Natural Convective Heat Transfer From an Isothermal Vertical Square Cylinder Mounted on a Flat Adiabatic Base

2008 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Vertical Cylinder ◽  
Base Plate ◽  
Cylinder Surface ◽  
Vertical Side ◽  
Study Results ◽  
Wide Range

Natural convective heat transfer from an isothermal vertical cylinder with a square cross-section which has an exposed horizontal top surface has been numerically studied. The exposed upper surface is maintained at the same temperature as the vertical walls of the cylinder. The cylinder is mounted on a flat horizontal adiabatic base plate. The interest in this situation stems from the fact that it is an approximate model of some electrical component cooling situations. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the three-dimensional governing equations, these equations being written in terms of dimensionless variables. The numerical solution has been obtained using a commercial finite element method based code, FIDAP. The solution has the following parameters: the Rayleigh number, Ra, based on the height of the heated cylinder, h, and the overall temperature difference Tw − Tf, the dimensionless size of the square cross-section of the cylinder surface, W = w/h, w being the size of the cross-section, and the Prandtl number, Pr. Because of the applications that motivated this study, results have only been obtained for Pr = 0.7. A wide range of the other governing parameters has been considered. The conditions under which the heat transfer from the exposed upper surface can be neglected compared to that from the vertical side walls in the evaluation of the mean Nusselt number for the entire cylinder have been explored.

Natural Convective Heat Transfer From an Inclined Isothermal Cylinder With an Exposed Top Surface Mounted on a Flat Adiabatic Base

2009 ◽  
Author(s):  
Abdulrahim Kalendar ◽  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Base Plate ◽  
Fluid Temperature ◽  
Governing Equations ◽  
Study Results ◽  
Wide Range ◽  
The Mean

Natural convective heat transfer from an inclined isothermal cylinder with a circular cross-section and which has an exposed “top” surface has been numerically studied. The cylinder is mounted on a flat adiabatic base plate, the cylinder being normal to the base plate. The situation considered is an approximate model of that which occurs in some electrical and electronic component cooling problems. One of the main aims of the present work was to determine how the diameter-to-height ratio of the cylinder, i.e., D/h, influences the mean heat transfer rate from the cylinder at various angles of inclination between vertically upwards and vertically downwards. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the governing equations, these equations being written in terms of dimensionless variables. These dimensionless governing equations, subject to the boundary conditions, have been solved using the commercial cfd solver, FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. The solution has been used to derive the values of the mean Nusselt number for the cylinder. The solution has the following parameters: the Rayleigh number, Ra, based on the cylinder height and the cylinder surface to fluid temperature difference; the dimensionless cylinder diameter, i.e., the ratio of the diameter to the height of the heated cylinder; the Prandtl number, Pr; and the angle of inclination of the cylinder relative to the vertical, φ. Because of the applications that motivated this study, results have only been obtained for Pr = 0.7. Values of φ between 0° and 180° and a wide range of Ra and Dh values have been considered. The effects of Dh, Ra, and φ on the mean Nusselt number for the entire cylinder and for the mean Nusselt numbers for the cylinder side wall and the exposed “top” surfaces have been examined.

Natural Convective Heat Transfer From a Vertical Cylinder With an Exposed Upper Surface

2007 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Vertical Cylinder ◽  
Curved Surface ◽  
Curvature Effects ◽  
Study Results ◽  
Wide Range ◽  
The Mean

Natural convective heat transfer from a vertical cylinder which has a uniform heat flux at its surface and which has an exposed horizontal top surface has been numerically studied. The cylinder is mounted on an adiabatic cylindrical base which has the same diameter as the heated cylinder. In some circumstances the mean Nusselt number for the curved surface of the cylinder can be adequately predicted using vertical flat plate equations, i.e., by ignoring curvature effects, and in some circumstances the overall mean Nusselt number for the system considered can be adequately predicted by ignoring the heat transfer from the exposed upper surface of the cylinder. The flow has been assumed to be axisymetric about the vertical cylinder axis and to be steady and laminar. It has also been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the governing equations, these equations being written in terms of dimensionless variables and the solution being obtained using a commercial finite element method based code, FIDAP. Because of the applications that motivated this study, results have only been obtained for Pr = 0.7. A wide range of the other governing parameters have been considered. The conditions under which the heat transfer from the exposed upper surface can be neglected compared to that from the cylindrical wall in the evaluation of the mean Nusselt number has been deduced and the conditions under which curvature effects can be ignored in evaluating the mean Nusselt number for the curved surface of the cylinder have been investigated.

Natural Convective Heat Transfer From an Inclined Isothermal Square Cylinder With an Exposed Top Surface Mounted on a Flat Adiabatic Base

2009 ◽  
Author(s):  
Abdulrahim Kalendar ◽  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Base Plate ◽  
Approximate Model ◽  
Fluid Temperature ◽  
Governing Equations ◽  
Wide Range ◽  
The Mean

Natural convective heat transfer from an isothermal inclined cylinder with a square cross-section and which has an exposed top surface and is, in general, at an angle to the vertical has been numerically studied. The cylinder is mounted on a flat adiabatic base plate, the cylinder being normal to the base plate. The situation considered is an approximate model of that which occurs in some electrical and electronic component cooling problems. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the governing equations, these equations being written in terms of dimensionless variables using the height, h, of the cylinder as the length scale and Tw – TF as the temperature scale, TF being the undisturbed fluid temperature far from the cylinder and Tw being the uniform surface temperature of the cylinder. These dimensionless governing equations subject to the boundary conditions have been solved using the commercial cfd solver, FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. The solution has been used to derive the values of the mean Nusselt number for the cylinder, Nu. The solution has the following parameters: the Rayleigh number, Ra, the dimensionless cylinder width, i.e., the ratio of the width to the height of the heated cylinder, W = w/h, the Prandtl number, Pr, and the angle of inclination of the cylinder relative to the vertical, φ. Results have only been obtained for Pr = 0.7. Values of φ between 0° and 180° and a wide range of Ra and W have been considered. The effects of W, Ra, and φ on the mean Nusselt number, Nu, for the entire cylinder and for the mean Nusselt numbers for the various surfaces that make up the cylinder have been examined.

Development and validation of an incompressible Navier-Stokes solver including convective heat transfer

2015 ◽  
Vol 25 (4) ◽  
pp. 861-886 ◽  
Author(s):  
Konstantinos Stokos ◽  
Socrates Vrahliotis ◽  
Theodora Pappou ◽  
Sokrates Tsangaris
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Content Type ◽  
Strongly Coupled ◽  
Loosely Coupled ◽  
Wide Range ◽  
Coupled Solution

Purpose – The purpose of this paper is to present a numerical method for the simulation of steady and unsteady incompressible laminar flows, including convective heat transfer. Design/methodology/approach – A node centered, finite volume discretization technique is applied on hybrid meshes. The developed solver, is based on the artificial compressibility approach. Findings – A sufficient number of representative test cases have been examined for the validation of this numerical solver. A wide range of the various dimensionless parameters were applied for different working fluids, in order to estimate the general applicability of our solver. The obtained results agree well with those published by other researchers. The strongly coupled solution of the governing equations showed superiority compared to the loosely coupled solution as inviscid effects increase. Practical implications – Convective heat transfer is dominant in a wide variety of practical engineering problems, such as cooling of electronic chips, design of heat exchangers and fire simulation and suspension in tunnels. Originality/value – A comparison between the strongly coupled solution and the loosely coupled solution of the Navier-Stokes and energy equations is presented. A robust upwind scheme based on Roe’s approximate Riemann solver is proposed.

Convective Heat Transfer From a Sphere Due to Acoustic Streaming

1993 ◽  
Vol 115 (2) ◽  
pp. 332-341 ◽  
Author(s):  
A. Gopinath ◽  
A. F. Mills
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Acoustic Streaming ◽  
Reynolds Numbers ◽  
Materials Processing ◽  
Acoustic Levitation ◽  
Simple Experiment ◽  
Wide Range ◽  
Prandtl Numbers

Convective heat transfer from a sphere due to acoustic streaming is examined for large streaming Reynolds numbers. Analytical and numerical solution techniques are used to obtain Nusselt number correlations for a wide range of Prandtl numbers with particular emphasis on the case of Pr~1. A simple experiment performed to confirm some of the predictions is described. The results obtained can be used for the thermal analysis of containerless materials processing in space using acoustic levitation.

On the Convective Heat Transfer in a Tube of Elliptic Cross Section Maintained Under Constant Wall Temperature

1986 ◽  
Vol 108 (1) ◽  
pp. 33-39 ◽  
Author(s):  
M. A. Ebadian ◽  
H. C. Topakoglu ◽  
O. A. Arnas
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Wall Temperature ◽  
Elliptic Cross Section ◽  
Constant Wall Temperature ◽  
Elliptic Cross

The convective heat transfer problem along the portion of a tube of elliptic cross section maintained under a constant wall temperature where hydrodynamically and thermally fully developed flow conditions prevail is solved in this paper. The successive approximation method is used for the solution utilizing elliptic coordinates. Analytical expressions for temperature distribution and Nusselt number corresponding to the first cycle of approximation are obtained in terms of the ellipticity of the cross section. In the case of a circular section, the first cycle approximation of the Nusselt number is obtained as 3.7288 compared to the exact value of 3.6568. Representative temperature distribution curves are plotted and compared to those corresponding with constant wall heat flux conditions.

Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Pamela Vocale ◽  
Gian Luca Morini ◽  
Marco Spiga
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Slip Flow ◽  
The Cross ◽  
Cross Section Geometry

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

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