Natural convection in porous cavity with sinusoidal bottom wall temperature variation

Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20–500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment.     

Investigation of a large top wall temperature on the natural convection plume along a heated vertical wall in a square cavity

The characteristics of the laminar natural convection in an air-filled square cavity heated and cooled on the side walls was studied for cases where the temperature of the top wall was significantly larger than the heated vertical wall. Experiments were performed for a horizontal Grashof number of 1.3 × 10⁸, and non-dimensional top wall temperatures from 1.4 to 2.3. The results show that the plume formed on the heated vertical wall separated from this wall before reaching the top wall. As a result, three different regions were observed in the cavity: a stratified core region, a buoyant plume region, and a highly stratified region above the plume after it had separated from the vertical wall. The highly stratified region above the plume became larger and more stable with an increase of the top wall temperature, stabilizing the motion of the plume across the cavity. The similarity solutions developed by Kulkarni et al. [A.K. Kulkarni, H.R. Jacobs, J.J. Hwang, Similarity solution for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium, Int. J. Heat Mass Transfer 30 (1987) 691–698] to characterize the natural convection heat transfer along an isothermal single vertical plate did not agree with the results for the current measurements; however, the non-similarity model of Chen and Eichhorn [C.C. Chen, R. Eichhorn, Natural convection from a vertical surface to thermally stratified fluid, J. Heat Transfer 98 (1976) 446–451] was in good agreement over most of the wall. There were some discrepancies in the temperature distributions and the heat transfer characteristics, especially at y/H ? 0.8 due to the separated flow in this region.     

Weakly non-linear stability of stratified natural convection in a vertical cavity with lateral temperature gradient

Stability of free convection is examined in a vertical cavity with a fixed lateral temperature difference on the walls, which is also heated from the bottom by a constant heat flux causing vertical stratification of the base flow. Weakly nonlinear stability equations are derived, under the assumption of fully developed flow conditions. Critical Rayleigh numbers and Landau coefficients are determined in terms of the Prandtl number and stratification parameter. It is found that critical disturbances are always two-dimensional, for stationary and oscillating instabilities as well. Alternatives are considered for the calculation of the Landau coefficient. Analysis reveals that unstationary instability is the preferred mode at the codimension point.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one-, two- and three-undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one, two and three undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Laminar natural convection in an inclined cavity with a wavy wall

In the present work, a numerical study of the effect of a hot wavy wall of a laminar natural convection in an inclined square cavity, differentially heated, was carried out. This problem is solved by using the partial differential equations, which are the vorticity transport, heat transfer and stream function in curvilinear co-ordinates. The tests were performed for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. Two geometrical configurations were used namely one and three undulations.The results obtained show that the hot wall undulation affects the flow and the heat transfer rate in the cavity. The mean Nusselt number decreases comparing with the square cavity. The trend of the local heat transfer is wavy. The frequency of the latter is different from the undulated wall frequency.     

Magnetohydrodynamic co-rotating flow in a vertical cylindrical container

ABSTRACT

The effect of an external axial magnetic field on the liquid metal flow produced by co-rotation of the top and bottom disks in a vertical cylindrical container with a vertical temperature gradient is numerically analyzed. The governing Navier–Stokes, energy, and potential equations along with appropriate boundary conditions are solved using the finite-volume method. Comparisons with the previous results were performed and found to be in excellent agreement. It was observed that the Reynolds number is increased, and the axisymmetric basic state loses stability for circular patterns of axisymmetric vortices and spiral waves. In the mixed convection case the axisymmetric mode disappears, giving an asymmetric mode m = 1. It was also found that the primary thresholds, Re_cr corresponding to modes m = 1 and 2, increase with an increase in Hartmann number (Ha). We can therefore conclude that when the magnitude of the magnetic field exceeds a certain value, the instability becomes a steady bifurcation. Finally, stability diagrams were established according to the numerical results of this investigation. These diagrams show the evolution of primary thresholds as a function of Hartmann number for various values of Richardson number.     

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.     

Magnetohydrodynamic natural convection in trapezoidal cavities

A computational numerical work has been done to see the effects of magnetic field on natural convection for a trapezoidal enclosure. Both inclined walls and bottom wall have constant temperature where the bottom wall temperature is higher than the inclined walls. Top wall of the cavity is adiabatic. To investigate the effects, finite element method is used to solve the governing equations for different parameters such as Rayleigh number, Hartmann number and inclination angle of inclined wall of the enclosure. It is found that heat transfer decreased by 20.70% and 16.15% as φ increases from 0 to 60 at Ra = 10⁵ and 10⁶ respectively. On the other hand, heat transfer decreased by 20.28% and 13.42% as Ha increases from 0 to 50 for Ra = 10⁵ and 10⁶ respectively.     

Some transformations for natural convection on a vertical flat plate embedded in porous media with prescribed wall temperature

This study analyzes transformation for boundary layer equations for two-dimensional steady natural convection along a vertical flat plate embedded in porous media. Three different boundary conditions (uniform, power law, and exponential variation), which result in different wall temperature, are identified and processed. Based on the distance along flat plate, governing equations after transformation divide the flow pattern into three subregions. These three subregions characterize the distinct relationship among patterns for pure fluid flow, non-Darcian flow expressed in nonsimilar equations, and pure porous flow. It is also found that similarity solution exists for the whole flow region as the wall temperature distribution is in linear variation and the inertia resistance is without consideration.     

Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall

Double — diffusive natural convection in fluid saturated porous medium has been investigated using a generalised porous medium model. One of the vertical walls of the porous cavity considered is subjected to convective heat and mass transfer conditions. The results show that the flow, heat and mass transfer become sensitive to applied mass transfer coefficient in both the Darcy and non-Darcy flow regimes. It is also observed that the Sherwood number approaches a constant value as the solutal Biot number increases.     

Heat transfer by thermosolutal natural convection in a vertical composite fluid-porous cavity

Double diffusive natural convection of a binary fluid is studied in a rectangular enclosure partially filled with a porous matrix. The study is focused on the influence of the porous layer permeability on the overall heat transfer. The numerical results show that the convective flow structure, and consequently the heat transfer, results from a complex interaction between the viscous drag in the porous layer and the driving force enhancement due to the flow penetration.     

Flow visualization of natural convection in a tall,air-filled vertical cavity

Natural convection of air in a tall vertical cavity was studied using a smoke patterns and interferometry. Experiments covered Rayleigh numbers of 4850 < Ra < 54,800 and aspect ratio A ≈ 40. Secondary cells were noted at Ra as low as 6228. The flow was stable at Ra < 10⁴. As Ra exceeded 10⁴ the flow became irregular, the core flow became increasingly unsteady and 3-D motion became evident. Interferometry showed that most of the temperature drop exists in boundary layers near the walls. The core is well mixed and of relatively uniform temperature with little or no vertical stratification.     

Free convection in a vertical cylindrical enclosure

The problem of transient natural convection which occurs in a vertical cylinder opened at both ends, filled with a fluid saturated porous medium and heated with a periodical lateral heat flux density is outlined. The present study is carried out by the use of the Darcy flow model, and it assumes local thermal equilibrium between the solid and fluid phases. The wall heat conduction is taken into account. Numerical simulations provide us with the evolution of flow and temperature fields within the cylinder. The analysis of flow and thermal field response to any changes in the period of heat pulsation values, the ratio of the wall thermal diffusivity to the porous medium thermal diffusivity and the thickness of the wall are reported in the course of this study.     

Cooling of cylindrical vertical tanks submitted to natural internal convection

A numerical and an experimental analysis of velocity and temperature fields inside a storage tank submitted to natural convection is presented. The analysis was performed in two stages. In the first stage, the temperature profile along the vertical axis of the storage tank was obtained experimentally and numerically, for cooling time ranging from 45 to 60 h. The numerical analysis was carried out using a transient bi-dimensional model in cylindrical co-ordinates. In the second stage, after the numerical code validation, 40 cases of cooling with four aspect ratios, five insulation thicknesses, and two different volumes were simulated. In all simulations, thermal losses for the environment in all tank walls (side, top and bottom) were considered. Two correlations for the Nusselt number, encompassing all the forty cases, were obtained with these results.     

Transient natural 2D convection in a cylindrical cavity with the upper face cooled by thermoelectric Peltier effect following an exponential law

The present study is based on a numerical calculation involving the finite volume method. The transient 2D natural convection in vertical cylindrical cavities is addressed.Two cases have been examined. First we study the case of an adiabatic air-filled cavity whose upper face is submitted to a cooling following an exponential law observed experimentally, imposed by a Peltier’s module. Furthermore, we study the convection in an insuline-filled cylindrical cavity whose partition has a very weak thermal resistance.Space–time evolutions of temperature and velocity are presented, with the influence of the main representative parameters of the investigation. Local and mean thermal exchanges have been calculated, and we propose a Nusselt–Rayleigh type relation.The aim of this study is to determine the heat transfer in a long autonomy isothermal cavity designed for the conservation of insulin cartridges or any other product.     

A numerical investigation of the effect of sinusoidal temperature on mixed convection flow in a cavity filled with a nanofluid with moving vertical walls

The aim of this study is to investigate numerically the effect of sinusoidal temperature on mixed convection flow in a cavity filled with nanofluid and moving vertical walls by using a new temperature function, where thermal heating takes the form of the sinusoidal temperature; and could be found in various natural processes and industries such as solar energy, and cooling of electronic components. The heating is concentrated in the center and then distributed to both ends at different values of Rayleigh numbers, Reynolds numbers, and volumetric fractions of nanoparticles ranging from 1.47 × 10³ to 1.47 × 10⁶, 1 to 100, and 0 to 0.1, respectively. The impact of nanoparticle size on thermal characteristics and hydrodynamics was considered and evaluated. From the results, the volume fraction concentration of nanoparticles affects the flow shape and thermal performance in the case of a constant Reynolds number. Moreover, the effect of nanoparticles decreases with the increase of the Reynolds number. Besides this, with increasing the volume percentage of nanoparticles, the rate of heat transmission increases. It is worth noting that the presence of nanoparticles results in height convective heat transfer coefficient. On the other hand, the thickness of thermal boundary layers decreases with increasing Rayleigh number. The current investigation found that the (sinusoidal) temperature change significantly affects heat transfer.     

Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium

The problem of conjugate natural convection about a vertical cylindrical fin with uniform lateral mass flux in a fluid-saturated porous medium has been studied numerically. Solutions based on the third level of truncation are obtained by the local nonsimilarity method. The effects of the surface mass flux, the conjugate convection-conduction parameter, and the surface curvature on fin temperature distribution, local heat transfer coefficient, local heat flux, average heat transfer coefficient, and total heat transfer rate are presented. A comparison with finite-difference solutions for the case of constant wall temperature was made, and found in a good agreement.     

Entropy generation for compressible natural convection with high gradient temperature in a square cavity

Entropy generation due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subjected to different side wall temperatures for compressible and incompressible natural convection flows. Based on the obtained velocity and temperature values, the distributions of local entropy generation, average entropy generation and average Bejan number are determined and compared for compressible and incompressible regimes. It is found that the entropy generated for compressible flow always is more than incompressible flow. The study is performed for Ra = 10⁴–10⁸, ε = 0.01(incompressible regime) and 0.6 (compressible regime), Ge = 10⁻⁵ and Pr = 0.7.