Natural convection heat transfer in partially open inclined square cavities

A numerical study has been carried out on inclined partially open square cavities, which are formed by adiabatic walls and a partial opening. The surface of the wall inside the cavity facing the partial opening is isothermal. Steady-state heat transfer by laminar natural convection in a two dimensional partially open cavity is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10³ to 10⁶, dimensionless aperture size from 0.25 to 0.75, aperture position at high, center and low, and inclination of the opening from 0° (facing upward) to 120° (facing 30° downward). It is found that the volume flow rate and Nusselt number are an increasing function of Rayleigh number, aperture size and generally aperture position. Other parameters being constant, Nusselt number is a non-linear function of the inclination angle. Depending on the application, heat transfer can be maximized or minimized by selecting appropriate parameters, namely aperture size, aperture position and inclination angle at a given operation Rayleigh number.     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Numerical simulation of natural convection in a horizontal enclosure with a heat-generating conducting body

The physical model considered here is a horizontal layer of fluid heated below and cold above with heat-generating conducting body placed at the center of the layer. The dimensionless thermal conductivities of body considered in the present study are 0.1, 1 and 50. The dimensionless temperature difference ratios considered are 0.0, 0.25, 2.5 and 25. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral methodology for variety of Rayleigh number from 10³ to 10⁶. Multi-domain technique is used to handle square-shaped heat-generating conducting body. The fluid flow, heat transfer and time- and surface-averaged Nusselt number are investigated for various ranges of Rayleigh number, thermal conductivity ratio and dimensionless temperature difference ratio. The results for the case of conducting body with heat generation are also compared to those without heat generation to see the effects of heat generation from the conducting body on the fluid flow and heat transfer in the enclosure.     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

Numerical Studies on Natural Convection in a Trapezoidal Enclosure With Discrete Heating

Abstract

A steady state laminar natural convection flow in a trapezoidal enclosure with discretely heated bottom wall, adiabatic top wall, and constant temperature cold inclined walls is performed. The finite volume based commercial code “ANSYS-FLUENT” is used to investigate the influence of discrete heating on natural convection flows in a trapezoidal cavity. The numerical solution of the problem covers various Rayleigh numbers ranging from 10³ to 10⁶, non-dimensional heating length ranging from 0.2 to 0.8 and Prandtl number is 0.7. The performance of the present numerical approach is represented in the form of streamfunction, temperature profile and Nusselt number. Heat transfer increases with increase of Rayleigh numbers at the corners of the cavity for same heating length from center of the bottom wall. However, the heat transfer rate is less and almost constant for the Rayleigh numbers considered. It is found that the average Nusselt number monotonically increases with increase of Rayleigh number and length of heat source. The variation of local and average Nusselt numbers is more significant for larger length of heating than smaller one. The heat transfer correlations useful for practical design problems have been predicted.     

Effects of thin fin on natural convection in porous triangular enclosures

A two-dimensional solution of natural convection in solid adiabatic thin fin attached to porous right triangular enclosures has been analyzed numerically. The vertical wall of the enclosure is insulated while the bottom and the inclined walls are isothermal. The temperature of the bottom wall is higher than the temperature of the inclined wall. Governing equations, which are written using Darcy model, are solved via the finite difference technique. The Successive Under Relaxation (SUR) method was used to solve linear algebraic equations. Dimensionless location of the thin fin from 0.2 to 0.6, the aspect ratio of triangular enclosure from 0.25 to 1, Rayleigh number from 100 to 1000 and the dimensionless height of the fin from 0.1 to 0.4 are used as governing parameters that are effective on heat transfer and fluid flow. Results for the mean Nusselt number, velocity profiles, the contour maps of the streamlines and isotherms are presented. It is observed that the thin fin can use as a passive control element for flow field, temperature distribution and heat transfer.     

Conjugate natural convection heat transfer in a partitioned differentially-heated square cavity

In this study numerical results for conjugate natural convection flow and heat transfer in a differentially-heated square cavity divided by a partition with finite thickness and thermal conductivity are presented. A series of numerical simulation is carried out using the finite volume method over a wide range of the Rayleigh number (10⁵–10⁹), with three dimensionless partition thicknesses (0.05, 0.1 and 0.2) and three dimensionless partition positions (0.25, 0.5 and 0.75), both are non-dimensionalized by the cavity width. The results show that the average Nusselt number increases with the Rayleigh number but decreases with partition thickness. It is also found that the partition position has a negligible effect on the average Nusselt number for the whole range of Rayleigh number considered.     

NATURAL CONVECTION AND ENTROPY GENERATION FROM A CYLINDER WITH HIGH CONDUCTIVITY FINS

The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average effective Nusselt number was studied over a wide range of Rayleigh numbers. The results showed that there was an optimal combination of number of fins and fin height for maximum heat transfer from the cylinder for a given value of Rayleigh number. A high number of short fins slightly decreased the heat transfer from the cylinder. The calculated velocity and temperature profiles also were used to study the total entropy generation. The total entropy production was dominated by entropy generation due to thermal effects. The exception was at Ra _D = 10³ and a large cylinder diameter where entropy generation was dominated by entropy generation due to viscous effects. This information can be used to access the changes in the thermodynamic efficiency due to the addition of fins to enhance the natural convection heat transfer from a horizontal cylinder.     

Electrohydrodynamic enhancement of heat transfer in vertical fin array using computational fluid dynamics technique

Electrohydrodynamic enhanced heat transfer of the natural convection inside an enclosure with a vertical fin array is numerically investigated via a computational fluid dynamics technique. The parameters considered in a numerical modeling are supplied voltage, Rayleigh number, inclined angle, number of electrodes, electrode arrangement, number of fins, and fin length. The results reveal that the flow and heat transfer enhancements are significantly dependent on the number and position of electrodes around the fins. Moreover, the heat transfer coefficient is substantially improved by the electric field especially at the large number of fins and the long fin length.     

Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures

Conjugate turbulent natural convection and surface radiation in rectangular enclosures heated from below and cooled from other walls, typically encountered in Liquid Metal Fast Breeder Reactor (LMFBR) subsystems, have been investigated by a finite volume method for various aspect ratios. The formulation comprises the standard two equation k–ε turbulence model with physical boundary conditions (no wall functions), along with the Boussinesq approximation, for the flow and heat transfer. As far as radiation is concerned, the radiosity – irradiation formulation for a transparent fluid of Prandtl number 0.7 has been employed. The conjugate coupling on the walls has been handled by using a fin type formulation. The Rayleigh number based on the width of the enclosure is varied from 10⁸ to 10¹² and the aspect ratio is varied from 0.5 to 2.0. Detailed results including stream lines, temperature profiles, and convective, radiative and overall Nusselt numbers are presented. A correlation for the mean convection Nusselt number in terms of Rayleigh number and aspect ratio is proposed for design purposes. The influence of the wall emissivity and the external heat transfer coefficient on the heat transfer from the enclosure has also been investigated.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

An experimental investigation on the effect of a perforated fin on free convection heat transfer from a confined horizontal cylinder

Natural convection heat transfer from an isothermal horizontal fin attached to a cylinder, confined between two adiabatic walls of constant height is investigated by the Mach–Zehnder interferometry technique. This study is focused on the effect of a perforated fin attached to the bottom of a cylinder while the vertical position of the cylinder (Y ) changes between two walls with a constant distance of W measuring 1.5 times the cylinder diameter. The cylinder's average Nusselt numbers are determined for three ratios of vertical position to its diameter, Y /D = 0.5, 1.5, 2, and 3. The Rayleigh number ranges from 4.5 × 10³ to 1.2 × 10⁴. The distance between the walls is chosen to be 1.5 D, that is, an optimum distance at which the Nusselt number is maximum. The effect of the perforated fin on free convection heat transfer is investigated and compared with other works. Results show outstanding enhancement in heat transfer, with a minimum result of 40% and maximum of 90%. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21041     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Magnetohydrodynamic Natural Convection in a Square Enclosure with Four Circular Cylinders Positioned at Different Rectangular Locations

We deploy a finite volume numerical computation to investigate the two-dimensional hydromagnetic natural convection in a cooled square enclosure in the presence of four inner heated circular cylinders with identical shape. The inner circular cylinders are placed in a rectangular array with equal distance away from each other within the enclosure and moving along the diagonals of the enclosure. All the walls of the enclosure are kept isothermal with temperatures less than that of the cylinders. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. All solid walls are assumed electrically insulated. Simulations are performed for a range of the controlling parameters such as the Rayleigh number 10³ to 10⁶, Hartmann number 0 to 50, and the dimensionless horizontal and vertical distance from the center of a cylinder to center of another cylinder 0.3 to 0.7. The study specifically aims to understand the effects of the location of the cylinders in the enclosure on the magnetoconvective transport, when they moved along the diagonals of the enclosure. It is observed that the unsteady behavior of the flow and thermal fields at relatively larger Rayleigh numbers and for some cylinder position are suppressed by imposition of the magnetic field. The heat transfer strongly depends on the position of the cylinders and the strength of the magnetic field. Hence, by controlling the position of the objects and the magnetic field strength, a significant control on the hydrodynamic and thermal transport can be achieved.     

Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure

In this paper, numerical simulations of laminar, steady, two-dimensional natural convection flows in a square enclosure with discrete heat sources on the left and bottom walls are presented using a finite-volume method. Two different orientated wall boundary conditions are designed to investigate the natural convection features. The computational results are expressed in the form of streamlines and isothermal lines for Rayleigh numbers ranging from 10² to 10⁷ in the cavity. In the course of study, a combination of third-order and exponential interpolating profile based on the convective boundedness criterion is proposed and tested against the partially heated cavity flow up to the highest Rayleigh number 10⁷. The effects of thermal strength and heating length on the hydrodynamic and thermal fields inside the enclosure are also presented. Numerical results indicate that the average Nusselt number increases as Rayleigh number increases for both cases. Moreover, it is seen that the effect of the heat transfer rate due to the heating strength on the left wall is different from the one on the bottom. For the heater size effect, it is observed that by increasing the length of heat source segment, the heat transfer rate is gradually increased for both cases.     

Entropy generation for natural convection by heated partitions in a cavity

Entropy generation for natural convection in a partitioned cavity, with adiabatic horizontal and isothermally cooled vertical walls, is studied numerically by both a FORTRAN code and the commercially available CFD-ACE software. Effects of the Rayleigh number, the position of the heated partition, and the dimensionless temperature difference on the local and average entropy generation rate are investigated. Proper scale analysis of the problem showed that, while fluid friction term has nearly no contribution to entropy production, the heat transfer irreversibility increases monotonically with the Nusselt number and the dimensionless temperature difference.     

Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side

A numerical study has been carried out in rectangular enclosures, which have a vertical active wall with all the other walls insulated. The equally divided active sidewall is heated and cooled with sinusoidal temperature profiles. Two cases have been considered: the first is the lower part is heated while the upper part is cooled and the second, the upper part is heated and lower part is cooled. Steady state heat transfer by laminar natural convection has been studied by numerically solving equations of mass, momentum and energy, to determine the thermal penetration in the enclosures and heat transfer as a function of Rayleigh number, the aspect ratio and the position of side heating with respect to side cooling. Rayleigh number was varied from 10³ to 10⁶ and the aspect ratio from 0.2 to 5, and the results are presented in the form of streamlines and isotherms, local and average Nusselt number, and heat penetration length. It is found that the penetration approaches to 100% at high Rayleigh numbers when the lower part is heated while the higher part is cooled. In the case of the higher part is heated and the lower part is cooled, the penetration is limited to 70% passing through maxima at Rayleigh number below 10⁶.     

Numerical study of laminar free convection about a horizontal cylinder with longitudinal fins of finite thickness

Conjugate numerical solution of laminar free convection about a horizontal cylinder with external longitudinal fins of finite thickness has been carried out. Fins alone contribute very small to the total heat transfer but they greatly influence the heat transfer from the uncovered area of the cylinder. Among the various fin parameters, thickness has the greatest influence on heat transfer. The rate of heat transfer is above that for the free cylinder only when the attached fins are very thin. For thin fins, there exist a fin length, which maximizes the rate of heat transfer. The optimum number and dimensionless length of the fins were obtained as 6 and 0.2 respectively when fin thickness is 0.01, the thinnest among those investigated in this study.     

Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure

Laminar conjugate conduction-natural convection heat transfer in a 3-D inclined cubic enclosure comprised of finite thickness conductive walls and central cavity is numerically investigated. The dimensionless governing equations describing the convective flow and wall heat conduction are solved by the high accuracy multidomain pseudospectral method. Computations are performed for different Rayleigh numbers (10³ ≤ Ra* ≤ 10⁶), thermal conductivity ratios (1 ≤ k ≤ 100), dimensionless wall thickness (0 ≤ s ≤ 0.25), and enclosure inclinations (?30° ≤ α ₁ ≤ 30°, 0° ≤ α ₂ ≤ 45°). The effects of the above controlling parameters on the heat transfer performances of the enclosure system are investigated in detail, with emphases on the variations of wall conduction and fluid convection heat transfer, and the interactive heat transfer conditions between solid walls and fluid in the central cavity. Numerical results reveal that the existence of enclosure walls reduces the temperature gradient across the cavity and alters the temperature distribution within the solid walls; thus, the fluid convection is complexly determined by the combined effects of k and s, and is greatly affected by enclosure inclinations at high Rayleigh numbers. Moreover, the temperature distributions and solid-fluid interactive heat transfer conditions are provided for further interpretation and demonstration of the effects of the solid walls.     

Conjugate natural convection in an enclosure with a heat source of constant heat transfer rate

A numerical study of two-dimensional transient natural convection in a rectangular enclosure having finite thickness heat-conducting walls with a heat source of constant heat transfer rate located on the inner side of the left wall in conditions of convection–radiation heat exchange with an environment on one of the external boundaries has been performed. Mathematical simulation has been carried out in terms of the dimensionless variables such as stream function – vorticity – temperature. Stream function, vorticity and energy equations have been solved by finite difference numerical method. The relevant governing parameters were: the Grashof number from 10⁶ to 10⁸, the Prandtl number, Pr = 0.7 and the conductivity ratio. Detailed results including streamlines and temperature profiles have been obtained.