Correlation Equations for Natural Convective Heat Transfer From Two Inclined Vertically Spaced Narrow Isothermal Flat Plates

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Abdulrahim Kalendar ◽  
Ahmed Kalendar ◽  
Sayed Karar ◽  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Edge Effect ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Primary Objective ◽  
Flat Plates ◽  
Plate Height ◽  
Adiabatic Surface ◽  
Plate Width

Natural convective flow over narrow plates induces an inward flow near the edges of the plate causing the flow to be three-dimensional near the edges of the plate. This influences the heat transfer rate near the edges of the plate and is referred to as the edge effect. The primary objective of this paper is to numerically study this edge effect and the interaction of the flows over two inclined vertically separated narrow heated plates of the same size embedded in a plane adiabatic surface. The cases where the plates and surrounding adiabatic surface are inclined at positive or negative angles to the vertical have been considered. Results were obtained by numerically solving the full three-dimensional form of governing equations using the commercial finite volume based software Fluent©. Results have only been obtained for a Prandtl number of 0.7; this being the value existing in the application which involved airflow that originally motivated this study. The results presented here cover Rayleigh numbers between 103 and 107, at all values of W considered, plate width-to-height ratios between 0.2 and 1.2, gap, at all values of W considered, to the plate height ratios of between 0 and 1.5, and, at all values of W considered, angles of inclination of between −45 deg and +45 deg. The effects of the Rayleigh number, dimensionless plate width, dimensionless gap between plates, and inclination angle on the heat transfer rate have been studied in detail. Empirical correlations defining the effect of these parameters on the heat transfer rate have been derived.

An Interaction of Natural Convective Heat Transfer From Two Adjacent Isothermal Narrow Vertical and Inclined Flat Plates

2009 ◽  
Author(s):  
Abdulrahim Kalendar ◽  
Patrick H. Oosthuizen ◽  
Bader Kalandar
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Three Dimensional ◽  
Flat Plates ◽  
Plate Height ◽  
Fluid Properties ◽  
Adiabatic Surface ◽  
Plate Width

Natural convective heat transfer from a two narrow adjacent rectangular isothermal flat plates of the same size embedded in a plane adiabatic surface, the adiabatic surface being in the same plane as the surfaces of the heated plates, has been numerically investigated. The two plates have the same surface temperature and they are aligned with each other but are separated form each other by a relatively small gap. Results for the case where the plates are vertical and where they are inclined at positive or negative angles to the vertical have been obtained. 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 using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical center plane between the two plates. The solution has been obtained by numerically solving the full three-dimensional form of governing equations, these equations being written in dimensionless form. The solution was obtained using the commercial finite volume method based cfd code, FLUENT. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, the dimensionless gap between two flat plates, and the Prandtl number as parameters. Results have only been obtained for a Prandtl number of 0.7 Results have been obtained for Rayleigh numbers between 103 and 107 for plate width-to-height ratios of between 0.15 and 0.6, for gap between the adjacent edges to plate height ratios of between 0 and 0.2, for angles of inclination between +45° and −45°.

Natural Convective Heat Transfer From an Inclined Narrow Isothermal Flat Plate

2008 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Abdulrahim Kalendar
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Adiabatic Surface ◽  
Plate Width

Natural convective heat transfer rate from an isothermal flat plate inclined at moderate angles to the vertical has been numerically studied. When the plate is wide compared to its height the flow can be adequately modeled by assuming two-dimensional flow. However, when the width of the plate is relatively small compared to its height, the heat transfer rate can be considerably greater than that predicted by these two-dimensional flow results. The heat transfer from a narrow isothermal plate embedded in a plane adiabatic surface, the adiabatic surface being in the same plane as the heated plate and inclined at an angle to the vertical has been numerically considered. Results for both positive and negative inclination angles have been numerically determined here. Attention was restricted to results for a Prandtl number of 0.7; this being approximately the value existing in the application that originally motivated this study. 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. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in dimensionless form. The solution was obtained using a commercial finite element method based code, FIDAP. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, and the Prandtl number as parameters. Results have been obtained for Rayleigh numbers between 103 and 107 for ratios of the plate width to the plate height of between 0.3 and 1.5 and for angles of inclination between +45° and −45°.

A Numerical Study of Three-Dimensional Natural Convective Heat Transfer From a Plate With a “Wavy” Surface

2001 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Matt Garrett
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Wavy Surface ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
The Mean

Abstract 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 parallel to the direction of flow over the surface and have a relatively small amplitude. Two types of wavy surface have been considered here — saw-tooth and sinusoidal. Surfaces of the type considered are approximate models of situations that occur in certain window covering applications, for example, and are also sometimes used to try to enhance the heat transfer rate from the surface. The flow has been assumed to be laminar. Because the surface waves are parallel to the direction of flow, the flow over the surface will be three-dimensional. 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 type approximation. The governing equations have been written in dimensionless form, the height of the surface being used as the characteristic length scale and the temperature difference between the surface temperature and the temperature of the fluid far from the plate being used as the characteristic temperature. The dimensionless equations have been solved using a finite-element method. Although the flow is three-dimensional because the surface waves are all assumed to have the same shape, the flow over each surface thus being the same, and it was only necessary to solve for the flow over one of the surface waves. The solution has the following parameters: the Grashof number based on the height, the Prandtl number, the dimensionless amplitude of the surface waviness, the dimensionless pitch of the surface waviness, and the form of the surface waviness (saw-tooth or sinusoidal). Results have been obtained for a Prandtl number of 0.7 for Grashof numbers up to 106. The effects of Grashof number, dimensionless amplitude and dimensionless pitch on the mean heat transfer rate have been studied. It is convenient to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface. A comparison of the values of these quantities gives a measure of the effectiveness of the surface waviness in increasing the mean heat transfer rate. The results show that while surface waviness increases the heat transfer rate based on the frontal area, the modifications of the flow produced by the surface waves are such that the increase in heat transfer rate is less than the increase in surface area.

Pressure Drop and Heat Transfer Characteristics of Louvered Fin Heat Exchangers

2013 ◽  
Vol 465-466 ◽  
pp. 500-504 ◽  
Author(s):  
Shahrin Hisham Amirnordin ◽  
Hissein Didane Djamal ◽  
Mohd Norani Mansor ◽  
Amir Khalid ◽  
Md Seri Suzairin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Heat Transfer Rate ◽  
Heat Exchangers ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Considerable Effect ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Louvered Fin

This paper presents the effect of the changes in fin geometry on pressure drop and heat transfer characteristics of louvered fin heat exchanger numerically. Three dimensional simulation using ANSYS Fluent have been conducted for six different configurations at Reynolds number ranging from 200 to 1000 based on louver pitch. The performance of this system has been evaluated by calculating pressure drop and heat transfer coefficient. The result shows that, the fin pitch and the louver pitch have a very considerable effect on pressure drop as well as heat transfer rate. It is observed that increasing the fin pitch will relatively result in an increase in heat transfer rate but at the same time, the pressure drop will decrease. On the other hand, low pressure drop and low heat transfer rate will be obtained when the louver pitch is increased. Final result shows a good agreement between experimental and numerical results of the louvered fin which is about 12%. This indicates the capability of louvered fin in enhancing the performance of heat exchangers.

Investigation of the effects of geometrical parameters, eccentricity and perforated fins on natural convection heat transfer in a finned horizontal annulus using three dimensional lattice Boltzmann flux solver

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mahyar Ashouri ◽  
Mohammad Mehdi Zarei ◽  
Ali Moosavi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Lattice Boltzmann ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Maximum Heat ◽  
Content Type ◽  
Dimensional Lattice ◽  
Fin Spacing

Purpose The purpose of this paper is to investigate the effects of geometrical parameters, eccentricity and perforated fins on natural convection heat transfer in a finned horizontal annulus using three-dimensional lattice Boltzmann flux solver. Design/methodology/approach Three-dimensional lattice Boltzmann flux solver is used in the present study for simulating conjugate heat transfer within an annulus. D3Q15 and D3Q7 models are used to solve the fluid flow and temperature field, respectively. The finite volume method is used to discretize mass, momentum and energy equations. The Chapman–Enskog expansion analysis is used to establish the connection between the lattice Boltzmann equation local solution and macroscopic fluxes. To improve the accuracy of the lattice Boltzmann method for curved boundaries, lattice Boltzmann equation local solution at each cell interface is considered to be independent of each other. Findings It is found that the maximum heat transfer rate occurs at low fin spacing especially by increasing the fin height and decreasing the internal-cylindrical distance. The effect of inner cylinder eccentricity is not much considerable (up to 5.2% enhancement) while the impact of fin eccentricity is more remarkable. Negative fin eccentricity further enhances the heat transfer rate compared to a positive fin eccentricity and the maximum heat transfer enhancement of 91.7% is obtained. The influence of using perforated fins is more considerable at low fin spacing although some heat transfer enhancements are observed at higher fin spacing. Originality/value The originality of this paper is to study three-dimensional natural convection in a finned-horizontal annulus using three-dimensional lattice Boltzmann flux solver, as well as to apply symmetry and periodic boundary conditions and to analyze the effect of eccentric annular fins (for the first time for air) and perforated annular fins (for the first time so far) on the heat transfer rate.

scholarly journals Three-dimensional transient mathematical model to predict the heat transfer rate of a heat pipe

2015 ◽  
Vol 7 (2) ◽  
pp. 168781401456781 ◽  
Author(s):  
S Boothaisong ◽  
S Rittidech ◽  
T Chompookham ◽  
M Thongmoon ◽  
Y Ding ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Pipe ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Three Dimensional

Numerical Study of the Heat Transfer Rate in a Helical Static Mixer

2006 ◽  
Vol 128 (8) ◽  
pp. 769-783 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Numerical Study ◽  
Three Dimensional ◽  
Static Mixer ◽  
Flow Conditions ◽  
Modern Approach ◽  
Static Mixers

In chemical processing industries, heating, cooling, and other thermal processing of viscous fluids are an integral part of the unit operations. Static mixers are often used in continuous mixing, heat transfer, and chemical reactions applications. In spite of widespread usage, the flow physics of static mixers is not fully understood. For a given application, besides experimentation, the modern approach to resolve this is to use powerful computational fluid dynamics tools to study static mixer performance. This paper extends a previous study by the authors on an industrial helical static mixer and investigates heat transfer and mixing mechanisms within a helical static mixer. A three-dimensional finite volume simulation is used to study the performance of the mixer under both laminar and turbulent flow conditions. The turbulent flow cases were solved using k−ω model. The effects of different flow conditions on the performance of the mixer are studied. Also, the effects of different thermal boundary conditions on the heat transfer rate in static mixer are studied. Heat transfer rates for a flow in a pipe containing no mixer are compared to that with a helical static mixer.

Three-dimensional numerical simulation of ferrofluid magnetoconvection in cubical enclosure heated with an inner spherical hot block

2021 ◽  
pp. 2150042
Author(s):  
Boubaker Dhibi ◽  
Brahim Ben-Beya
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Working Fluid ◽  
Cubical Enclosure ◽  
Sphere Radius ◽  
Number Formula

In this study, three-dimensional computational analysis is performed to investigate the magnetoconvection of ferrofluid ([Formula: see text]-water) within a cubical enclosure heated by an inner spherical hot block. The ferrofluid, considered as a working fluid, is modeled as a single-phase fluid. The inner spherical block is put at high temperature while all the remaining walls of the enclosure are exposed to low temperature. Two radii values ([Formula: see text] and [Formula: see text]) of the inner hot sphere are examined. Governing equations with corresponding boundary conditions are solved numerically applying a second-order accurate finite volume method on a staggered grid system, using an accelerated multigrid model. Simulations are carried out based on various flow-governing parameters such as Rayleigh number [Formula: see text], Hartmann number [Formula: see text] and ferrofluid nanoparticle volume fraction [Formula: see text]. The effects of the pertinent parameters in the performance of the system are also studied. The flow and thermal fields, the local and surface-averaged Nusselt numbers on the sphere and the enclosure for both configurations are detailed. The flow remains steady and laminar for all Rayleigh numbers regardless of the sphere radius. Obviously, heat transfer rate improves with [Formula: see text] augmentation and minimizes with Ha decrease. At the highest Ra and lowest Ha, higher inner sphere radius shows significantly better heat transfer rate (more than [Formula: see text]). Useful correlations are presented to quantify the surface-averaged heat transfer rate through the cubical enclosure.

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