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.     

Laminar Free Convection Around a Horizontal Cylinder with External Longitudinal Fins

The numerical solution of the laminar free convection of air around a horizontal cylinder with external longitudinal fins has been reported in this paper. The cylinder surface as well as the surfaces of each fin were assumed to be at a uniform temperature. The fluid drawn over a large angular domain moves out through a narrow, almost vertical strip known as plume, the thickness of which reduces with increasing buoyancy. The heat transfer increases with an increase in Grashof number, the number of fins, and fin length. For a constant fin surface, more fins of lower length result in a better heat transfer for Gr beyond about 10 ³ .     

Constructal design of vertical multiscale triangular fins in natural convection

Constructal design of vertical multiscale triangular fins in natural convection is investigated in this paper. The design consists of two parts. The first part is for single-scale triangular fins. The objective in the first design is to reach to the highest heat transfer density from the fins for three fin angles (15°, 30°, and 45°). The single-scale fins are placed in a horizontal array and considered as isothermal fins. The degrees of freedom are the fin angle, and the fin-to-fin spacing. The constraint is the fin height. The second part is for multiscale fins where small fins are placed between the large fins which are optimized in the first part. In the second part, the angles of the large and small scales fins are kept constant at (15°). The optimal fin-to-fin spacing which is obtained in the first part is considered a constraint in the second part. The Rayleigh numbers in this design are (Ra = 10³, 10⁴, and 10⁵). The two-dimensional mass, momentum, and energy equations for natural convection are solved with the finite volume method. The results show that there is a benefit of placing the small-scale fins where the percentage increase in the heat transfer density is (10.22%) at (Ra = 10³), and (50.6%) at (Ra = 10⁵) due to existence of the small fins between the large fins.     

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.     

Natural convection from a confined horizontal cylinder: the optimum distance between the confining walls

The laminar natural convection from an isothermal horizontal cylinder confined between vertical walls, at low Rayleigh numbers, is investigated by theoretical, experimental and numerical methods. The height of the walls is kept constant, however, their distance is changed to study its effect on the rate of the heat transfer. Results are incorporated into a single equation which gives the Nusselt number as a function of the ratio of the wall distance to cylinder diameter, t/D, and the Rayleigh number. There is an optimum distance between the walls for which heat transfer is maximum.     

Numerical validation of natural convection heat transfer with horizontal rectangular fin array using straight knurling patterns on fins—correlation for Nusselt number

Natural convection heat transfer from horizontal rectangular fin array with various knurling patterns has been studied experimentally by the present authors to investigate the effect of knurl‐produced surface roughness of fin on the heat transfer rate. The parameters like knurling height from base, knurling depth, fin spacing, and supply wattage were considered for parametric study. In the present paper, numerical method (CFD) is used to simulate natural convection phenomena with knurled fins and results are validated with the experimental data available from literature. The numerical results show similar trends compared with experimental data and one can use this method to study various fin configurations for knurling patterns. The flow patterns from experiments and numerical method are compared for different supply wattages and fin spacing to back up the conclusion. It is also observed that the variation in nondimensional roughness depth and spacing (D _kn/H and S/H) have more effect on Nusselt number than roughness height parameter (H _kn/H). Further, the method is extended to study numerically large number of fin configurations with knurling patterns to gather sufficient data for Nusselt number with respect to fin geometric parameters as above and establish correlation for heat transfer coefficient for such type of fins.     

Natural convection heat transfer and entropy generation inside porous quadrantal enclosure with nonisothermal heating at the bottom wall

In this work, we study numerically the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bottom wall. The effect of Darcy number is significant in dictating the Nusselt number only for higher values of Rayleigh number and the variation is more profound for larger values of Darcy number. The variation of entropy generation rate is significant with the Darcy number only for higher values of Rayleigh number. The entropy generation due to heat transfer is the significant contributor of irreversibility at low values of Darcy number, while for larger values of Darcy number and Rayleigh number entropy generation due to fluid friction becomes dominant.     

A computational fluid dynamics modeling of natural convection in finned enclosure under electric field

Numerical modeling of the electric field effect on natural convection in the square enclosures with single fin and multiple fins is investigated. The interactions between electric, flow, and temperature fields are analyzed using a computational fluid dynamics technique. The parameters considered are the supplied voltage, Rayleigh number, size of enclosure, electrode arrangement, number of fins, and fin length. It can be concluded that the flow and heat transfer enhancements are the decreasing function of Rayleigh number. Moreover, the heat transfer coefficient is substantially improved by the electric field effect especially at the high number of fins and long fin length. Surprisingly, the maximum average velocity and heat transfer enhancement occur at the different electrode arrangements for the single fin and multiple fins.     

Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure

ABSTRACT

In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with a porous medium. There is a significant alteration in Nusselt number with the orientation of the enclosure at higher values of Rayleigh number. It reveals that the variation of entropy generation rate with the inclination angle is significant for higher values of Darcy number. The dominant source of irreversibility is due to heat transfer at low values of Darcy number, whereas entropy generation due to fluid flow dominates over that due to heat transfer for larger values of Darcy number.     

Entropy generation due to natural convection from a horizontal isothermal cylinder in oil

Local entropy generation due to natural convection from a heated horizontal isothermal cylinder in oil was investigated numerically. The effect of viscous dissipation on entropy generation profiles was studied over a wide range of Rayleigh and Brinkman numbers. The results showed that viscous dissipation had minimal effect on entropy generation even when using a highly viscous oil.     

ANALYSIS OF COMBINED NATURAL AND FORCED CONVECTION IN VERTICAL SEMICIRCULAR DUCTS WITH RADIAL INTERNAL FINS

A numerical analysis of combined natural and forced convection is conducted for the fully developed laminar flow and heat transfer in a vertical semicircular duct with radial, internal longitudinal fins. Accurate solutions for heating upward flow are obtained by the finite difference method based on a fine grid, while the hydraulic and thermal conditions of the fins are ascertained. The results represent a range of Rayleigh numbers and various values of fin lengths and number of fins. The fully developed f Re and Nu values for pure forced convection in the finned semicircular duct are also documented. It is found that both the friction factor and the Nusselt number in the finned tube increase as the Rayleigh number increases. The effect of buoyancy is significant in semicircular ducts with short fins. By comparing the results of finless ducts with those of finned ducts, it was concluded that heat transfer in combined natural and forced convection in the semicircular duct is dramatically enhanced by using radial internal fins.     

Natural convection in cavities with a thin fin on the hot wall

A numerical study has been carried out in differentially heated square cavities, which are formed by horizontal adiabatic walls and vertical isothermal walls. A thin fin is attached on the active wall. Heat transfer by natural convection 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 10⁴ to 10⁹, dimensionless thin fin length from 0.10 to 0.90, dimensionless thin fin position from 0 to 0.90, dimensionless conductivity ratio of thin fin from 0 (perfectly insulating) to 60. It is found that Nusselt number is an increasing function of Rayleigh number, and a decreasing function of fin length and relative conductivity ratio. There is always an optimum fin position, which is often at the center or near center of the cavity, which makes heat transfer by natural convection minimized. The heat transfer may be suppressed up to 38% by choosing appropriate thermal and geometrical fin parameters.     

Heat transfer from a horizontal fin array by natural convection and radiation—A conjugate analysis

The problem of natural convection heat transfer from a horizontal fin array is theoretically formulated by treating the adjacent internal fins as two-fin enclosures. A conjugate analysis is carried out in which the mass, momentum and energy balance equations for the fluid in the two-fin enclosure are solved together with the heat conduction equations in both the fins. The numerical solutions by using alternating direction implicit (ADI) method yield steady state temperature and velocity fields in the fluid, and temperatures along the fins. Each end fin of the array is exposed to limited enclosure on one side and to infinite fluid medium on the other side. Hence a separate analysis is carried out for the problem of end fin exposed to infinite fluid medium with appropriate boundary conditions. From the numerical results, the heat fluxes from the fins and the base of the two-fin enclosure, and the heat flux from the end fin are calculated. Making use of the heat fluxes the total heat transfer rate and average heat transfer coefficient for a fin array are estimated. Heat transfer by radiation is also considered in the analysis. The results obtained for a four-fin array are compared with the experimental data available in literature, which show good agreement. Numerical results are obtained to study the effectiveness for different values of fin heights, emissivities, number of fins in a fixed base, fin base temperature and fin spacing. The numerical results are subjected to non-linear regression and equations are obtained for heat fluxes from the two-fin enclosure and single fin as functions of Rayleigh number, aspect ratio and fin emissivity. Also regression equations are obtained to readily calculate the average Nusselt number, heat transfer rate and effectiveness for a fin array.     

Improvement of the basic correlating equations and transition criteria of natural convection heat transfer

In this paper, improvements in the basic physical laws of natural convection heat transfer were implemented in two major respects by incorporating recent research findings in this field. A preferred transition criterion was adopted in this paper to correlate all of the experimental data. Since transition correlations are primarily flow stability problems, the Grashof number, instead of the Rayleigh number, was found to be the preferred criterion. Furthermore, in the case of natural convection heat transfer from a horizontal cylinder, a series of experimental data in the high‐Rayleigh‐number regions recently became available. These data made it possible to establish new reliable correlations and also to test the validity of previous correlations. It is concluded that the previous correlation for a horizontal cylinder in high‐Rayleigh‐number regions was based on unreliable experimental results. The transition correlation for a horizontal cylinder occurred at much higher values of Rayleigh number than the previous recommendation. In the case of natural convection heat transfer from a vertical plate, more accurate property values for air under pressurized conditions are now available. This made it possible to replot the reliable data of Saunders. From this result and the experimental result of Warner and Arpaci, a new set of basic correlations in natural convection heat transfer for laminar, transitional, and turbulent regimes are recommended. These recommendations reflect a better understanding of the basic physical laws in the field of heat convection. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 293–300, 2001     

Performance of annular fins with different profiles subject to variable heat transfer coefficient

Performance of annular fins of different profiles subject to locally variable heat transfer coefficient is investigated in this paper. The performance of the fin expressed in terms of fin efficiency as a function of the ambient and fin geometry parameters has been presented in the literature in the form of curves known as the fin-efficiency curves for different types of fins. These curves, that are essential in any heat transfer textbook, have been obtained based on constant convection heat transfer coefficient. However, for cases in which the heat transfer from the fin is dominated by natural convection, the analysis of fin performance based on locally variable heat transfer coefficient would be of primer importance. The local heat transfer coefficient as a function of the local temperature has been obtained using the available correlations of natural convection for plates. Results have been obtained and presented in a series of fin-efficiency curves for annular fins of rectangular, constant heat flow area, triangular, concave parabolic and convex parabolic profiles for a wide range of radius ratios and the dimensionless parameter m based on the locally variable heat transfer coefficient. The deviation between the fin efficiency calculated based on constant heat transfer coefficient, reported in the literature, and that presently calculated based on variable heat transfer coefficient, has been estimated and presented for all fin profiles with different radius ratios.     

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 prediction of entropy generation due to natural convection from a horizontal cylinder

Entropy generation due to natural convection has been calculated for three radii and a wide range of Rayleigh numbers for an isothermal cylinder. It was predominantly caused by conduction. The viscous contribution was negligible. Locations of high local entropy generation were identified for different configurations. The total entropy generation decreased with increasing cylinder size for a given value of the Rayleigh number.     

Optimum design of a longitudinal fin array with convection and radiation heat transfer using a genetic algorithm

In the present work, the optimization of a longitudinal fin array is investigated. Heat is transferred by conduction along the fins and dissipated from the fin surface via natural convection to the ambient and radiation to other fin surfaces and surrounding. The aim of the optimization is to find the optimum geometry and the number of fins in such a way that the rate of heat transfer from the array is maximized. A modified genetic algorithm is used to maximize the objective function which is defined as the net heat rate from the fin surface for a given length. The fin profile is represented by B-spline curves, where the shape of fin is determined by the positions of a set of control points. The effects of the base temperature, the fin length and the height of array on the optimum geometry and on the number of fins are investigated by comparing the results obtained for several test cases. In addition, the contributions of convective heat transfer and radiative heat transfer in net heat transfer are studied for these cases. The enhancement of heat transfer due to the optimum fin geometry is examined by comparing the results obtained for the optimum fin profile with those with conventional profiles.     

Numerical modelling and optimisation of natural convection heat loss suppression in a solar cavity receiver with plate fins

This study details the numerical modelling and optimization of natural convection heat suppression in a solar cavity receiver with plate fins. The use of plate fins attached to the inner aperture surface is presented as a possible low cost means of suppressing natural convection heat loss in a cavity receiver. In the first part of the study a three-dimensional numerical model that captures the heat transfer and flow processes in the cavity receiver is analyzed, and the possibilities of optimization were then established. The model is laminar in the range of Rayleigh number, inclination angle, plate height and thickness considered. In the second part of the study, the geometric parameters considered were optimized using optimization programme with search algorithm. The results indicate that significant reduction on the natural convection heat loss can be achieved from cavity receivers by using plate fins, and an optimal plate fins configuration exit for minimal natural convection heat loss for a given range of Rayleigh number. Reduction of up to a maximum of 20% at 0° receiver inclination was observed. The results obtained provide a novel approach for improving design of cavity receiver for optimal performance.     

Natural convection about a cylindrical pin element on a horizontal plate

Numerical study of laminar free convection about a single pin fin attached to a horizontal base plate has been reported in this article. Fluid at the far field moves horizontally towards the fin and then rises almost vertically along the fin and finally leaves through the top. With the increase in fin diameter heat transfer increases while the heat flux at fin base decreases establishing the advantage of large number of small diameter fins over fewer fins of bigger diameter. Correlation has been developed to predict the base heat flux for a given fin diameter to length ratio and Grashof number. This may be used to estimate the upper limit of free convection heat transfer from any horizontal heat sink with an array of circular pin elements.