In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10 5 ), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10 2 b Ra b 10 5 , 10 − 4 b ϕ b 10 − 2 , and Pr = 0.7.

Kozeny-Carman permeability equation is an important relation for the determination of permeability in porous media. In this study, the permeabilities of porous media that contains rectangular rods are determined, numerically. The applicability of Kozeny-Carman equation for the periodic porous media is investigated and the effects of porosity and pore to throat size ratio on Kozeny constant are studied. The continuity and NavierStokes equations are solved to determine the velocity and pressure fields in the voids between the rods. Based on the obtained flow field, the permeability values for different porosities from 0.2 to 0.9 and pore to throat size ratio values from 1.63 to 7.46 are computed. Then Kozeny constants for different porous media with various porosity and pore to throat size ratios are obtained and a relationship between Kozeny constant, porosity and pore to throat size ratio is constructed. The study reveals that the pore to throat size ratio is an important geometrical parameter that should be taken into account for deriving a correlation for permeability. The suggestion of a fixed value for Kozeny constant makes the application of Kozeny-Carman permeability equation too narrow for a very specific porous medium. However, it is possible to apply the Kozeny-Carman permeability equation for wide ranges of porous media with different geometrical parameters (various porosity, hydraulic diameter, particle size and aspect ratio) if Kozeny constant is a function of two parameters as porosity and pore to throat size ratios.

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity-stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10 3 b Ra b 10 6 ) and thermal conductivity ratio (0 b K b 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.

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a b s t r a c tHeatline visualization technique is used to understand heat transport path in an inclined non-uniformly heated enclosure filled with water based CuO nanofluid. The cavity has square cross-section and it is nonuniformly heated from a wall and cooled from opposite wall while other walls are adiabatic. The governing equations which are continuity, momentum and energy equations are solved using finite volume method. The dimensionless heatfunction for nanofluid heat flow is defined and solved to determine heatline patterns. Calculations were performed for Rayleigh numbers of 10 3 , 10 4 and 10
5, inclination angle of 0°, 30°, 60°and 90°, and nanoparticle fraction of 0, 0.02, 0.04, 0.06, 0.08 and 0.1. It is observed that heat transfer in the cavity increases by adding nanoparticles. The rate of increase is greater for the enclosures with low Rayleigh number. Visualization of heatline is successfully applied to nanoparticle convective flows. Based on the heatline patterns, three heat transfer regions are observed and discussed in details.

In this study, fully developed heat and fluid flow in a parallel plate channel partially filled with porous layer is analyzed both analytically and numerically. The porous layer is located at the center of the channel and uniform heat flux is applied at the walls. The heat and fluid flow equations for clear fluid and porous regions are separately solved. Continues shear stress and heat flux conditions at the interface are used to determine the interface velocity and temperature. The velocity and temperature profiles in the channel for different values of Darcy number, thermal conductivity ratio, and porous layer thickness are plotted and discussed. The values of Nusselt number and friction factor of a fully clear fluid channel (N u cl = 4.12 and f Re cl = 24) are used to define heat transfer increment ratio (ε th = N u p /N u cl ) and pressure drop increment ratio (ε p = f Re p / f Re cl ) and observe the effects of an inserted porous layer on the increase of heat transfer and pressure drop. The heat transfer and pressure drop increment ratios are used to define an overall performance (ε = ε th /ε p ) to evaluate overall benefits of an inserted porous layer in a parallel plate channel. The obtained results showed that for a partially porous filled channel, the value of ε is highly influenced from Darcy number, but it is not affected from thermal conductivity ratio (k r ) when k r > 2. For a fully porous material filled channel, the value of ε is considerably affected from thermal conductivity ratio as the porous medium is in contact with the channel walls.

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