Numerical study of conjugate natural convection in a square enclosure with top active vertical wall.

In this paper, we consider a two-dimensional numerical study of laminar conjugate natural convection in a square enclosure. The left vertical wall of the enclosure is thick, while the other three walls are taken to be of zero thickness. The enclosure is subjected to horizontal temperature gradient. The right vertical wall has constant temperature θc, while the outer surface of the left vertical wall is partially heated in the top θh, with θh>θc. The remaining left portion in the vertical wall and the two horizontal walls are considered adiabatic. The governing equations are solved by finite volume method using SIMPLER algorithm and Hybrid scheme. The parameters considered are: Rayleigh number (500≤ Ra ≤106), Prandtl number (Pr=0.71), wall to fluid thermal conductivity ratio (0.1≤ Kr ≤100), the ratio of wall thickness to its heigh (0.2≤ D≤ 0.5) and wall to fluid thermal diffusivity ratio (R=1). The main focus of the study is on examining the effect of Ra, Kr and D on the flow and heat transfer in the enclosure. A comparison with the special isothermal wall case is also studied. The obtained results show that for a given thickness, either increasing the Rayleigh number and the thermal conductivity ratio, can increase the average Nusselt number, the interface temperature and the flow velocity. Generally it is found that the increase of the thickness of the bounded wall can decrease , especially for Kr > 1 and Ra < 104 increases with the increase of D. The wall-fluid interface temperature is found to be quite non- uniform. This non uniformity tends to make the flow pattern in the enclosure asymmetric. For low Rayleigh number and low conductivity ratio, the flow velocity is neglected and conduction heat transfer is dominated in the enclosure

Effect of Wall Conductivity on Conjugate Natural Convection in a Square Enclosure with Finite Vertical Wall Thickness

Abstract In this work, we consider a two-dimensional numerical study of conjugate natural convection in a square enclosure. The left vertical wall of the enclosure is thick with a finite thermal conductivity, while the other three walls are taken to be of zero thickness. The enclosure is subjected to horizontal temperature gradient: the vertical boundaries are isothermal at different temperatures whereas the remaining walls are adiabatic. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on five parameters: Rayleigh number (500≤Ra≤1

Natural Convection in Inclined Porous Square Enclosure

Steady, laminar, natural convection flow in porous square enclosure with inclination angle is considered. The enclosure is filled with air and subjected to horizontal temperature gradient. Darcy- Brinkman-Forchheimer model is considered. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on five parameters: Rayleigh number (Ra =103-106), Prandtl number (Pr=0.71), Darcy number (Da=0.01), inclination angle φ=(0°-227°), porosity of the medium (ε=0.7) and the aspect ratio of the enclosure (A=1). The main focus of the study is on examining the effect of Rayleigh number on fluid flow and heat transfer rates. The effect of inclination angle is also considered. The results including streamlines, isotherm patterns, flow velocity and the average Nusselt number for different values of Ra and φ. The obtained results show that the increase of Ra leads to enhance heat transfer rate. The fluid particles move with greater velocity for higher thermal Rayleigh number. Also φ affects the fluid motion and heat transfer in the enclosure. Velocity and heat transfer are more important when φ takes the value (30°)

Natural convection in a Square Enclosure with Partially Active Vertical Wall

Steady, laminar, natural convection flow in a square enclosure with partially active vertical wall is considered. The enclosure is filled with air and subjected to horizontal temperature gradient. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on three parameters: Rayleigh number (Ra =103-106), Prandtl number (Pr=0.71), and the aspect ratio of the enclosure (A=1). The active location takes two positions in the left wall: top (T) and middle (M). The main focus of the study is on examining the effect of Rayleigh number on fluid flow and heat transfer rate. The results including the streamlines, isotherm patterns, flow velocity and the average Nusselt number for different values of Ra. The obtained results show that the increase of Ra leads to enhance heat transfer rate. The fluid particles move with greater velocity for higher thermal Rayleigh number. Also by moving the active location from the top to the middle on the left vertical wall, convection and heat transfer rate are more important in case (M). Furthermore for high Rayleigh number (Ra=106), Convection mechanism in (T) case is principally in the top of the enclosure, whereas in the remaining case it covers the entire enclosure

Conjugate natural convection in a square enclosure under horizontal magnetic field effect

Steady, laminar, conjugate natural convection flow in a square enclosure is considered. Both effects: conduction in a vertical wall and the presence of a magnetic field are taken together. The enclosure is filled with liquid gallium and subjected to horizontal temperature gradient. The main focus of the study is examining the effect of Hartmann number on fluid flow and heat transfer. The effect of Rayleigh number and conduction in the left wall is also considered. The obtained result show in the absence of a magnetic field that natural convection can be strengthed by the increase of both Rayleigh number and conductivity ratio, because of the increase of the effective temperature difference driving the flow. For poor conducting wall, where the solid part is an insulated material and the thermal resistance is more important the average Nusselt number is approximately constant and having low values comparing with equal and high conducting wall, indicating that most of heat transfer is by heat conduction. In the presence of a magnetic field the results show that for a given Rayleigh number, as the value of Hartmann number increases, convection is suppressed progressively and the rate of heat transfer is reduced in the enclosure