Simple correlation equations for optimum design of annular fins with uniform thickness

Simple correlation equations for optimum design of annular fins with uniform cross section are obtained in the present work. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rates. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins of uniform thickness.     

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.     

Heat transfer from rotating annular fins

Experiments have been performed to determine the heat transfer coefficients for arrays of shaft-attached, rotating annular fins. The experiments encompassed a wide range of rotational speeds and interfin spacings (including the limiting case of the single annular fin). The efficiency of the fins was equal to one. It was found that the fin heat transfer coefficient decreased with decreasing interfin spacing, the extent of the decrease being of major proportions at low rotational speeds but being quite moderate at high speeds. Thus, closely spaced fins can be used at high rotational speeds without a significant spacing-related decrease in the transfer coefficient, but at low speeds the fins must be farther apart to avoid overly low values of the coefficient. The heat transfer coefficient also decreased as the rotational speed decreased, with a particularly rapid dropoff at low speeds when the interfin spacing was small. For the most part, the fin heat transfer coefficients substantially exceeded those for an unfinned rotating shaft, thereby providing an incentive for finning. It was also found that at high rotational speeds, the heat transfer coefficient for a rotating disk served as a lower bound for the annular-fin heat transfer coefficients. To facilitate the use of the results for design, a correlation was developed which represents the fin heat transfer coefficient as a continuous function of the investigated independent parameters.     

Performance analysis and optimization of elliptic fins circumscribing a circular tube

The performance of elliptic disc fins has been analyzed using a semi-analytical technique. It has been shown that the efficiency of such fins can also be predicted very closely using the sector method. However, the equivalent annulus method is not suitable for this fin geometry. A method for the optimum design of fins, using a constraint of either fin volume or rate of heat dissipation has also been suggested. Optimum elliptical fins dissipate heat at a higher rate compared to an annular fin when space restriction exists on both sides of the fin. Even when the restriction is on one side only, the performance of elliptical fin is comparable to that of eccentric annular fin for a wide parametric range.     

Heat and mass transfer studies on metal-hydrogen reactor filled with MmNi4.6Fe0.4

A transient, three-dimensional computational investigation of coupled heat and mass transfer in an annular cylindrical hydrogen storage tank, equipped with fins and filled with MmNi_4.6Fe_0.4, is presented. The effects of different parameters such as length, thickness and thermal conductivity of fins and overall heat transfer coefficient on the hydrogen storage performance of the tank are studied. The predicted hydrogen storage capacity at different supply pressures showed good agreement with the experimental data reported in the literature. In addition, it is observed that the use of fins enhances heat transfer within the hydride bed and consequently 40% improvement of the time required for 90% storage can be achieved over the case without fins.     

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.     

Improvement of heat transfer through fins: A brief review of recent developments

Fins or extended surfaces are generally used in heat exchangers to enhance heat transfer between the main surface and ambient fluid. Various types of simple‐shaped fins, namely, rectangular, square, annular, cylindrical, and tapered, have been used with different geometrical combinations. To satisfy industrial demand, different trials have also been carried out for designing optimized fins. The optimization of fins can be performed either by enhancing heat dissipation at an exact fin weight or by diminishing the weight of the fin by precise heat dissipation. Recently a notable amount of work on some typical fins, like, porous fins and perforated fins, has also been carried out. This paper presents a brief review on heat transfer enhancement using fins of different types considering variable thermophysical and geometric parameters, which will also be useful for future use of geometrical modifications of extended surfaces, based on the cost and availability of space.     

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.     

Performance analysis and optimization of straight taper fins with variable heat transfer coefficient

In the present paper, the thermal analysis and optimization of straight taper fins has been addressed. With the help of the Frobenius expanding series the temperature profiles of longitudinal fin, spine and annular fin have been determined analytically through a unified approach. Simplifying assumptions like length of arc idealization and insulated fin tip condition have been relaxed and a linear variation of the convective heat transfer coefficient along the fin surface has been taken into account. The thermal performance of all the three types of fin has been studied over a wide range of thermo-geometric parameters. It has been observed that the variable heat transfer coefficient has a strong influence over the fin efficiency. Finally, a generalized methodology has been pointed out for the optimum design of straight taper fins. A graphical representation of optimal fin parameters as a function of heat duty has also been provided.     

B-spline curve based optimum profile of annular fins using multiobjective genetic algorithm

Thermal stress in annular fins, which influences the life of a fin, still needs its detail analysis. Heat transfer in annular fins is studied here as a multiobjective optimization problem. Representing fin profiles by B-spline curves, fin geometries are obtained primarily by maximizing heat transfer rate and minimizing thermal stress. Fin performance is further assessed by minimizing fin volume and maximizing fin efficiency and effectiveness. Evaluating temperature and thermal stress by hybrid spline difference method, non-dominated sorting genetic algorithm II is applied to approximate the Pareto-optimal front. The proposed procedure would be helpful for designers to adopt suitable fin configurations from the Pareto front.     

Heat transfer enhancement in annular fins using functionally graded material

This study presents a new approach on the heat transfer enhancement of annular fins with constant thickness using functionally graded materials. The thermal conductivity of the annular fin is assumed to be graded along the fin radius as a power‐law function. The resulting fin equation is solved by an approximate analytical method using the mean value theorem. The variable coefficients of second and third terms in the second‐order differential equation of the fin are replaced with their mean values along the fin radius. Several different graphs regarding the computed temperature profile, fin tip temperature, and fin efficiency are plotted with respect to the radii ratio thermo‐geometric parameter, and inhomogeneity parameter. It is demonstrated that the inhomogeneity parameter plays an important role on the heat transfer enhancement of the annular fin. However, for large radii ratios the effect of the inhomogeneity parameter decreases. Finally, it is stated that application of the functionally graded material in the annular fins, enhances the heat transfer rate between the fin and surrounding fluid resulting from the higher fin efficiency in comparison to the homogeneous annular fin. It is hoped that the results obtained from this study arouse interest among thermal designers and heat exchanger industries. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 603–617, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21053     

Approximate analytic temperature solution for uniform annular fins by adapting the power series method

The primary specification faced by thermal engineers when designing annular fins is the amount of heat transfer from a finned tube to a fluid. The temperature along annular fins of uniform thickness is governed by an ordinary differential equation of second order with variable coefficients, called the modified Bessel equation of zero order. Approximate temperature distributions and fin efficiencies, both of good quality, have been obtained by adapting a power series method for solving this Bessel equation with symbolic algebra software such as Maple or Mathematica. Students of heat transfer courses can benefit from this simple computational procedure that circumvents the use of Bessel functions and still produces approximate analytic results of good caliber.     

Transient response of annular fins subjected to constant base temperatures

A hybrid method is used to investigate the transient response of annular fins of various shapes subjected to constant base temperatures. The time-dependent terms in the governing equations are removed by using the Laplace transformation, and the integral method is used to solve the transformed boundary value problem. The inverse Laplace transform is calculated by applying the Fourier series technique with modification. It is shown that the Biot number and geometrical parameters have pronounced effect on the transient heat transfer in annular fins.     

An Inverse Design Problem of Estimating the Optimal Shape of Annular Fins Adhered to a Bare Tube of an Evaporator

The optimum shapes for annular fins adhered to a bare tube are estimated in the present inverse design problem using the conjugate gradient method (CGM), based on the desired fin efficiency and fin volume. The shape of the annular fins adhered to the bare tube must be optimally designed to produce a greater cold-producing effect in the evaporator. One of the advantages of using the present inverse algorithm in this inverse design problem is that it can handle problems with a large number of unknown parameters easily and converge rapidly. The results obtained using the CGM to solve the inverse design problem are justified based on numerical experiments. The study shows that when the Biot number and fin volume are varied, the optimum fin efficiency and optimum fin shape will also change; however, the optimum shape of an annular fin can always be obtained, and its fin efficiency is always better than that of five common annular fins.     

Analysis of Transient Heat Transfer in Annular Fins of Various Shapes with a Base Subjected to a Decayed Exponential Function of Time in Heat Flux

Abstract

This theoretical study of the heat flow within finned heat exchangers is of considerable practical importance because of the extensive utilization of finned surfaces for heat transfer enhancement in applications varying from air-cooled heat exchanges in the process industries to heat-rejection equipment in space vehicles.

This article investigates the transient heat transfer in two-dimensional annular fins of various shapes with a base subjected to a decayed exponential function of time in heat flux. In order to obtain the solutions of the governing partial differential equation, the following procedures of analysis are performed:

1. Normalize the governing partial differential equation subject to the appropriate initial and boundary conditions.

2. Take the Laplace transform with respect to time.

3. Utilize the integral method to solve the transformed system.

4. Achieve the inverse Laplace transform by the Fourier series technique, and the transient temperature distribution of the annular fins of various shapes are obtained as a base subjected to a decayed exponential function of time in heat flux.

5. Typical results in the form of graphs are also presented.     

Thermal Analysis of Orthotropic Pin Fins With Contact Resistance: A Closed-Form Analytical Solution

Light weight composite fins are considered to deal with thermal management problems for many microelectronic components. These composite fins are inherently anisotropic, therefore cannot be handled by a traditional one-dimensional approach; however, these materials can be designed to provide high thermal conductivity values in the desired direction to handle application-specific demands. In this article, we present analytical solutions for temperature distribution and heat transfer rate for orthotropic two-dimensional pin fins subject to convective-tip boundary condition and the contact resistance at the fin base. The generalized results are presented in terms of fin aspect ratio (fin length-to-radius ratio) and three dimensionless fin parameters that relate the internal conductive resistance to three convective resistances discussed in terms of dimensionless variables such as contact, tip, and axial Biot numbers, in addition to the axial-to-radial conductivity ratio. Several special cases including the insulated tip boundary condition are presented. It is demonstrated that the temperature distribution and heat transfer rate from the two-dimensional isotropic annular fin introduced earlier in the literature, can easily be recovered from the benchmark solutions presented in this article. Furthermore, dimensionless heat transfer rates are presented for the pin fins with contact resistance that can help to solve design and optimization problems of many natural-to-forced convection composite fins that are typically encountered in many microelectronic applications.     

Stability of Boiling on Annular Fin Surfaces

A theoretical investigation was conducted to understand the stability of boiling on annular fin surfaces with different boundary conditions. Lyapunov's function was derived for boiling on annular fin surfaces; its characteristics near the steady distribution are particularly investigated. With no pre-assumed functional form for the temperature perturbation to be imposed to the boiling system, a general stability analysis was established by optimizing Lyapunov's function. The steady temperature distribution with isothermal or isoflux condition was obtained numerically, and the boiling heat transfer characteristic was noted to be dependent of the fin configuration and boundary conditions. Annular fin surfaces can significantly benefit the heat transfer, and the fins with small inner radii have better performance of base heat flux or temperature. The most unstable mode and maximum eigenvalue were employed to describe the boiling stability under various boundary conditions, and characteristics of the obtained maximum eigenvalue very well match with those of the boiling heat transfer on annular fin surfaces.     

Approximate Techniques for the Performance Analysis and Optimization of Two-Dimensional Plate Fins Circumscribing Circular Tubes Plate

Efficiency of noncircular fins circumscribing circular tubes is generally determined by one of two approximate techniques, the equivalent annulus method or the sector method. In the present work the predictions of these two methods are compared with results obtained from a semianalytical technique for square, hexagonal, and eccentric annular fins. It is observed that the accuracy of the equivalent annulus method reduces with the increase of the two-dimensionality of the fins. However, the sector method guarantees very close agreement with the semianalytical technique over a wide range of parametric variations for all the fins. An improved definition of fin efficiency for the sector method is also put forward to take care of the heat loss from fin tips. Finally, it is shown that the optimum dimensions of the fins determined by the sector method closely match the predictions of the semianalytical technique.     

Optimization of a Thermally Asymmetric Convective and Radiating Annular Fin

In this study, convective and radiating annular fins of rectangular profile under thermally asymmetric conditions are examined using an analytical method. For the fin base condition, it is assumed that heat transfer from the fluid to the inside surface of the pipe is equal to the heat transfer through the fin base. The temperature distribution along the fin height at the fin tip is presented to demonstrate the effects of the thermally asymmetric condition. The heat loss and fin tip radius for fixed fin height are optimized as a function of the fin top convection characteristic number. Also, for fixed fin volume, the heat loss and fin dimensions are optimized based on the top, bottom, and tip convection characteristic numbers, radiation characteristic numbers, fin base radius, and fin volume. The fin effectiveness as a function of the top convection characteristic number and annular fin length are also presented.     

CONJUGATE NATURAL CONVECTION HEAT TRANSFER IN A VERTICAL ANNULUS WITH INTERNAL CIRCUMFERENTIAL FINS

A numerical investigation is carried out to study natural convection heat transfer in a vertical annular enclosure with circumferential fins mounted on the inner cylinder. Heat is generated within the inner solid cylinder, while the top, the bottom, and the outer walls are exposed to convection. The results show that, even though the presence of fins does not alter the main features of the flow in the large-scale recirculation zone, it reduces the mean temperature of the inner cylinder by a maximum of 9.6% at low Rayleigh numbers. Also, the number and length of fins have a pronounced effect on the mean temperature.