IJERT-Analysis of Mixed Convection Flow Characteristics in Square Cavity with Uniformly Heated Bottom Wall by Finite Volume Method (original) (raw)
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International journal of engineering research and technology, 2014
Mixed convection from a uniform heat source on the bottom of a square cavity is studied numerically. Twodimensional forms of non-dimensional Navier-Stokes equations are solved by using control volume based finite volume technique. Three typical values of the Reynolds numbers are chosen as Re = 1, 10, and 100 and steady, laminar results are obtained in the values of Richardson number as Ri = 0, 1 and 10 and the values of Prandtl numbers as Pr = 0.1, 0.71, 1 and 10. The parametric studies for a wide range of governing parameters show consistent performance of the present numerical approach to obtain as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented based on the value of Re and Pr. The computational results indicate that the heat transfer is strongly affected by Reynolds number and Richardson number. In the present investigation, bottom wall is uniformly heated while the two vertical walls are maintained at constant cold temperature and...
Analysis of mixed convection flows within a square cavity with linearly heated side wall(s)
International Journal of Heat and Mass Transfer, 2009
Finite element simulations have been performed to investigate the influence of linearly heated side wall(s) or cooled right wall on mixed convection lid-driven flows in a square cavity. It is interesting to note that multiple circulation cells appear inside the cavity with the increase of Pr for Re ¼ 10 and Gr ¼ 10 5 in the case of linearly heated side walls. For Pr ¼ 0:015, only two circulation cells are formed inside the cavity. As Pr increases to 0.7, three circulation cells are formed inside the cavity. Further increase in Pr to 10, leads to the formation of four circulation cells inside the cavity. On the other hand, only two circulation cells are formed inside the cavity for the case of cooled right wall. A detailed analysis of flow pattern shows that as the value of Re increases from 1 to 10 2 , there occurs a transition from natural convection to forced convection depending on the value of Gr irrespective of Pr. It is observed that the secondary vortex at the top left corner disappears for Re ¼ 10 2 and Gr ¼ 10 5 due to enhanced motion of the upper lid in the case of cooled right wall while a small secondary vortex exist at the bottom right corner in the case of linearly heated side walls. The local Nusselt number (Nu b ) plot shows that heat transfer rate is equal to 1 at the edges for the case of linearly heated side walls case and that is zero at the left edge and thereafter that increases for the case of cooled right wall. It is interesting to observe that Nu b is large within 0:4 6 X 6 0:6 due to compression of isotherms for Pr ¼ 0:7 and 10 in the case of linearly heated side wall. It is also observed that Nu r or Nu l exhibits oscillations especially for Pr ¼ 10 at higher Gr due to the presence of multiple circulations. It is also observed that Nu r or Nu l vs Gr plots show oscillation for two case studies. Average Nusselt numbers at the bottom and right walls are strong functions of Grashof number at larger Prandtl numbers whereas average Nusselt number at the left wall at a specific Pr is a weaker function of Gr.
A Study of Mixed Convection in an Enclosure with Different Inlet and Outlet Configurations
SIJ transactions on computer networks and communication engineering, 2016
A constant flux heat source was heated vertical wall with the fluid considered being air. The other side walls including the top and bottom of the enclosure were assumed to be adiabatic. The inlet opening, located on the left vertical wall, was placed at varying locations. The outlet opening was placed on the opposite heated wall at a fixed location. The basis of the investigation was the two-dimensional numerical solutions of governing equations by using Finite Difference Method (FDM).Significant parameters considered were Richardson number (Ri) and Reynolds number (Re). Results are presented for Richardson number 0 to 10 at Pr=0.71 and Re=50,100,200.The effects of Richardson number and position of the inlet on dimensional temperature inside the enclosure was investigated. The resulting interaction between forced external air stream and buoyancy-driven flow by the heat source are presented in the form of velocity profile and temperature distribution within the enclosure by patterns of graphs. The computational results indicate that heat transfer is strongly affected by Reynolds and Richardson numbers. As the value of Ri increases, there occurs a transition from forced convection to buoyancy dominated flow at Ri>1. A detailed analysis of flow pattern shows that natural or forced convection is based on the parameter Ri.
International Journal of Thermal Sciences, 2012
In this article, numerical investigation is carried out for mixed convection heat transfer within square cavities for various thermal boundary conditions on bottom and side walls based on thermal aspect ratio (A). A penalty finite element analysis with bi-quadratic elements has been used to investigate the results in terms of isotherms, streamlines, heatlines and average Nusselt numbers for a wide range of parameters (1 Re 100, 0.015 Pr 10, 10 3 Gr 10 5). A detailed analysis of flow pattern shows that natural convection or forced convection depends on both parameters: Ri (Ri ¼ Gr/Re 2) and Pe (Pe ¼ Re$Pr). Results indicate that, at low Pr (Pr ¼ 0.015) with low Gr (Gr ¼ 10 3), isotherms are decoupled with flow profile and conduction dominant heat transfer is observed irrespective of Re, due to low Peclet number. At Gr ¼ 10 3 , lid-driven force dominates and the non-symmetric flow distribution occurs irrespective of Re (1,10 and 100), Pr (0.015, 0.7 and 10) and thermal aspect ratio (0.1, 0.5 and 0.9). At Gr ¼ 10 5 with Re ¼ 1, natural convection dominates the flow irrespective of Pr and A. Considerably smaller dominance of liddriven force is observed over buoyancy force at Gr ¼ 10 5 with Re ¼ 10 irrespective of Pr for A ¼ 0.1 and 0.5, whereas strong effect of lid-driven force is found at Gr ¼ 10 5 with Re ¼ 100 irrespective of Pr and A. Multiple circulations are found in streamlines and heatlines especially for A ¼ 0.5 and 0.9 at high Reynolds number (Re ¼ 100) with Pr ¼ 10 and Gr ¼ 10 5. It is found that, streamlines and heatlines circulation cells follow qualitatively similar pattern for higher Pr (Pr ! 0.7) at Gr ¼ 10 5 irrespective of Re. Thermal gradient is found to be high at the center of the bottom wall for A ¼ 0.1 due to highly dense heatlines at that zone whereas that is low for A ¼ 0.9 irrespective of Re, Pr and Gr. It is also found that, as thermal aspect ratio increases, the average Nusselt number decreases for Pr ¼ 0.015 and Pr ¼ 0.7 irrespective of Re. Finally, it is concluded that overall heat transfer rates are higher for A ¼ 0.1 as compared to other thermal aspect ratios (A ¼ 0.5, A ¼ 0.9) irrespective of Pr (0.015 Pr 10), Re (1 Re 100) and Gr (10 3 Gr 10 5).
Combined free and forced convection in a square cavity filled with a viscous fluid characterized by a small Prandtl number is studied numerically. The left wall is moving with a constant velocity v and is maintained at a local cold temperature Tc, while the right wall is fixed and maintained at a local hot temperature Th (Tc <Th). The top and bottom walls of the cavity is assumed to be adiabatic. The governing Navier-Stokes, and energy equations along with appropriate boundary conditions are solved using the finite-volume method. The flow and temperature fields are presented by stream function and isotherms, respectively. The effects of important parameters such as Reynolds number (1 ≤ Re ≤ 600), Prandtl number (Pr = 0,015 and 0,71), and Grashof number (24,5 ≤ Gr ≤ 33480) on the transition from forced convection to mixed convection are investigated. Results indicate that increasing Reynolds number results to fluid acceleration and, thus, to flow transition. Results also show that Grashof and Prandtl's numbers influenced the conditions for the transition to the mixed convection regime. It is found that the parameter that specifies the predominating forced convection regime for Pr = 0,71 is Gr/Re 1. 6096 and for Pr = 0,015 is Gr/Re 1.50235 .
IJERT-Effects Of Heat Source Location On Natural Convection In A Square Cavity
International Journal of Engineering Research and Technology (IJERT), 2014
https://www.ijert.org/effects-of-heat-source-location-on-natural-convection-in-a-square-cavity https://www.ijert.org/research/effects-of-heat-source-location-on-natural-convection-in-a-square-cavity-IJERTV1IS6332.pdf Natural convection in a closed square cavity has occupied the centre stage in many fundamental heat transfer analysis which is of prime importance in certain technological applications. Infact buoyancy driven convection in a sealed cavity with differentially heated isothermal walls is a prototype of many industrial applications such as energy efficient buildings, operation and safety of nuclear reactor and convective heat transfer associated with electronic cooling equipment. The internal flow problems are considerably more complex than external ones. In electronic systems normally the heat generating bodies exist within the cavity. The effect of the presence of heat source on the mass flow rate and heat transfer is considered in present case for investigation. In order to verify the methodology of using fluent, the commercial software, the available problem in the literature is verified for parametric study on the location of heat source and its strength is considered for study. In present work, the given source is split into two parts and its effect on the flow rate and heat transfer is studied. An attempt is made for the best location of the heat source in the cavity so that it can be used in the electronic equipment generating heat. Nomenclatures AR = Aspect ratios, H/L, Gr = Grashoff Number g = Acceleration due to gravity (m/s 2), Ra = Rayleigh number H = Height of the cavity (m), Pr = Prandtl number h = Convective heat transfer coefficient (W/m 2 K) k = Thermal conductivity (W/m.K), Nu = Nusselt number L = Length of the cavity (m), T = Temperature (K) q = Heat flux (W/m 2) Greek Symbols α = Thermal diffusivity (m 2 /s) β = Volume expansion coefficient (K-1) ρ = Fluid Density (kg/m 3) ν = Kinematic viscosity (m 2 /s) θ = Dimensionless temperature Subscript b = Bottom wall s = Side wall
International Communications in Heat and Mass Transfer, 2007
Combined convection heat transfer in a vertical circular cylinder has been experimentally studied for assisting, thermally developing and thermally fully developed laminar air flows under constant wall heat flux boundary conditions for Reynolds number range from 400 to 1600, and the heat flux is varied from 60 Wm − 2 to 400 Wm − 2 . This paper has examined the effect of the cylinder inclination angle on the mixed convection heat transfer process. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L / D = 30). The hydrodynamically developed condition has been achieved by using aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 1800 mm (L / D = 60), another one with length of 2400 mm (L / D = 80) and two short calming sections with lengths of 600 mm (L / D = 20), 1200 mm (L / D = 40). The results present the surface temperature distribution along the cylinder length, the local and average Nusselt number distribution with the dimensionless axial distance Z + . The results have clearly shown that the surface temperature values decrease as the cylinder inclination angle moves from θ = 90°vertical cylinder to θ = 0°horizontal cylinder. The results have demonstrated that an increase in the Nusselt number values as the heat flux increases and as the angle of cylinder inclination moves from θ = 90°vertical cylinder to θ = 0°horizontal cylinder. The mixed convection regime has been bounded by the convenient selection of Re number range and the heat flux range, so that the obtained Richardson numbers (Ri) varied approximately from 0.1 to 10. The average heat transfer results have been correlated with an empirical correlation by dimensionless groups as Log P Nu against Log P Ra= P Re, and compared with available literature and with laminar forced convection and showed satisfactory agreement.
IJERT-Numerical Investigation of Natural Convection Heat Transfer in a Square Cavity
International Journal of Engineering Research and Technology (IJERT), 2015
https://www.ijert.org/numerical-investigation-of-natural-convection-heat-transfer-in-a-square-cavity https://www.ijert.org/research/numerical-investigation-of-natural-convection-heat-transfer-in-a-square-cavity-IJERTV4IS070206.pdf Natural convection heat transfer in enclosures find many applications such as heating and cooling of building spaces, solar energy utilization, thermal energy storage, cooling of electrical and electronic components etc. In the present study, Numerical Investigation is conducted in a square cavity with one vertical wall maintained at a high temperature and with the opposing vertical wall at a low temperature. The influence of Grashof numbers ranging from 20000 to 200000 for Prandtl number 0.7 (air) is studied. The governing vorticity and energy equations are solved by finite difference methods including Alternating Direction Implicit (ADI) and Successive Over Relaxation (SOR) techniques with C coding. Steady state isothermal lines and streamlines are obtained for all the Grashof numbers considered. In addition, the average Nusselt number, over the hot wall for the range of Grashof numbers is calculated. The contours of streamlines and isothermal lines are presented for all the parameters investigated. Changes in the streamline and isothermal line patterns are observed with the change in Grashof numbers. The results obtained in this study are useful for the design of devices with enclosures subjected to high temperature differences.
Effects of thermal boundary conditions on natural convection flows within a square cavity
International Journal of Heat and Mass Transfer, 2006
A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10 3 6 Ra 6 10 5 and Prandtl number Pr, 0.7 6 Pr 6 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.