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.     

Performance and optimization analysis of SRC profile fins subject to simultaneous heat and mass transfer

Fin material near the tip of a uniform cross sectional (UC) fin does not participate actively in transferring heat. This effect may seem to have progressed much with the increase in fin length. A uniform cross sectional fin with a step reduction in local cross section (SRC) not only increases the effective utilization of fin material near the tip but also it promotes the ease of fabrication. In this study, an effort has been devoted to determine analytically the overall fin performance of both longitudinal and pin fins of SRC profile under fully dry, partially wet and fully wet conditions. The effect of various design and psychometric parameters on the fin performance of SRC fins has been investigated and compared it is with the corresponding UC fin. A scheme for optimizing SRC fins has also been demonstrated in the present work. From the result, it can be highlighted that the optimum values of Biot number and aspect ratio of SRC fins increase with the increase in relative humidity for the same fin volume. In comparison with the UC fin for the identical fin volume, the SRC fin transfers more rate of heat and consequently, this difference in heat transfer rate increases slowly with the relative humidity.     

A Nonlinear Fin Design Problem in Estimating the Optimal Shapes of Longitudinal and Spine Fully Wet Fins

In the present nonlinear fully wet fin design problem, the optimum shapes for the longitudinal and spine fins are estimated by using the conjugate gradient method (CGM) based on the desired fin efficiency and fin volume. For many practical engineering applications, thermal conductivity and heat transfer coefficient of fin are a function of temperatures. This makes the design problem nonlinear and complicated. For this reason, the present work is focused on examining these kinds of design problems. The validity of this design algorithm using CGM to solve the nonlinear fin design problems are justified based on the numerical experiments. Results show that when the Biot number, relative humidity, and thermal conductivity are varied, the optimum fin efficiency and optimum fin shape are also subjected to change, and any reasonable designs for fully wet fins can always be obtained.     

Optimization of Longitudinal Rectangular Fins Through the Concept of Relative Inverse Admittance

Introduced 7 years ago, the concept of relative inverse admittance represents a new fin performance parameter intended to encompass all the requirements needed for fin applications in thermal engineering. A noteworthy characteristic of this concept is that it serves as a vehicle to optimize a wide variety of longitudinal fins of rectangular profile. In this article, the relative inverse admittance is numerically calculated for longitudinal fins of rectangular profile under real two-dimensional (2-D) and quasi one-dimensional (1-D) conditions, with adiabatic and convective tips. In the case of an adiabatic tip, optimum fins are deduced from a double-entry abacus that uses effectiveness as a parameter. The connection between effectiveness and the Biot transversal number is also shown graphically. The independent design variables are the heat transfer coefficient/thermal conductivity ratio and the volume of the fin. The definition of Biot number provides the optimum thickness of the fin. For the convective tip condition, the double-entry abacus directly provides the optimum length for the same independent variables. From this optimum thickness, the Biot number provides the effectiveness through the graph that relates these two parameters.     

Optimum Profiles for Asymmetrical Longitudinal Fins in Annular Ducts

In the present work the geometry of annular ducts with asymmetrical longitudinal fins is optimized in order to enhance the heat transfer under laminar coolant flow conditions. The heat transferred is also maximized for a given amount of material or hydraulic resistance. Polynomial profiles are assigned to the two lateral fin surfaces. Velocity and temperature distributions on the annular duct cross section are determined with the help of a finite-element model. A global heat transfer coefficient and an equivalent Nusselt number are then calculated. Lastly, optimum asymmetrical fins obtained by means of a genetic algorithm are shown for different situations and their performance is compared with those of optimum symmetrical fins.     

Orthotropic thermal conductivity effect on cylindrical pin fin heat transfer

Analytical equations for temperature distribution and heat transfer rate from a cylindrical pin fin with orthotropic thermal conductivity, encountered in the use of thermally enhanced polymer composites, are derived and validated using detailed finite-element results. The thermal performance of such fins was found to depart from the classical fin solution with increasing radial conductivity-based Biot number. The in depth analysis of developed orthotropic axi-symmetric pin fin temperature and heat transfer rate equation is carried out to better understand the heat flow rate in such fins.     

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.     

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.     

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.     

Characteristics of forced convection heat transfer in vertical internally finned tube

This work presents a numerical investigation of a vertical internally finned tube subjected to forced convection heat transfer. The governing equations were solved numerically using the control volume technique. Nusselt number, Nu, and friction factor multiplied by Reynolds number, fRe, are influenced greatly by the height and number of the radial fins. The velocity and temperature distributions inside the tube depend on the number and height of the radial fins. This paper suggests that for best heat transfer to be achieved there is an optimum combination of fin numbers and height.     

A model on the basis of analytics for computing maximum heat transfer in porous fins

This study presents an analytical work on the performance and optimum design analysis of porous fin of various profiles operating in convection environment. Straight fins of four different profiles, namely, rectangular, convex parabolic and two exponential types are considered for the present investigation. An analytical technique based on the Adomian decomposition method is proposed for the solution methodology as the governing energy equations of porous fins for all the profiles are non-linear. A comparative study has been carried out among the results obtained from the porous and solid fins, and an appreciable difference has been noticed for a range of design conditions. Finally, the result shows that the heat transfer rate in an exponential profile with negative power factor is much higher than the rectangular profile but slightly higher than the convex profile. On the other hand, the fin performance is observed to be better for exponential profiles with positive power factor than other three profiles. A significant increase in heat transfer through porous fins occurs for any geometric fin compared to that of solid fins for a low porosity and high flow parameter.     

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.     

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.     

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.     

Two-Dimensional Effects and Design Criteria for Convective Extended Surfaces

Abstract

An analysis of the thermal performance of convective extended surfaces is presented that takes into account the primary function of the fins, which is to augment the heat transfer. The measure of the heat transfer augmentation is expressed by the removal number N_r, which we proposed should be O(10). It is shown that in order to satisfy this criterion the transverse Biot number hw/k must be of the order of 0.01. Further, it is argued that the fin is fully utilized if the aspect number is O(1). These criteria, B_i; = O(0.01) and u = 0(1), offer guidelines for designing fins and are applicable to longitudinal, annular, and pin fins, of uniform thickness or tapered profile. They must substitute the criterion that is frequently used, B_i < I, which was derived from the analysis of longitudinal fins. A very important consequence of this investigation is that fins designed to meet the above criteria can be analyzed using the classical one-dimensional method without introducing any appreciable error.     

Performance analysis and optimization of a thermally non-symmetric annular fin

Considering thermally non-symmetric convective boundary conditions, optimum dimensions of an annular fin which has a rectangular cross-section are investigated. Two-dimensional heat diffusion equation is solved analytically to obtain temperature distribution and heat transfer rate. In this work, fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rates. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found employing NCONF routine in the IMSL Library. The derived condition of optimality gives an open choice to the designer.     

Analysis of thermal performance and optimization of concentric circular fins under dehumidifying conditions

The analysis of wet fins was carried out by many investigators with the variation of a linear relationship between specific humidity and the corresponding saturation temperature of air adjacent to the fin surface. For determination of the fin surface temperature under this scheme, fin-tip temperature is essentially known a priori which can be employed to calculate the psychrometric parameters associated with the dehumidification process. On the other hand, the tip temperature is only known after the salving the governing equation and it is also a function of the psychrometric properties of air. Thus for the simplicity, dew point temperature is considered as the tip temperature for calculating only the psychrometric parameters of fully wet fins in a recent publication. Nevertheless, in the actual situation this dew point temperature never satisfies at the tip and therefore psychrometric parameters calculated with the assumption of the dew point temperature at the tip may be incorrect. In the present work, an iterative scheme is demonstrated for determination of the actual tip temperature and local fin surface temperature. With considering this aspect, thermal analysis of a new geometric fin, namely, annular step fin (ASF) is proposed for the more effective utilization of fin material in comparison with the annular disc fin. An optimization study has also been made by using the modified thermal analysis of fully wet fins and the analysis of partially wet fins, separately. A remarkable change in results has been noticed when they are compared with that of the published result. Finally, it is worthy to mention that the maximum heat transfer rate per unit volume for an ASF is always higher than that of the annular disc fin for the identical design condition.     

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.     

A spreadsheet solution of transient conduction in composite fins

Transient heat transfer through composite fins is investigated by numerical methods. In this regard, governing differential equations of the two‐dimensional fin and one‐dimensional cladding are studied to examine the effect of Biot number and ratio of thermal conductivities of the fin material to the cladding, on the dimensionless temperature profiles. In addition, the use of spreadsheet programs in solving the composite fin problems is investigated in somewhat more detail with regard to the solution as well as presentation of the graphical results. The results show that one‐dimensional analysis, traditionally used in fin analysis, is not applicable for composite fins, particularly when the conductivity ratio of the composite fin materials is very high. Copyright © 2002 John Wiley & Sons, Ltd.     

Parametric study on the performance of a heat exchanger with corrugated louvered fins

The Taguchi method is a well-known parametric study tool in engineering quality and experimental design. This study analyzes five experimental factors (flow depth, ratio of fin pitch and fin thickness, tube pitch, number of louvers and angle of louver) affecting the heat transfer and pressure drop of a heat exchanger with corrugated louvered fins using the Taguchi method. Fifteen samples are selected from experimental database and the heat transfer and flow friction characteristics are analyzed. The results show that flow depth, ratio of fin pitch and fin thickness and the number of the louvers are the main factors that influence significantly the thermal hydraulic performance of the heat exchanger with corrugated louvered fins. Therefore, these three factors are considered as the main factors for an optimum design of a heat exchanger.