, the Rayleigh number was varied over a range of approximately four decades. Two fundamental thermal boundary conditions were considered. One of these, commonly designed as heating from below, involved the imposition of a temperature at the lower bounding wall that is higher than that at the upper bounding wall. The side walls of the enclosure were maintained adiabatic for this case. The second employed boundary condition was side walls at different uniform temperatures and adiabatic upper and lower boundaries. For each aspect ratio and for both types of boundary conditions, the onset of natural convection from the regime of pure conduction occurred at a definitive value of the Rayleigh number, termed the critical Rayleigh number. Once that threshold value was exceeded, the Nusselt number increased markedly with increasing Rayleigh number, the sharpness of the increase being greater for the bottom-heated case. For that case and for aspect ratios (height/width) greater than one, the breakdown of a flow pattern characterized by a single recirculation zone caused a sudden halt to the increase of the Nusselt number. This breakdown was followed by a rapid reformation of the flow pattern into a pair of recirculation zones, one situated above the other. The critical Rayleigh number was insensitive to the aspect ratio for flat, wide enclosures but, on the contrary, the critical value increased markedly with increasing aspect ratio for tall, narrow enclosures. In general, a critical Rayleigh number for the bottom-heated case exceeded that for the side-heated case by a factor of 12.

Numerical simulation of double diffusive natural convection in rectangular enclosure in the presences of magnetic field and heat source

Double-diffusive convective flow in a rectangular enclosure with the upper and lower surfaces being insulated and impermeable is studied numerically. Constant temperatures and concentration are imposed along the left and right walls of the enclosure. In addition, a uniform magnetic field is applied in a horizontal direction. Laminar regime is considered under steady state condition. The transport equations for continuity, momentum, energy and spices transfer are solved. The numerical results are reported for the effect of thermal Rayleigh number, heat generation or absorption coefficient and the Hartmann number on the contours of streamline, temperature, and concentration as well as the dimensionless density. In addition, the predicted results for the average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for constant aspect ratio A = 2 , Lewis number Le = 1 and Prandtl number Pr = 0.7 . The study covers ranges for 10 3 ⩽ Ra T ⩽ 10 6 , 0 ⩽ Ha ⩽ 200 , − 50 ⩽ ϕ ⩽ 25 and − 10 ⩽ N ⩽ 10 .

Numerical Investigation of Laminar Natural Convection in Rectangular Enclosures of Porous Media

In this investigation, steady tow-dimensional natural convective heat transfer in rectangular porous cavity, (heated from below) with horizontal walls heated to uniform but different temperatures and adiabatic sides has been studied numerically. The numerical results of heat transfer rates are presented for porous Rayleigh numbers (Ra*), based on width of cavity, in the range (Ra*≤500), with layer aspect ratios (Ar), (height / width) ranging between (0.5≤Ar≤5). Plots of streamlines and isotherms to show the behavior of the flow and temperature distribution are presented. The current study shows that the Nusselt number is a strong function of the porous Rayleigh number, and the geometry of the cavity is represented by aspect ratios. Porous Rayleigh number has a large effect on the flow field, whereas any increase in (Ra*) results in changing the flow pattern from unicellular to multicellular flow. Correlation equation has been obtained to show the dependence of Nusselt number on the porous Rayleigh number, and aspect ratio (Ar), as this correlation will be beneficial in design of systems of thermal insulators in the energy storage engineering applications.

Forced convection in ducts with a boundary condition of the third kind

'Song, M., and Viskanta, R., Convection Flow and Heat Transfer Between a Fluid Layer and an Anisotropic Porous Layer within a Rectangular Enclosure, Heat Transfer in Enclosures, American Society of Mechanical Engineers, HTD-Vol. 177, 1991, pp. 1-12. Arquis, E., Caltagirone, J. P., and Langlais, C., Convection in Cavities Partially Filled with Permeable Porous Materials, Proceedings of the 8th International Heat Transfer Conference, Vol. 5 (San Francisco, CA), 1986, pp. 2653-2658. Beckermann, C., Ramadhyani, S., and Viskanta, R., Convection Flow and Heat Transfer Between a Fluid Layer and a Porous Layer Inside a Rectangular Enclosure, Journal of Heat Transfer, Vol. 109, May 1987, pp. 363-370. Tong, T. W., and Subramanian, E., Convection in Rectangular Enclosures Partially Filled with a Porous Medium, International Journal of Heat and Fluid Flow, Vol. 7, March 1986, pp. 310. Sathe, S. B., Tong, T. W., and Faruque, M. A., Experimental Study of Natural Convection in a Partially Porous Enclosure, Journal of Thermophysics and Heat Transfer, Vol. 1, 1987, pp. 260-267. Ozoe, H., Sayama, H., and Churchill, S. W., Convection in an Inclined Square Cavity, International Journal of Heat and Mass Transfer, Vol. 17, 1974, pp. 401-406. Prasad, V., Lauriat, G., and Kladias, N., Non-Darcy Natural Convection in a Vertical Porous Cavity, Heat and Mass Transfer in Porous Media, Elsevier, New York, 1992, pp. 293-314.

Oscillatory Natural Convection in Rectangular Enclosures Filled With Mercury

Lately, natural convection in low Prandtl number (Pr) fluids has gained importance because of growing interest in the transport phenomena in crystal growth processes. It is known that some of the undesirable striations encountered in crystals grown from the melt are caused by thermal instabilities associated with natural convection in the melt. In a typical crystal growth configuration the container aspect ratio Ar (depth/length ratio) is not very small (typically 0.1 to 1) nor is the width ratio Wr (width/depth ratio) very large (typically 1 to 10), so the instability is expected to be influenced by the parameters Ar and Wr. Thus the objective of the present work is to investigate experimentally the effects of Ar and Wr on the onset of thermal instability and the oscillation phenomenon.

Steady, Two-Dimensional, Natural Convection in Rectangular Enclosures With Differently Heated Walls

Numerical results are presented for steady natural convection in two-dimensional rectangular enclosures in which the side walls, top wall, and bottom wall are at uniform temperatures θs, θt, and θb, respectively, and θs > θt > θb. Raylight numbers ranging from 104 to 107 and aspect ratios of 1 and 1.5 were investigated. The top wall was modeled as an impermeable rigid surface or an impermeable free-moving boundary. The calculations reveal two flow regions. In the upper part of the enclosure two large counterrotating cells appear, separated by a descending plume of fluid. Near the bottom wall the flow is almost motionless and stably stratified. The temperature in the central portion of the enclosure is almost uniform due to mixing by the recirculating cells. A temperature inversion occurs near the top wall and is particularly noticeable at high Rayleigh numbers. At high Rayleigh numbers the flow breaks up into smaller cells. The result is that each main recirculation region develops a secondary counterrotating eddy within it. The condition of a free surface as the top wall boundary condition significantly affects the circulation and heat transfer throughout the flow domain. Numerical experiments reveal the extent to which the flow field in the enclosure is affected by an asymmetric specification of side-wall temperature boundary conditions.

Effect of Stabilizing Thermal Gradients on Natural Convection in Rectangular Enclosures

An experimental investigation is described of the effect of stabilizing thermal gradients on natural convection in silicone oils in rectangular enclosures with different aspect ratios. The Prandtl numbers are of the order of 105, Grashof numbers range up to 20, and the aspect ratios are 1 and 3. The thermal boundary conditions are established by imposing different temperatures on opposite walls of the enclosure so that there is simultaneous horizontal and vertical heat flow. The effect of stabilizing temperature gradients on flow established by horizontal gradients and the effect of horizontal temperature gradients on a stably stratified fluid are studied for ranges of the parameters. Streamline patterns are observed at steady-state and velocity profiles are calculated from streamline data and extrapolated with approximate theoretical calculations. It is found that the flow generated by a horizontal gradient is retarded by a stabilizing thermal gradient. The reduction is shown as a function of the relevent parameters. For the range of variables investigated complete stabilization of the fluid driven by a horizontal gradient does not seem possible by means of a vertical gradient. The steady state flow patterns obtained do not depend on the manner in which the flow is started, i.e., on the order in which the temperature differences are imposed.

Three-Dimensional Numerical Analysis of Transient Natural Convection in Rectangular Enclosures

A simple numerical technique of considerable practical utility for the solution of transient multidimensional natural convection problems is described. It is based on the solution of the conservation equations in primitive form. The technique can be extended to calculation of natural convection problems in porous media and in turbulent flows where the eddy viscosities and conductivities can be predicted. It has been applied to the solution of several two and three-dimensional natural convection problems. The solutions compare well with the numerical and experimental results published by other investigators.