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 Isothermal Vertical Cylinder With an Exposed Upper Surface Mounted on a Flat Adiabatic Base

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

Natural convective heat transfer from an isothermal vertical cylinder which has an exposed horizontal top surface has been numerically studied. The exposed upper surface is maintained at the same temperature as the cylindrical vertical wall of the cylinder. The cylinder is mounted on a flat horizontal adiabatic base plate. In some circumstances the heat transfer rate from the exposed upper surface can be neglected compared to that from the curved surface of the cylinder and in some circumstances the heat transfer rate from the curved surface can be adequately predicted using vertical flat plate equations, i.e., by ignoring curvature effects. The flow has been assumed to be axisymetric about the vertical cylinder axis. The flow has also 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, 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 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 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 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.

A Numerical Study of the Simultaneous Natural Convective Heat Transfer From the Upper and Lower Surfaces of a Thin Isothermal Horizontal Circular Plate

2016 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Abdulrahim Kalendar
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Heat Transfer Rate ◽  
Convective Heat ◽  
Transfer Rate ◽  
The Mean ◽  
Adiabatic Section

Natural convective heat transfer from the top and bottom surfaces of a thin circular isothermal horizontal plate which, in general, has a centrally placed adiabatic section has been numerically investigated. The temperature of the plate surfaces is higher than the temperature of the surrounding fluid. The range of conditions considered is such that laminar, transitional, and turbulent flow occurs over the plate. The heat transfer from the upper and lower surfaces of the plate as well as the mean heat transfer rate from the entire surface of the plate have been considered. The flow has been assumed to be axisymmetric and steady. The k-epsilon turbulence model with account being taken of buoyancy force effects has been used and the solution has been obtained using the commercial CFD solver ANSYS FLUENT©. The heat transfer rate from the heated plate has been expressed in terms of a Nusselt number based on the outside plate diameter and the difference between the plate temperature and the fluid temperature far from the plate. The mean Nusselt number is dependent on the Rayleigh number, the ratio of the diameter of the inner adiabatic section to the outer plate diameter, and the Prandtl number. Results have only been obtained for a Prandtl number of 0.74, i.e., effectively the value for air. The variations of the mean Nusselt number averaged over both the upper and lower surfaces and of the mean Nusselt numbers for the upper surface and for the lower surface with Rayleigh number for various adiabatic section diameter ratios have been studied. The use of a reference length scale to allow the correlation of these mean Nusselt number-Rayleigh number variations has been investigated.

Numerical Study of Natural Convective Heat Transfer From a Very Short Isothermal Cylinder Mounted on a Flat Adiabatic Base

2013 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Cylinder Surface ◽  
Ansys Fluent ◽  
Transfer Rates ◽  
Number Variation ◽  
The Mean

Natural convective heat transfer from a vertical isothermal cylinder mounted on a flat adiabatic base has been numerically studied. The cylinder has an exposed top surface. The cylinder is relatively very short, i.e., has a height that is equal to or less than the cylinder diameter. Both the cases where the cylinder is pointing upward and where it is pointing downward have been considered. The governing equations have been numerically solved using the commercial CFD solver ANSYS FLUENT©. Results have only been obtained for Prandtl number = 0.74. The mean heat transfer rates have been expressed in terms of a Nusselt number, consideration being given both to the heat transfer rate from the entire cylinder surface and to the heat transfer rates from the side and top surfaces of the cylinder. The effect of the dimensionless cylinder height–to–diameter ratio on the Nusselt number variation has been studied in detail.

A Study of Three-Dimensional Mixed Convective Heat Transfer From Short Vertical Cylinders in a Horizontal Forced Flow

2000 ◽  
Author(s):  
David A. Scott ◽  
P. H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Three Dimensional ◽  
Forced Flow ◽  
Low Velocity ◽  
Buoyancy Forces ◽  
The Mean ◽  
Mixed Convective Flow ◽  
Comparison Of The Results

Abstract Heat transfer from relatively short vertical isothermal cylinders in a horizontal forced fluid flow has been considered. The flow conditions are such that the buoyancy forces resulting from the temperature differences in the flow are in general significant despite of the presence of a horizontal forced flow of air, that is, mixed convective flow exists. Because the cylinders are short and the buoyancy forces act normal to the forced flow, three-dimensional flow exists. The experiments were performed in a low velocity, open jet wind tunnel. The study involved the experimental determination of the mean heat transfer coefficient and a comparison of the results with a previous numerical analysis. Mean heat transfer rates were determined using the ‘lumped capacity’ method. The mean Nusselt number has the Reynolds number, Grashof number and the height to diameter ratio of the cylinders as parameters. The results have been used to determine the conditions under which the flow departs from purely forced convection and enters the mixed convection regime, i.e., determining the conditions for which the buoyancy effects should be included in convective heat transfer calculations for short cylinders.

scholarly journals A numerical study of free convective heat transfer within domed skylight cavities

2021 ◽  
Author(s):  
AmirAbbas Sartipi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Control Volume ◽  
Energy Performance ◽  
Vortex Cell ◽  
Design Elements ◽  
Gap Ratio

Domed skylights are important architectural design elements to deliver daylight and solar heat into buildings and connect buildings' occupants to outdoors. To increase the energy efficiency of skylighted buildings, domed skylights employ a number of glazing layers forming enclosed spaces. The latter are subject to complex buoyancy-induced convection heat transfer. Currently, existing fenestration design computer tools and building energy simulation programs do not, however, cover such skylights to quantify their energy performance when installed in buildings. his work presents a numerical study on natural laminar convection within concentric and vertically eccentric domed cavities. The edges of domed cavities are assumed adiabatic and the temperature of the interior and exterior surfaces are uniform and constant. The concentric and vertically eccentric domed cavities were studied when heated from inside and heated from outside, respectively. A commercial CFD package employing the control volume approach is used to solve the laminar convective heat transfer within the cavity. The obtained results showed steady flow for small Grashof numbers. For moderate and large Grashof numbers, depending on the gap ratio and the cases of heating from inside or outside, the flow may be steady or transient periodic with a single vortex-cell or multi vortex-cells. The Nusselt number for the case of heated from inside is greater than the case of heated from outside. The numerical results show that the changes in the gap ratio have smaller effect on Nusselt number in high profile domed skylights than lower profile domed skylights.

Computational analysis of convective heat transfer properties of turbulent slot jet impingement

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anuj Kumar Shukla ◽  
Anupam Dewan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
High Efficiency ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Jet Impingement ◽  
Complex Flow ◽  
Content Type

Purpose Convective heat transfer features of a turbulent slot jet impingement are comprehensively studied using two different computational approaches, namely, URANS (unsteady Reynolds-averaged Navier–Stokes equations) and SAS (scale-adaptive simulation). Turbulent slot jet impingement heat transfer is used where a considerable heat transfer enhancement is required, and computationally, it is a quite challenging flow configuration. Design/methodology/approach Customized OpenFOAM 4.1, an open-access computational fluid dynamics (CFD) code, is used for SAS (SST-SAS k-ω) and URANS (standard k-ε and SST k-ω) computations. A low-Re version of the standard k-ε model is used, and other models are formulated for good wall-refined calculations. Three turbulence models are formulated in OpenFOAM 4.1 with second-order accurate discretization schemes. Findings It is observed that the profiles of the streamwise turbulence are under-predicted at all the streamwise locations by SST k-ω and SST SAS k-ω models, but follow similar trends as in the reported results. The standard k-ε model shows improvements in the predictions of the streamwise turbulence and mean streamwise velocity profiles in the zone of outer wall jet. Computed profiles of Nusselt number by SST k-ω and SST-SAS k-ω models are nearly identical and match well with the reported experimental results. However, the standard k-ε model does not provide a reasonable profile or quantification of the local Nusselt number. Originality/value Hybrid turbulence model is suitable for efficient CFD computations for the complex flow problems. This paper deals with a detailed comparison of the SAS model with URANS and LES for the first time in the literature. A thorough assessment of the computations is performed against the results reported using experimental and large eddy simulations techniques followed by a detailed discussion on flow physics. The present results are beneficial for scientists working with hybrid turbulence models and in industries working with high-efficiency cooling/heating system computations.

Convective Heat Transfer Enhancement in a Circular Tube Using Twisted Tape

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Zhi-Min Lin ◽  
Liang-Bi Wang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Secondary Flow ◽  
Convective Heat ◽  
Tube Wall ◽  
Twisted Tape ◽  
Transfer Enhancement ◽  
Thermal Boundary Conditions

The secondary flow has been used frequently to enhance the convective heat transfer, and at the same flow condition, the intensity of convective heat transfer closely depends on the thermal boundary conditions. Thus far, there is less reported information about the sensitivity of heat transfer enhancement to thermal boundary conditions by using secondary flow. To account for this sensitivity, the laminar convective heat transfer in a circular tube fitted with twisted tape was investigated numerically. The effects of conduction in the tape on the Nusselt number, the relationship between the absolute vorticity flux and the Nusselt number, the sensitivity of heat transfer enhancement to the thermal boundary conditions by using secondary flow, and the effects of secondary flow on the flow boundary layer were discussed. The results reveal that (1) for fully developed laminar heat convective transfer, different tube wall thermal boundaries lead to different effects of conduction in the tape on heat transfer characteristics; (2) the Nusselt number is closely dependent on the absolute vorticity flux; (3) the efficiency of heat transfer enhancement is dependent on both the tube wall thermal boundaries and the intensity of secondary flow, and the ratio of Nusselt number with twisted tape to its counterpart with straight tape decreases with increasing twist ratio while it increases with increasing Reynolds number for both uniform wall temperature (UWT) and uniform heat flux (UHF) conditions; (4) the difference in the ratio between UWT and UHF conditions is also strongly dependent on the conduction in the tape and the intensity of the secondary flow; and (5) the twist ratio ranging from 4.0 to 6.0 does not necessarily change the main flow velocity boundary layer near tube wall, while Reynolds number has effects on the shape of the main flow velocity boundary layer near tube wall only in small regions.

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