Laminar Natural Convection Heat Transfer Research Articles

Rarefied flow and heat transfer characteristics over a vertical stretched surface

Similarity solution for the steady-state two-dimensional laminar natural convection heat transfer for a rarefied flow over a linearly vertical stretched surface is being proposed. Similarity conditions are obtained for the boundary layer equations for the vertical flat plate subjected to power law for the temperature variations. It is found that the similarity solution exists for linear temperature variation and linear stretching surface. The study shows that there are three different parameters affecting the flow and heat transfer characteristics for the rarefied flow over a vertical linearly stretched surface. These parameters represent the effects of the velocity slip ( K1), temperature jump ( K2), and the Prandtl number ( Pr). The effects of these parameters are presented. It is found that the velocity slip parameter affects both the hydrodynamic and thermal behaviors of such flows. Correlations for the skin friction as well as Nusselt number are being proposed in terms of Grashof number ( Grx), the slip velocity parameter ( K1), and the temperature jump parameter ( K2).

Natural convection heat transfer of molten salts around a vertically aligned horizontal cylinder set

The heat transfer from the vertical arrays of a set of equally spaced cylinders in molten salts is studied numerically to obtain the laminar natural convection heat transfer mechanism of molten salts around a vertically aligned horizontal cylinder set. Simulations are performed for arrays of 2–10 horizontal cylinders at a Rayleigh number based on a cylinder diameter between 2×103 and 5×105. Results show that the natural convective heat transfer of molten salts from the bottom cylinder of the array remains the same as that from a single cylinder. By contrast, the downstream cylinders may either be enhanced or reduced mainly depending on their location in the array and on the tube spacing. Heat transfer dimensionless correlating equations are proposed for any individual cylinder in the two vertically aligned horizontal cylinders. The heat transfer mechanism from the horizontal cylinders set in a vertical array is also simulated, and the results show that cylinder spacing can influence the average heat transfer rate around the whole tube array. Thus, in real applications, adjusting the cylinder spacing better enhances the average heat transfer from the whole tube array.

Free convection in a trapezoidal cavity filled with a micropolar fluid

The present investigation deals with the study of steady laminar natural convective flow and heat transfer of micropolar fluids in a trapezoidal cavity. The bottom wall of the cavity is kept at high constant temperature, the inclined walls is kept at low constant temperatures while the top horizontal wall is adiabatic. Governing equations formulated in dimensionless stream function and vorticity variables has been solved by finite difference method of the second order accuracy. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. Computations have been carried out to analyze the effects of Rayleigh number, Prandtl number and vortex viscosity parameter both for weak and strong concentration cases. Obtained results have been presented in the form of streamlines, isotherms and vorticity profiles as well as the variation of the average Nusselt number and fluid flow rate. It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity.

Two dimensional analysis of low pressure flows in the annulus region between two concentric cylinders.

A numerical simulation of the steady two-dimensional laminar natural convection heat transfer for the gaseous low-pressure flows in the annulus region between two concentric horizontal cylinders is carried out. This type of flow occurs in “evacuated” solar collectors and in the receivers of the solar parabolic trough collectors. A finite volume code is used to solve the coupled set of governing equations. Boussinesq approximation is utilized to model the buoyancy effect. A correlation for the thermal conductivity ratio (kr = keff/k) in terms of Knudsen number and the modified Rayleigh number is proposed for Prandtl number (Pr = 0.701). It is found that as Knudsen number increases then the thermal conductivity ratio decreases for a given Rayleigh number. Also, it is shown that the thermal conductivity ratio kr increases as Rayleigh number increases. It appears that there is no consistent trend for varying the dimensionless gap spacing between the inner and the outer cylinder (overline{{L_{g} }}) on the thermal conductivity ratio (kr) for the considered spacing range.

Correlations for Natural Convective Heat Transfer from Isothermal Surface of Octagonal and Hexagonal Shapes of Different Aspect Ratios

The effect of surface shape on laminar natural convective heat transfer from vertical isothermal hexagonal and octagonal flat plates embedded in a plane adiabatic surface, the adiabatic surface being in the same plane as the surface of the heated plate, has been numerically investigated. Results for the hexagonal and octagonal surface shapes with different aspect ratios 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. 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©14.5. The solution has the surface shape, the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have only been obtained for a Prandtl number of 0.7 for Rayleigh numbers between 103 and 108 for various surface shapes with width‐to‐height ratios between 0 and 0.6. The effect of these parameters on the mean Nusselt number has been studied and empirical correlation equations for the mean heat transfer rate have been derived.

Natural convection analysis through a radiatively participating media within a rectangular enclosure

A computational approach for the modelling of combined gas radiation and laminar natural convection heat transfer within a rectangular enclosure is presented. One wall among the others is maintained at a constant higher temperature (Th) while the others are of a constant lower temperature (Tc). The discrete-ordinate method (DOM) through S12 directions is applied to resolve the radiative transport equation (RTE) while the 'statistical narrow band correlated-k' (SNBCK) model is adopted to provide gas radiative properties. The effect of radiative contribution, the enclosure tilt angle, the boundary and geometry conditions are presented. Special attention is given to the effect scales of these parameters on the average Nusselt numbers. The results show that radiative effect remarkably contributes to the acceleration of the vortexes, improving heat exchanges at walls.

Effects of Variant Positions of Cold Walls on Narural Convection in a Triangular Cavitiy

The effect of different configurations of partial cold walls on laminar natural convection heat transfer for a right-angle triangular cavity heated from below has been studied numerically. The enclosure is filled with water and heat transfer surfaces such as hot and cold walls are maintained at constant temperature. The side and hypotenuse walls of the enclosure are detached from the middle and have been arranged in four different configurations, namely AB, BC, AD and CD for cooling purpose. The finite volume method is used to solve the dimensionless governing mass, momentum and energy equations. The problem has been solved to explore the effects of the pertinent parameters i.e. different configurations of cold walls and variation of Rayleigh number (10 5 ≤ Ra ≤ 10 7 ). Results are obtained from numerical simulation using commercial software package, FLUENT and presented in the form of streamlines and isotherms. The thermal performance of the enclosure has been expressed by local and average Nusselt numbers. From the analysis, it is observed that the temperature distribution and flow field are significantly affected by these parameters. The high heat transfer rate has been observed for the position AB while low for the position CD. Also, the heat transfer rate enhances as the Rayleigh number (Ra) increases.

Three-dimensional natural convection of molten Lithium in a differentially heated rotating cubic cavity about a vertical ridge

Laminar natural convection heat transfer in three-dimensional molten Lithium filled differentially heated enclosure, rotating about the vertical ridge is studied numerically. Computations are performed for a wide range of dimensionless parameters including the rotational Rayleigh number, and Taylor number while the values of Rayleigh number and Prandtl numbers are maintained constant at Ra=2×104 and Pr=0.0321, respectively. The results indicate that Coriolis forces seem to have a dominant role to suppress the thermal buoyancy driven effects. Transverse velocity isovaleurs show three-dimensional characteristics of the flow. By increasing, the Taylor number, the maxima of heat transfer gradually reduced about 55%. In the contrast, high rotational Rayleigh number values are found to significantly alter the flow patterns by increasing mixing which turn enhances the heat transfer.

Higher order compact scheme for laminar natural convective heat transfer from a sphere

Steady laminar natural-convective heat transfer from a solid sphere is studied by solving the complete Navier–Stokes and energy equations using higher order compact scheme in spherical polar coordinates. Results are obtained for Grashof numbers in the range 0.05 –125 and for Prandtl numbers ranging from 0.72 to 7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity lines and isotherms are plotted. It is found that the scheme captures mushroom shaped front in temperature contours which has been observed experimentally in the literature. The same phenomenon is not captured by upwind method.

Numerical investigation of the thermal behavior of heated natural composite materials

In the present work numerical investigation was carried out for laminar natural convection heat transfer from natural composite material (NCM). Three types of natural materials such as seed dates, egg shells, and feathers are mixed separately with polyester resin. Natural materials are added with different volume fraction (10%, 20%, and 30%) are heated with different heat flux (1078W/m2, 928W/m2, 750W/m2, 608W/m2, and 457W/m2) at (vertical, inclined, and horizontal) position. Continuity and Navier-Stocks equations are solved numerically in three dimensions using ANSYS FLUENT package 12.1 software commercial program. Numerical results showed the temperature distribution was affected for all types at volume fraction 30% and heat flux is 1078 W/m2, for different position. So, shows that the plumes and temperature behavior are affected by the air and the distance from heat source. Numerical results showed acceptable agreement with the experimental previous results.

Effect of Prandtl Number on Free Convection from Two Cylinders in a Square Enclosure

This study explores the effect of Prandtl number on the laminar natural convection heat transfer to Newtonian fluids in a square enclosure consisting of one hot circular cylinder and one cold circular cylinder. The walls of the square enclosure are maintained isothermal and at the same temperature as the cold cylinder and the fluid medium. The governing partial differential equations have been solved numerically over the following ranges of conditions: Grashof number, 10 to 105; Prandtl number, 0.7 to 100 (or the range of Rayleigh numbers as 7 to 107); and relative positioning of the cylinders, −0.25 to 0.25. However, the ratio of the radius of the cylinder to the side of the enclosure is held fixed at 0.2. Extensive results on the streamline and isotherm contours, the local Nusselt number distribution, and the average Nusselt number are discussed to delineate the influence of Grashof and Prandtl numbers on them for a given location with respect to the horizontal center line. The surface-averaged Nusselt number shows a positive dependence on Grashof and Prandtl numbers for a fixed location of the two cylinders. The heat transfer results have been correlated as a function of the Rayleigh number and geometric parameters, thereby enabling its prediction in a new application.

Investigation of laminar natural convection heat transfer within tubular daylighting devices for winter conditions

Recent developments in lighting and energy efficiency such as Tubular Daylighting Devices (TDD) aim at reducing energy consumption and providing homogeneous illumination in buildings. This ensures energy savings by reducing lighting energy consumption.To prevent the increase of total energy consumption, the heat loss at the TDD should be taken into consideration when using TDD. This paper presents an experimental and numerical study on the laminar natural convection in TDD for winter conditions. The results show that the overall heat transfer coefficient of TDD can be decreased by using a separator plate in the TDD. Moreover, the overall heat transfer coefficient changes significantly with the position of the separator plate.

Experimental study of laminar natural convection heat transfer from a vertical cylinder to slush nitrogen under constant heat flux conditions

Natural convection heat transfer from a vertical cylinder immersed in slush and subcooled liquid nitrogen and subjected to constant heat fluxes was investigated in order to determine the relative merits of slush nitrogen (SlN2) for immersion cooling. A glass dewar was used as a test vessel in which a cylindrical heater was mounted vertically, and heat transfer measurements were carried out for SlN2 and subcooled liquid nitrogen (LN2) in the laminar flow range. The results revealed advantages of SlN2 over subcooled LN2 in natural convection cooling. The local temperatures of the heated surface surrounded by solid nitrogen particles are measured to increase at much slower rates than in subcooled LN2, which is due to the latent heat of fusion of solid nitrogen. Even after the solid nitrogen particles surrounding the heater are apparently depleted, the average heat transfer coefficients for SlN2 are still found to be greater than those for LN2 with the improvement in heat transfer being larger for lower Grashof number regime. Our analysis also indicates that solid nitrogen particles in close proximity to heated surface do not discourage local convection due to the porous nature of SlN2, making the heat transfer in SlN2 more effective than in the case of solid–liquid phase change of nitrogen involving melting and conduction processes.

Three-dimensional analysis and numerical optimization of combined natural convection and radiation heat loss in solar cavity receiver with plate fins insert

The numerical study and optimization of combined laminar natural convection and surface radiation heat transfer in solar cavity receiver with plate fins is presented in this paper. Minimizing heat loss in cavity receivers is seen as an effective way to enhance the thermal performance and the use of plate fins has been proposed as a low cost means to minimize heat loss. Firstly, the influence of operating temperature, emissivity of the surface, orientation and the geometric parameters on the total heat loss from the receiver was investigated. It was observed that convective heat loss is largely affected by the angle of inclination of the receiver, the presence of fins and the number of fins in the receiver. As for the radiation heat loss it was observed that it is mainly influenced by the properties of the cavity receiver surface. The radiation heat loss was found to be constant at all the angles of the receiver. Significant reduction in natural convection heat loss from the cavity receiver was accomplished by using the plate fins whereas radiation heat loss was marginally reduced by about 5%. Secondly, the optimization was conducted to obtain the optimal fin geometry and lastly, the overall thermal efficiency of the receiver was presented at different operating temperatures. The overall cavity efficiency marginally increased by approximately 2% with the insertion of fin plates although the convective heat loss was suppressed by about 20%. This is due to the fact that radiation heat loss dominates at high operating temperatures compared to convective heat loss.

Benchmark results for natural and mixed convection heat transfer in a cavity

Purpose – The purpose of this paper is to numerically investigate steady, laminar natural and mixed convection heat transfer in a two-dimensional cavity by using a finite volume method with a fourth-order approximation of convective terms, with and without the presence of nanoparticles. Highly accurate benchmark results are also provided. Design/methodology/approach – A finite volume method on a non-uniform staggered grid is used for the solution of two-dimensional momentum and energy conservation equations. Diffusion terms, in the momentum and energy equations, are approximated using second-order central differences, whereas a non-uniform four-point fourth-order interpolation (FPFOI) scheme is developed for the convective terms. Coupled mass and momentum conservation equations are solved iteratively using a semi-implicit method for pressure-linked equation method. Findings – For the case of natural convection problem at high-Rayleigh numbers, grid density must be sufficiently high in order to obtain grid-independent results and capture reality of the physics. Heat transfer enhancement for natural convection is observed up to a certain value of the nanoparticle volume fraction. After that value, heat transfer deterioration is found with increasing nanoparticle volume fraction. Originality/value – Developed a non-uniform FPFOI scheme. Highly accurate benchmark results for the heat transfer of Al2O3-water nanofluid in a cavity are provided.

Laminar Natural Convection Heat Transfer Characteristics of Molten Salt Around Horizontal Cylinder

Abstract In order to obtain the laminar natural convection heat transfer mechanism of molten salt, the natural convection heat transfer of multi-component molten salts around a cylinder with different diameters was studied by simulation. The result showed that the natural convective heat transfer of molten salt in the Rayleigh number range of 1.57×10-2 -2.03×106 cound be predicted by Fand's correlation that took the viscous dissipation into consideration, in addition to Prandtl and Rayleigh numbers. With the increasing in Rayleigh number, the effect of viscous dissipation decreased, so the other correlations that neglected the effect of viscous dissipation cound also predict the natural convection of molten salt well. Those results cound be a foundation for predicting the natural convection heat transfer of molten salt.

Laminar natural convection heat transfer in a differentially heated cavity with a thin porous fin attached to the hot wall

Laminar natural convection heat transfer in a differentially heated square cavity with a thin porous fin attached to the hot wall is studied numerically under steady state condition. Various pertinent parameters were employed, such as the Rayleigh number, Darcy number, fin inclination angle, length and position of the fin. Three different fin lengths (L=0.2, 0.35, and 0.5) and positions (S=0.25, 0.5, and 0.75) are considered. The inclination fin angle is varied between 30° and 150°. The left wall of the cavity, to which the fin is attached, is assumed uniformly heated while the right wall is kept at a lower temperature. In addition, the horizontal walls of the cavity were considered insulated. Furthermore, the governing transport equations within the porous media are treated according to the volume-average theory while the Navier–Stokes equations were employed to represent the transport phenomena in the rest of the cavity. Moreover, the governing equations are solved using a finite element formulation based on the Galerkin method of weighted residuals. The results of this investigation showed that the presence of a porous fin increases the average Nusselt number when compared with the differentially heated cavity for various lengths, positions, and inclination angle of the fin. To achieve optimum heat transfer, the present results suggests that the porous fin should be placed either close to the bottom surface or in the middle of the vertical hot surface and an angle of 90°. Finally, a numerical correlation for the average Nusselt number was developed as a function of the employed range of the Rayleigh number, Darcy number, fin’s length and position.

Nu-Ra correlations for natural convection at high Ra numbers in air-filled tilted hemispherical cavities with dome oriented upwards. Disk submitted to constant heat flux

Purpose – The purpose of this paper is to propose correlations between Nusselt and Rayleigh numbers for the case of inclined and closed air-filled hemispherical cavities. The disk of such cavities is subjected to a constant heat flux. The study covers a wide range of Rayleigh numbers from 5×107 to 2.55×1012. Design/methodology/approach – Correlations are obtained from numerical approach validated by experimental measurements on some configurations, valid for several angles of inclination of the cavity between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°. Findings – The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones. Practical implications – The proposed correlations provide solutions for applications in several fields of engineering such as solar energy, aerospace, building, safety and security. Originality/value – The new relations proposed are the first published for high Rayleigh numbers for this type of geometry. They supplement the knowledge of natural convection in hemispherical inclined cavities and constitute a useful tool for application in various engineering areas as solar energy (thermal collector, still, pyranometer, albedometer, pyrgeometer), aerospace (embarked electronics), building, safety and security (controlling and recording sensors).

Transient free convection within air-filled hemispherical enclosures. Nu-Ra-Fo relationships for isothermal and inclined disk with dome oriented upwards

Purpose – Nusselt-Rayleigh-Fourier type correlations are proposed to quantify the temporal evolution of convective heat transfer occurring within air-filled hemispherical enclosures whose disk, initially at ambient temperature, is suddenly maintained at a higher temperature. The temperature difference imposed between this hot wall and the isothermal cold dome involves Rayleigh number varying between 104 and 2.55×1012. Depending on the application, the disk can be inclined with respect to the horizontal plane by an angle varying between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°. The paper aims to discuss these issues. Design/methodology/approach – The results are obtained by means of a numerical approach based on the finite volume method. The proposed correlations linked to the steady state Nusselt-Rayleigh internships recently published, concerning the same inclination angle and Rayleigh ranges. Findings – The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones. Practical implications – The proposed relationships can be applied in several engineering fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics. Originality/value – The new relationships proposed in this paper provide important information on the evolution of convective heat transfer during the transient regime.

Laminar natural convection heat transfer and air flow in three-dimensional cubic enclosures with a partially heated wall

In the present study, a finite volume computational procedure and a full multigrid technique are used to investigate laminar natural convection in partially heated cubic enclosures. Effects of heated strip disposition in the enclosure on the heat transfer rate are studied. Results are presented in the form of flow lines, isotherms plots, average Nusselt numbers, and average temperature on the heat source surface. Statistical distributions of temperature and average velocity fields and their root-mean-square values are presented and discussed.