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Laminar mixed convection in a two-dimensional symmetrically and partially heated vertical channel is investigated. The heaters are located on both walls and uniform temperature is applied on the heated sections. The number of heaters is considered as 1, 4, 8, and 10. Aluminum oxide/water nanofluid is considered as working fluid and the inlet velocity is uniform. The continuity, momentum and energy equations with appropriate boundary conditions are solved in dimensionless form, numerically. The study is performed for Richardson number of 0.01 and 10, Reynolds number of 100 and 500, and nanofluid volume fraction of 0% and 5%. Based on the obtained velocity and temperature distributions, the local and mean Nusselt number is calculated and plotted for different cases. The variation of the mean Nusselt number with the number of the heated portions is also discussed. It is found that the addition of nanoparticles into the base fluid increases mean Nusselt number but the rate of increase depends on Reynolds, Richardson numbers and number of heated portions. It is possible to increase mean Nusselt number 138% by increasing Reynolds number from 100 to 500, Richardson number from 0.01 to 10 and number of heated portions from 1 to 10 when volume fraction value is 5%.

In this study, the total heatfunction equation which includes diffusion and convection transport is divided into the corresponding heatfunction equations. The superposition rule is used to obtain the mathematical definitions of diffusion and convection heatfunctions and corresponding boundary conditions. It is observed that the separate visualization of diffusion and convection heatlines provides significant information on understanding of the mechanism of heat transfer in a convective flow. The direction of the diffusion and convection heat transport as well as the strength of convection compared to the conduction in entire or in a portion of a domain can be visualized. The diffusion heatlines demonstrate a potential flow like behavior while convective heat flow rotates due to the source term of the convection heatfunction equation, similar to the rotation of fluid flow generated by fluid flow vorticity. The similarity between the streamfunction and the total heatfunction yields a concept of heat flow vorticity, Omega(t). The obtained results show that the maximum absolute value of the convection heatfunction may be an appropriate parameter for determination of the convection strength. The diffusion and convection heatfunction equations for natural convection in a differentially heated square cavity for four different length of the heated surface on the right vertical wall as s(p) = L/4, L/2, 3L/4 and L and a fixed length of the cooled surface on the right vertical wall as L/4 are obtained and corresponding heatlines are drawn. The values of the conduction heatfunction are positive while the sign of convection heatfunction values is negative for the studied cases. Based on the distribution of total heatlines, two regions are detected in the cavity, an active region with the positive values of heatlines signifying dominant conduction heat transfer and a passive region with the negative heatfunction values in where convection heat flow is dominant and heat only rotates in a closed contour pattern. The variations of average Nusselt number, average of heat flow vorticity. maximum absolute values of convection heatfunction and streamfunction at different Rayleigh numbers and lengths of the heated surface are presented. (C) 2009 Elsevier Ltd. All rights reserved. (Less)

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) < Ra < 10(5), 10(-4) < 0 < 10(-2), and Pr = 0.7. (Less)

The issue of laminar natural convection and conduction in enclosures divided by a partition with different thicknesses is investigated numerically. The partition is accepted as conductive at different thermal conductivity ratio. The cavity is filled with air, and it is heated differentially from vertical walls while horizontal walls are adiabatic. The problem is solved for different values of Rayleigh number (103 ≤ Ra ≤ 106), thickness ratio of the partition, and thermal conductivity ratio (0.1 ≤ k ≤ 10.0). It is found that both heat transfer and flow strength strongly depend on the thermal conductivity ratio of the solid material of partition and Rayleigh numbers.

Heatline 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 non-uniformly 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. © 2012 Elsevier Ltd. All rights reserved.

Effects of a ceiling-mounted barrier on natural convection heat transfer in a square cavity with differentially heated wall are numerically investigated. A limit case, in which the partition has small thickness and low thermal conductivity, is studied. The study is performed for nine different locations of barrier on the ceiling, two different lengths of barrier as 15 and 50% of the side wall, and Rayleigh numbers from 103 to 106. The vorticity and streamfunction approach is used to obtain velocity distribution, and the energy equation is solved to determine temperature field in the cavity. The variations of the local Nusselt number on the hot and cold walls and the change of mean Nusselt number with the location of barrier in the cavities with different Rayleigh numbers are presented. The obtained results show that a wall-mounted barrier can be used to reduce heat transfer rate through the cavity; however, its effectiveness depends on length and location of barrier and Rayleigh number.

A conjugate conduction-(natural)convection problem is numerically studied in order to present the application of dimensionless heatfunction for entire computational domain including solid and fluid regions in an enclosure with thick solid ceiling. The modified dimensionless heatfunction for solid region is defined to provide continuity of dimensionless heatfunction on solid-fluid interface. The enclosure is differentially heated from vertical walls, and horizontal walls are adiabatic. Finite difference method is employed to solve the set of governing equations. The dimensionless governing parameters for computations are: Rayleigh number (from 103 to 106), dimensionless ceiling wall thickness (0.05 and 0.5) and thermal conductivity ratio (from 1 to 100). The obtained results shows that the heat and fluid flows in the enclosure are considerably influenced by Rayleigh number and thermal conductivity ratio. Dimensionless wall thickness comparatively has less effect on heat transfer rate through the cavity. © 2008 Elsevier Ltd. All rights reserved.

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 (103 < Ra < 106) and thermal conductivity ratio (0 < K < 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.

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10 3≤ Ra ≤ 10 6), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X h < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10 3), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.