Governing Equations of Convective Heat Transfer

2013 ◽  
pp. 49-78
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Governing Equations

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 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.

Natural Convective Heat Transfer on an Unheated Vertical Plate Attached to an Upstream Isothermal Plate

1983 ◽  
Vol 105 (4) ◽  
pp. 759-766 ◽  
Author(s):  
K. Kishinami ◽  
N. Seki
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Thermal Radiation ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Plate Thickness ◽  
Thermal Conductivity Ratio ◽  
Governing Equations ◽  
Difference Form ◽  
The Common

A numerical and experimental investigation on natural convective heat transfer with the coupling of heat conduction and thermal radiation from a vertical unheated plate connected to an upstream isothermal plate is carried out. The governing equations for conduction in the unheated plate and for convection in the boundary layer are written in finite difference form and are analyzed numerically by using an iterative technique coupled through the common heat flux with thermal radiation. The numerical results are discussed after comparing with the experimental results of temperature and velocity profiles and heat transfer coefficient. The coupling effects of heat conduction in the unheated plate and thermal radiation from the surface on laminar natural convective heat transfer from the plate connected to an isothermal heated upstream plate is greatly influenced by the plate-fluid thermal conductivity ratio and plate thickness, and the radiation emissivity of the plate.

A Numerical Study of Natural Convective Heat Transfer From an Inclined Isothermal Plate Having a Square Wave Surface

2011 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Jane T. Paul
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Boussinesq Approximation ◽  
Heated Plate ◽  
Governing Equations ◽  
Cross Sectional

Natural convective heat transfer from a wide isothermal plate which has a “wavy” surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The surface waves run in the horizontal direction, i.e., are normal to the direction of flow over the surface, and have relatively small amplitude. Attention has been restricted to the case where the waves have a rectangular cross-sectional shape. The plate is, in general, inclined to the vertical, consideration only being given to inclination angles at which the heated plate is facing upwards. The range of Rayleigh numbers considered extends from values that for a non-wavy vertical plate would be associated with laminar flow to values that would be associated with fully turbulent flow. The flow has been assumed to be steady and fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq approximation. The Reynolds averaged governing equations in conjunction with a standard k-epsilon turbulence model with buoyancy force effects fully accounted for have been used in obtaining the solution. The governing equations have been solved using the commercial cfd code FLUENT. The solution has the following parameters: (i) the Rayleigh number based on the height of the heated plate, (ii) the Prandtl number, (iii) the ratios of the amplitude of the surface waviness and of the pitch of the surface waves to the height of the plate, and (iv) the angle of inclination of the plate to the vertical. Results have only been obtained for a Prandtl number of 0.74. The effects of the other dimensionless variables on the mean surface Nusselt number have been numerically studied.

Numerical Investigation of Forced Convective Heat Transfer Around and Through a Porous Circular Cylinder With Internal Heat Generation

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Mohammad Sadegh Valipour ◽  
Ariyan Zare Ghadi
Keyword(s):  
Heat Transfer ◽  
Circular Cylinder ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Staggered Grid ◽  
Polar Coordinate System ◽  
Governing Equations

In this study, convective heat transfer around and through a porous circular cylinder together with internal heat generation has been investigated numerically. Governing equations containing continuity, momentum, and energy equations have been developed in polar coordinate system in both porous and nonporous media based on single-domain approach. However, governing equations in porous medium are derived using intrinsic volume averaging method. The equations are solved numerically based on finite volume method over staggered grid arrangement. Also, pressure correction-based iterative algorithm, SIMPLE, is applied for solving the pressure linked equations. Reynolds and Peclet numbers (based on cylinder diameter and velocity of free stream) are from 1 to 40. Also, Darcy number (Da) varies within the range of 10-6≤Da≤10-2 and porosity is considered 0.9 for all calculations. The influence of Da and Re numbers on local and average Nu numbers has been investigated. It is found that the local and average Nu numbers increase with any increase in Da number. Two correlations of average Nu number are presented for high and low Da numbers.

An Semi-Empirical Model of Turbulent Convective Heat Transfer to Fluids at Supercritical Pressure

2008 ◽  
Author(s):  
J. Derek Jackson
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Critical Pressure ◽  
Supercritical Pressure ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Governing Equations ◽  
Semi Empirical

Recently, there has been a renewed interest in heat transfer to fluids at supercritical pressure because of the consideration now being given to the Supercritical Pressure Water-cooled Reactor (SPWR). This will supply high temperature ‘steam’ to turbines at pressures well above the critical value. The particular feature of fluids at pressures just above the critical pressure which makes them of special interest is that as they change from being liquid-like to gaseous the transition occurs in a continuous manner over a narrow band of temperature without the discontinuous behaviour encountered when phase occurs in fluids at sub-critical pressure. However, when heat takes place within fluids at supercritical pressure, extreme non-uniformities of physical and transport properties can be present. The governing equations for flow and convective heat transfer have to be written in a form which takes account of the temperature dependence of the properties. They are complicated, highly non-linear and strongly inter-dependent. The proportionality between heat flux and temperature difference found in constant property forced convection no longer exists. Also, the effectiveness of heat transfer can be very sensitive to imposed heat flux. Particular problems arise due to the non-uniformity of density by virtue of the fluid being caused to accelerate where the bulk density is falling or as a consequence of the flow field and turbulence being modified by the influence of buoyancy. Severe impairment on heat transfer can be encountered due to such effects. The requirements for achieving similarity and the approach to the correlation of data on heat transfer to fluids at supercritical pressure are matters that need to be carefully considered and soundly based. This necessitates representing the general form of the governing equations and the boundary conditions in non-dimensional form to identify the parameters that are involved. In this paper, an extended model of turbulent heat transfer to fluids at supercritical pressure is presented which utilises a semi-empirical multiplier to account for the combined effects of flow acceleration and buoyancy.

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