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.     

Performance of plastic solar air heating collectors with a porous absorber

The thermal performance of solar air heaters consisting of a porous textile absorber between two PVC foils has been investigated. The efficiency of the heaters depends strongly on the characteristics of the textile forming the absorber and on the back insulation. For an incident solar radiation of 687 W/m² at the collector's surface, a temperature rise of 16-6°C in the air flowing through the solar collector at a rate of 800 m³/h, was achieved, thus yielding an efficiency of nearly 71 percent. Further it was found that the linear approximation for the Hottel-Bliss equation leads to erroneous estimations for the collector's parameters when the absorber is porous; for the same type of collector with a denser textile as absorber, however, such an approximation yields, as usual, correct numerical values for the characteristic parameters of the collector.     

Natural convection in right-angle porous trapezoidal enclosure partially cooled from inclined wall

A numerical study is conducted to investigate the steady free convection flow in a two-dimensional right-angle trapezoidal enclosure filled with a fluid-saturated porous medium. The left vertical wall of the cavity is heated; the inclined wall is partially cooled; and the remaining walls are insulated (adiabatic). Three different cases are considered. While in Case I the cooler wall is located adjacent to the top wall, in Case II it is located in the middle inclined wall. In Case III, it is located adjacent to the bottom wall. Flow and heat transfer characteristics are studied for a range of parameters: the Rayleigh number, Ra, 100 ≤ Ra ≤ 1000; and the aspect ration, AR = 0.25, 0.50 and 0.75. Numerical results indicate that there exist significant changes in the flow and temperature fields as compared with those of a differentially heated square porous cavity. These results lead, in particular, to the prediction of a position of minimum heat transfer across the cavity, which is of interest in the thermal insulation of buildings and other areas of technology.     

Natural convection in porous triangular enclosures with a solid adiabatic fin attached to the horizontal wall

A numerical analysis has been performed to investigate the effects of fin location onto the bottom wall of a triangular enclosure filled with porous media whose height base ratio is 1. The temperature of the bottom wall is higher than that of the inclined wall while the vertical wall is insulated. Thus, the fin divides the heated bottom wall to two separate regions. Finite difference method was applied to solve governing equations which are written using Darcy method. Solutions of algebraic equations were made by Successive Under Relaxation (SUR) technique. The effective parameters on flow and temperature fields are: Rayleigh number, location center of fin, dimensionless fin height, and dimensionless fin width. The obtained results indicated that the fin can be used as a control element for heat transfer and fluid flow.     

Natural convection with coupled mass transfer in porous media

For certain types of packed beds used for thermal energy storage, high discharge rates can be achieved if the effective conductance is increased over that achievable with stagnant gases and liquids. A packed bed containing a fluid mixture with one condensing component and with the fluid mixture simultaneously convecting may achieve the required high conductances.An analogy has been developed with a similar system with no coupled mass transfer. It provides some useful insights into the role of gas/vapour mixture properties on the effective conductivity of such systems, and suggests that very large increases in effective conductivity are achievable.     

Natural convection in a square porous annulus

The current study is focused to investigate the natural convective heat transfer characteristics in a porous square annulus. Finite element method is used as a tool to simplify the partial differential equations that govern the heat and fluid flow characteristics inside the porous medium. A simple three noded triangular element is used to divide the porous domain into smaller segments known as elements. The algebraic set of equations resulting from the finite element equation are assembled into a global matrix and then solved iteratively to get the solution variables. Thermal equilibrium as well as non equilibrium in porous domain is considered. The effect of various geometric and physical parameters are investigated. The boundary conditions are such that the inner walls of the annulus are heated isothermally to temperature T_h, and the outer surfaces are exposed to cool temperature T_c. The width ratio defined as the ratio of hollow portion to the length of the cavity is varied from 0.125 to 0.875. Results are discussed with respect to width ratio, Rayleigh number, radiation parameter and viscous dissipation parameter.     

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.     

Natural convection flow visualization in porous media

Flow visualization experiments were conducted in water saturated porous media in a rectangular cavity heated from the vertical walls. Two different glass (6 mm and 12mm) beads were used. In general, the natural convection currents were found to be weak in the presence of smaller glass beads. When both the wall temperatures were above the density inversion temperature of water (4°C), unicellular flow was observed. The flow was bicellular when one of the walls of the cavity was below and the other was above 4°C. When both the wall temperatures were below 4°C, the flow could not be visualized for the effects of diffusion were stronger than convection.     

Natural convection in a concentric annulus with a porous sleeve

Analytical solutions obtained through perturbation method and Fourier transform are presented for natural convection in concentric cylinders with a porous sleeve. The porous sleeve is press-fitted to the inner surface of the outer cylinder. Both the inner and outer cylinders are kept at constant temperatures with the inner surface at a slightly higher temperature than that of the outer. The main objective of the present study is to investigate the buoyancy-induced flow as affected by the presence of the porous layer. A parametric study has been performed to investigate the effects of Rayleigh number, Darcy number, porous sleeve thickness, and relative thermal conductivity on the heat transfer results.     

Natural convection in a thin horizontal porous annulus

The possible modes of time-dependent natural convection in a horizontal annulus of finite length are considered. The annulus is filled with porous material and the annular thickness is assumed small in comparison with the mean radius. All boundaries are impermeable and adiabatic; heating is through a circumferentially distributed volumetric heat source. The governing equations reduce to a set of two non-linear ordinary differential equations. Steady non-linear oscillations exist for the special case of infinite Rayleigh number and symmetric heating about the vertical. For lower Rayleigh numbers, damped oscillations are obtained, the degree of damping increasing with the inclination of the line of symmetry and with decreasing Rayleigh number. Multiple stable steady states are obtained for small inclinations. Chaotic motions do not develop for non-inertial Darcy flows.     

Natural convection along a vertical porous surface

This paper describes an experimental study on natural convection along a vertical porous surface consisting of a bank of parallel plates with constant gaps. Compared with a smooth surface, the heat transfer for a porous surface with streamwise gaps is somewhat enhanced owing to enthalpy transport due to flow within the gaps and that with spanwise gaps is enhanced due to the leading- and trailing-edge effects of solid-phase micro surfaces. Observations show that no clear transition to turbulent flow occurs at a critical Rayleigh number for a smooth surface and that the boundary layer oscillates with a dominant frequency at higher Rayleigh numbers. The dominant frequency for a porous surface is nearly the same as that for a smooth surface. This fact obviously indicates that the oscillations of natural convection are almost independent of the porous structure of the heating surface and are mainly dependent on the behavior of the outer boundary layer. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 385–397, 1997     

Natural convection in porous triangular enclosure with a centered conducting body

A numerical work was performed to examine the heat transfer and fluid flow due to natural convection in a porous triangular enclosure with a centered conducting body. The center of the body was located onto the gravity center of the right-angle triangular cavity. The Darcy law model was used to write the governing equations and they were solved using a finite difference method. Results are presented by streamlines, isotherms, mean and local Nusselt numbers for the different parameters such as the Rayleigh number, thermal conductivity ratio, and height and width of the body. It was observed that both height and width of the body and thermal conductivity ratio play an important role on heat and fluid flow inside the cavity.     

Natural convection flows in porous trapezoidal enclosures with various inclination angles

Simulations were carried out using penalty finite element analysis with bi-quadratic elements to investigate the influence of uniform and non-uniform heating of bottom wall within a trapezoidal enclosure of various inclination angles $(\phi )$. Parametric study has been carried out for a wide range of Rayleigh number $(\mathit{Ra})({10}^3?\mathit{Ra}?{10}^6)$, Prandtl number $(\mathit{Pr})(0.026?\mathit{Pr}?988.24)$ and Darcy number $(\mathit{Da})({10}^{-3}?\mathit{Da}?{10}^{-5})$. Numerical results are presented in terms of stream functions, isotherm contours and Nusselt numbers. The heat transfer is primarily due to conduction at lower values of Darcy number $(\mathit{Da})$ and convection dominant heat transfer is observed at higher Da values. The intensity of circulation increases with increase in Darcy number. Increase in the intensity of circulations and larger temperature gradient are also observed with increase in $\phi$ from 0° to 45° especially at larger Pr and Ra. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating at all Rayleigh and Darcy numbers, but average Nusselt number is lower for non-uniform heating. Local heat transfer rates are found to be relatively greater for $\phi =0°$. It is observed that the local heat transfer rate at the central portion of bottom wall is larger for non-uniform heating case. Average Nusselt number plots show higher heat transfer rates at the bottom wall for $\phi =0°$ as compared to $\phi =45°$ and $\phi =30°$. It is observed that the average heat transfer rate at the bottom wall is found to be invariant with respect to $\phi$ at higher Ra for non-uniform heating. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and the power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regimes.     

Natural convection heat transfer and entropy generation inside porous quadrantal enclosure with nonisothermal heating at the bottom wall

In this work, we study numerically the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bottom wall. The effect of Darcy number is significant in dictating the Nusselt number only for higher values of Rayleigh number and the variation is more profound for larger values of Darcy number. The variation of entropy generation rate is significant with the Darcy number only for higher values of Rayleigh number. The entropy generation due to heat transfer is the significant contributor of irreversibility at low values of Darcy number, while for larger values of Darcy number and Rayleigh number entropy generation due to fluid friction becomes dominant.     

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

A numerical work was performed to determine the heat transfer and fluid flow due to buoyancy forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio.     

Natural convection in cavities with a thin fin on the hot wall

A numerical study has been carried out in differentially heated square cavities, which are formed by horizontal adiabatic walls and vertical isothermal walls. A thin fin is attached on the active wall. Heat transfer by natural convection 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 10⁴ to 10⁹, dimensionless thin fin length from 0.10 to 0.90, dimensionless thin fin position from 0 to 0.90, dimensionless conductivity ratio of thin fin from 0 (perfectly insulating) to 60. It is found that Nusselt number is an increasing function of Rayleigh number, and a decreasing function of fin length and relative conductivity ratio. There is always an optimum fin position, which is often at the center or near center of the cavity, which makes heat transfer by natural convection minimized. The heat transfer may be suppressed up to 38% by choosing appropriate thermal and geometrical fin parameters.