Interaction of Natural Convection Wakes Arising From Thermal Sources on a Vertical Surface

1985 ◽  
Vol 107 (4) ◽  
pp. 883-892 ◽  
Author(s):  
Y. Jaluria
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Numerical Study ◽  
Finite Difference Methods ◽  
Heat Removal ◽  
Temperature Fields ◽  
Electronic Components ◽  
Wide Range ◽  
Wall Plume

A numerical study of the interacting natural convection flows generated by isolated thermal energy sources, such as electronic components, located on a vertical adiabatic surface is carried out. Of particular interest were the effects of the wake on the heat transfer from and the flow over a downstream heat source and the nature of the wall plume far from the sources. This consideration is related to the positioning of finite-sized electronic components and the relevant heat removal process. A two-dimensional flow is considered, without making the boundary-layer assumptions. The full elliptic equations governing the flow are solved numerically, employing finite-difference methods. The results are compared with the boundary layer solutions, obtained in earlier studies, in order to determine the nonboundary-layer effects. This is an important consideration in several practical circumstances that involve small heat inputs, sources of relatively small heights, and small separation distances between the sources. It is found that the flow downstream rapidly approaches the characteristics of an idealized wall plume due to a line source. A boundary-layer flow arises far from the heat sources and this flow provides the boundary conditions for the elliptic problem. The nature of the velocity and temperature fields is studied in detail for a wide range of governing parameters and the heat transfer coefficients for the heated elements determined. The relevance of the results obtained to practical systems is outlined, particularly for small Grashof numbers which necessitate a solution of the full equations.

Effect of 3D Diffusion Over Vertical Thin Rectangular Geometries in Natural Convection Heat Transfer

2006 ◽  
Author(s):  
Mustafa Gursoy ◽  
Mehmet Arik ◽  
Tunc Icoz ◽  
Michael Yovanovich ◽  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Motion ◽  
Heat Removal ◽  
Air Entrainment ◽  
Published Data ◽  
Diffusion Term ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Rayleigh Numbers

Natural convection over vertical plates is a very well known problem in heat transfer. There are many available correlations to predict Nusselt numbers for a wide range of Rayleigh numbers. These benchmark studies on natural convection for vertical plates were conducted on rather large surfaces leading to Rayleigh numbers in the range of 0.1 to 109. In natural convection the sole driving force of fluid motion is the change in fluid density, when the diffusive limit is small compared to convective heat transfer. However, conduction to air, as well as air entrainment from sides also contributes to the heat removal from heater surfaces. An experimental study has been carried out with small and large heaters compared to published data for 2×103<Ra<4×107. Square surfaces of 12.5 and 25.4 mm, and rectangular heaters of sizes 25.4×101.6 and 25.4×203.2 mm were tested for a range of heat inputs such that the surface temperatures are controlled between 30 °C and 80 °C. It is found that published correlations underpredict the Nusselt numbers as much as 20%. It is observed that widely known correlations underpredict the experimental values since the 3D conduction and side air drifts on heat transfer are not accounted for in these correlations. However, the cuboid model which includes the 3D diffusion term showed much better agreement with the experimental results.

Radiation effect on natural convection boundary layer flow over a vertical wavy frustum of a cone

2009 ◽  
Vol 223 (7) ◽  
pp. 1605-1614 ◽  
Author(s):  
M M Molla ◽  
M A Hossain ◽  
R S R Gorla
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Boundary Layer Flow ◽  
Average Rate ◽  
Local Heat Transfer ◽  
Convection Boundary Layer ◽  
Local Skin ◽  
Wide Range ◽  
Layer Flow

The effect of thermal radiation on a steady two-dimensional natural convection laminar boundary layer flow of a viscous incompressible optically thick fluid over a vertical wavy frustum of a cone has been investigated. The boundary layer regime when the Grashof number Gr is large is considered. Using appropriate transformations, the basic governing equations are transformed into a dimensionless form and then solved numerically employing two efficient methods, namely: (a) implicit finite difference method together with Keller-box scheme and (b) direct numerical scheme. Numerical results are presented by streamline, isotherms, velocity and temperature distribution of the fluid, as well as the local shearing stress in terms of the local skin-friction coefficient, the local heat transfer rate in terms of local Nusselt number, and the average rate of heat transfer for a wide range of the radiation—conduction parameter or Planck number Rd and the surface heating parameter θw.

A Multigrid Accelerated Code for Simulating Unsteady Conjugate Natural Convection Boundary Layers

2016 ◽  
Vol 846 ◽  
pp. 30-35
Author(s):  
Mehdi Khatamifar ◽  
Emma Lee Wood ◽  
Wen Xian Lin ◽  
David Holmes ◽  
Steven W. Armfield ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Layers ◽  
Numerical Study ◽  
Viscous Boundary Layer ◽  
Central Difference ◽  
Simulation Accuracy ◽  
Conjugate Natural Convection ◽  
Wide Range ◽  
Convection Boundary

This paper presents a numerical study on the flow dynamics and heat transfer behaviour of unsteady conjugate natural convection boundary layers (CNCBLs) in a partitioned, air filled square cavity. An unsteady two-dimensional multigrid-assisted solver is developed in the C#.NET programming language on stretched Cartesian meshes. The finite volume method is used to discretise the governing equations. To solve the coupled pressure and velocity, the SIMPLE algorithm is used, and to increase simulation accuracy the Adam-Bashforth, QUICK and central difference schemes are employed for time, convection, and diffusion terms respectively. The Poisson pressure equation is solved through the use of the multigrid method. The developed code is used to model CNCBLs which typically require a large amount of simulation time. The numerical results provide detailed descriptions of unsteady CNCBLs and associated heat transfer behaviour over a wide range of Ra, such as the thermal and viscous boundary layer thicknesses, temperature and velocity distributions, and maximum velocities within the CNCBLs.

Natural convection in an enclosure having a vertical sidewall with time-varying temperature

1996 ◽  
Vol 329 ◽  
pp. 65-88 ◽  
Author(s):  
Ho Sang Kwak ◽  
Jae Min Hyun
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Time Varying ◽  
Vertical Sidewall ◽  
Boussinesq Fluid

A numerical study is performed for time-varying natural convection of an incompressible Boussinesq fluid in a sidewall-heated square cavity. The temperature at the cold sidewall Tc is constant, but at the hot sidewall a time-varying temperature condition is prescribed, $ T_H = \overline{T_H} + \Delta T^{\prime} \sin ft $. Comprehensive numerical solutions are found for the time-dependent Navier–Stokes equations. The numerical results are analysed in detail to show the existence of resonance, which is characterized by maximal amplification of the fluctuations of heat transfer in the interior. Plots of the dependence of the amplification of heat transfer fluctuations on the non-dimensional forcing frequency ω are presented. The failure of Kazmierczak & Chinoda (1992) to identify resonance is shown to be attributable to the limitations of the parameter values they used. The present results illustrate that resonance becomes more distinctive for large Ra and Pr ∼ 0(1). The physical mechanism of resonance is delineated by examining the evolution of oscillating components of flow and temperature fields. Specific comparisons are conducted for the resonance frequency ωr between the present results and several other previous predictions based on the scaling arguments.

scholarly journals Solution Of Natural Convection Boundary Layer Flow Above A Semi-Infinite Porous Horizontal Plate Under Similarity Transformations With Suction And Blowing

1970 ◽  
Vol 6 (1) ◽  
pp. 43-51 ◽  
Author(s):  
MM Touhid Hossain ◽  
Rita Mojumder ◽  
Mohammad Arif Hossain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Differential Equations ◽  
Skin Friction ◽  
Similarity Transformation ◽  
Porous Plate ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Suction And Blowing

In the present study we have confined our attention to the laminar boundary layer equations for the unsteady free convection flow over a heated horizontal semi-infinite porous plate by simplifying them using the Boussinesq approximation. Similarity requirements for an incompressible fluid are sought on the basis of detailed analysis in order to reduce the governing coupled partial differential equations into a set of ordinary differential equations. Numerical results are displayed graphically for some selected values of the controlling parameters provided by the similarity transformation. The influence of suction and blowing on the flow and temperature fields and other flow factors like skin friction and heat transfer coefficients are extensively investigated. It is found that a small value of suction or blowing play a vital role on the patterns of flow and temperature fields as well as on the coefficients of skin friction and heat transfer. Keywords: Natural convection; Boussinesq approximation; Similarity transformation; Suction; blowing. DOI: http://dx.doi.org/10.3329/diujst.v6i1.9333 DIUJST 2011; 6(1): 43-51

Natural Convection From L-Shaped Corners With Adiabatic and Cold Isothermal Horizontal Walls

1993 ◽  
Vol 115 (1) ◽  
pp. 149-157 ◽  
Author(s):  
D. Angirasa ◽  
R. L. Mahajan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Numerical Study ◽  
Outer Region ◽  
Vertical Side ◽  
Layer Flow ◽  
Horizontal Side

A numerical study of two-dimensional fluid flow and heat transfer by natural convection from L-shaped corners is reported. The vertical side is hot isothermal, and the horizontal side is either adiabatic or cold isothermal at the ambient temperature. The effect of changing the aspect ratio (length of the horizontal side/height of the vertical side) on the transport from the vertical side is studied in detail. It is shown that when the length of the horizontal wall is of the order of the boundary layer thickness on the vertical side, the entrainment flow as well as the boundary layer flow are influenced significantly by a change in the length of the horizontal surface. The heat transfer rate from the vertical side also decreases with increasing length. For values of the aspect ratio > 0.3 (Pr = 0.7), the Nusselt number for the vertical side of the L-shaped body is about 10 percent less than that for the vertical plate. As the length of the horizontal plate increases further, the flow in the outer region undergoes a significant change, but the heat transfer from the vertical heated leg remains unaffected. As the aspect ratio approaches = 2.0, increasing the length of the horizontal side ceases to have any further influence on the entire flow field. Comparison of Nusselt number with past experimental data for air shows good agreement. Finally, Nusselt number correlations in the range of Rayleigh number from 105 to 109 are presented.

Interaction Between Film Condensation on One Side of a Vertical Wall and Natural Convection on the Other Side

1986 ◽  
Vol 108 (3) ◽  
pp. 560-566 ◽  
Author(s):  
D. Poulikakos
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Vertical Wall ◽  
Flow Characteristics ◽  
The Other ◽  
Film Condensation ◽  
Convection Boundary Layer ◽  
Wide Range

This paper reports a theoretical study of conjugate film condensation on one side of a vertical wall and boundary layer natural convection on the other side. Each phenomenon is treated separately and the solutions for each side are matched on the wall. The main heat transfer and flow characteristics in the two counterflowing layers, namely, the condensation film and the natural convection boundary layer, are documented for a wide range of the problem parameters. In addition, the wall heat flux and the wall temperature distribution resulting from the interaction of the two heat transfer modes (condensation and natural convection) are determined. Important engineering results regarding the overall heat flux from the condensation side to the natural convection side are summarized at the end of the study.

Effect of Solid Subcooling on Natural Convection Melting of a Pure Metal

1989 ◽  
Vol 111 (2) ◽  
pp. 416-424 ◽  
Author(s):  
C. Beckermann ◽  
R. Viskanta
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Numerical Study ◽  
Pure Metal ◽  
Liquid Region ◽  
Cold Wall ◽  
Fusion Temperature ◽  
Local Flow ◽  
Wide Range

A combined experimental and numerical study is reported of melting of a pure metal inside a vertical rectangular enclosure with natural convection in the liquid and conduction in the solid. The numerical model is successfully verified by conducting a series of experiments covering a wide range of hot and cold wall temperatures. It is found that solid subcooling significantly reduces the melting rate when compared to melting with the solid at the fusion temperature. Because the cooled wall is held below the fusion temperature of the metal, the solid/liquid interface eventually reaches a stationary position. For moderate values of the subcooling parameter the steady-state interface is almost vertical and parallel to the cold wall. Strong subcooling results in an early termination of the melting process, such that natural convection in the relatively small liquid region cannot fully develop. For moderate subcooling, correlations have been derived for the steady-state volume and heat transfer rates. While many aspects of melting with solid subcooling appear to be similar to ordinary nonmetallic solids, important differences in the local flow structures and heat transfer mechanisms are observed.

Natural Convection From a Layered Porous Cavity With Non-Uniform Sublayers

2007 ◽  
Author(s):  
R. L. Marvel ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
System Analysis ◽  
Numerical Study ◽  
Temperature Fields ◽  
Square Cavity ◽  
Porous Cavity ◽  
Differential Heating ◽  
Vertical Walls

A numerical study has been performed to further investigate the flow and temperature fields in layered porous cavity. The geometry considered is a square cavity with 3 or 4 non-uniform sublayers and is subjected to differential heating from the vertical walls. The results obtained are used to further evaluate the feasibility of using the lumped-system analysis for heat transfer in layered porous cavities as proposed in the previous study. To this end, the effective permeabilities based on the arithmetic and harmonic averaging schemes are examined for their use in the conjunction with the lumped-system analysis.

scholarly journals Numerical Study of Natural Convection within a Wavy Enclosure Using Meshfree Approach: Effect of Corner Heating

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Sonam Singh ◽  
R. Bhargava
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Side Wall ◽  
Integration Scheme ◽  
Square Enclosure ◽  
Wide Range

This paper presents a numerical study of natural convection within a wavy enclosure heated via corner heating. The considered enclosure is a square enclosure with left wavy side wall. The vertical wavy wall of the enclosure and both of the corner heaters are maintained at constant temperature,TcandTh, respectively, withTh>Tcwhile the remaining horizontal, bottom, top and side walls are insulated. A penalty element-free Galerkin approach with reduced gauss integration scheme for penalty terms is used to solve momentum and energy equations over the complex domain with wide range of parameters, namely, Rayleigh number (Ra), Prandtl number (Pr), and range of heaters in thex- andy-direction. Numerical results are represented in terms of isotherms, streamlines, and Nusselt number. It is observed that the rate of heat transfer depends to a great extent on the Rayleigh number, Prandtl number, length of the corner heaters and the shape of the heat transfer surface. The consistent performance of the adopted numerical procedure is verified by comparison of the results obtained through the present meshless technique with those existing in the literature.

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