Optimization of heat transfer through finned dissipators cooled by laminar flow

In the present work, the problem of optimizing the shape and the spacing of the fins of a thermal dissipator cooled by a fluid in laminar flow is studied. For a particular finned conduit, the velocity and temperature distributions on the transversal section are determined with the help of a finite element model and a global heat transfer coefficient is calculated. A polynomial lateral profile is proposed for the fins and the geometry is optimized in order to make the heat transfer coefficient as high as possible with the smallest dimensions or the lowest hydraulic resistance to the flow. The optimum fin profile and spacing, obtained by means of a genetic algorithm, are finally shown for different situations. Increases of 45% are obtained in the heat transfer coefficient referring to the maximum values which can be obtained with rectangular fin profiles.     

Optimization of convective fin systems: a holistic approach

 A numerical analysis of natural convection heat transfer and entropy generation from an array of vertical fins, standing on a horizontal duct, with turbulent fluid flow inside, has been carried out. The analysis takes into account the variation of base temperature along the duct, traditionally ignored by most studies on such problems. One-dimensional fin equation is solved using a second order finite difference scheme for each of the fins in the system and this, in conjunction with the use of turbulent flow correlations for duct, is used to obtain the temperature distribution along the duct. The influence of the geometric and thermal parameters, which are normally employed in the design of a thermal system, has been studied. Correlations are developed for (i) the total heat transfer rate per unit mass of the fin system (ii) total entropy generation rate and (iii) fin height, as a function of the geometric parameters of the fin system. Optimal dimensions of the fin system for (i) maximum heat transfer rate per unit mass and (ii) minimum total entropy generation rate are obtained using Genetic Algorithm. As expected, these optima do not match. An approach to a `holistic' design that takes into account both these criteria has also been presented. Received on 22 February 2001 / Published online: 29 November 2001     

Comparison of heat transfer performance of tube bank fin with mounted vortex generators to tube bank fin with punched vortex generators

The results obtained from naphthalene sublimation heat/mass analogy experiments in selecting the optimum geometrical parameters of tube bank fin heat exchanger with fins mounted with vortex generators are compared with the results obtained from the condensing experiments of the real heat exchangers with vortex generators punched out on the fins. The results declare that VGs pouched or mounted on fin surfaces have only limited effects on heat transfer performance in the studied configurations; naphthalene sublimation method can be used to select fin patterns with reasonable reliability.     

Optimization of annular fins on a horizontal tube

A combination of uniform-thickness annular fins evenly spaced on a tube is a common extended-surface heat exchanger configuration. An analytical model is developed and is verified by comparing total heat transfer predicted by the model to available experimental data. A direct-pattern search technique is applied to the model to optimize the fin/ tube geometry. Optimum dimensions and spacing of fins are established to provide the maximum free convection heat transfer from a fin/tube combination. The optimum arrangement is dependent on fin thermal conductivity, tube diameter, volume of fin material per unit length of tube, and temperature difference between the tube and the surrounding air. Calculated results indicate that a fin in the optimum fin/tube system is shorter and thicker than an isolated fin optimized for minimum material (with no consideration of the effects of fin spacing).     

Comparison of rectangular and triangular fins when condensation occurs

In this study rectangular and triangular fins have been compared when condensation occurs. The temperature distributions and the heat transfer found using quasilinearization techniques and those found by using Gauss-Seidel iteration method are compared and this approximation proved to be quite satisfactory. The fin temperature and the fin effectiveness of the triangular and rectangular fins have been determined with and without condensation and optimum fin dimensions have been given as a function of Biot number.     

Performance analysis and optimization of convective annular fins with internal heat generation

An analysis of the thermal performance for convective annular fins, having a general trapezoidal profile and internal heat generation, is presented. The solution of the optimal problem is also given when either the heat dissipation rate or the volume of the fin is specified. The results are expressed in suitable nondimensional variables that are specified by the problem, and presented graphically. The effect of the fin's profile and thermal conductivity upon the optimum dimensions is discussed. It is shown that the presence of heat generation reduces the ability of the fin to convect heat. Furthermore, certain limiting values of the heat generation that may be imposed on the fin for a feasible optimization are also derived.     

The optimum shape for converting rectangular fins when condensation occurs

There may be condensation on the fin surfaces of the air conditioning systems due to the temperature of the fin surfaces being below the dew point temperature of the water vapor in the surrounding air. Heat and mass transfer occur from the saturated air layer to the liquid water film and the latent heat of condensation is transferred to the fin. This study presents a quasilinearization solution for vertical rectangular fins when condensation occurs, assuming that the average convective heat and mass transfer coefficients are constant along the height of the fin. Rectangular fins with and without condensation on the surface have been compared and optimum fin dimensions have been given. The optimum fin length, the fin effectiveness and the average fin temperature in the case of condensation were found to be smaller than in the case of no condensation.     

Performance analysis and optimization of radiating fins with a step change in thickness and variable thermal conductivity by homotopy perturbation method

Although tapered fins transfer more rate of heat per unit volume, they are not found in every practical application because of the difficulty in manufacturing and fabrications. Therefore, there is a scope to modify the geometry of a constant thickness fin in view of the less difficulty in manufacturing and fabrication as well as betterment of heat transfer rate per unit volume of the fin material. For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the homotopy perturbation method has been used to evaluate the temperature distribution within the straight radiating fins with a step change in thickness and variable thermal conductivity. The temperature profile has an abrupt change in the temperature gradient where the step change in thickness occurs and thermal conductivity parameter describing the variation of thermal conductivity has an important role on the temperature profile and the heat transfer rate. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found. The derived condition of optimality gives an open choice to the designer.     

Optimum fin spacing of rectangular fins on a vertical base in free convection heat transfer

The steady-state natural convection heat transfer from aluminum vertical rectangular fins extending perpendicularly from vertical rectangular base was investigated experimentally. Thirty different fin configurations were tested. Experiments were performed for fin lengths of 250 and 340 mm. Fin thickness was kept fixed at 3 mm. Fin height and fin spacing were varied from 5 to 25 mm and 5.75 to 85.5 mm, respectively. Five heat inputs ranging from 25 to 125 W were supplied for all fin configurations, hence; the base-to-ambient temperature differences were measured in order to evaluate the heat transfer rates from fin arrays. The results of experiments have shown that the convective heat transfer rate from fin arrays depends on geometric parameters and base-to-ambient temperature difference. The separate roles of fin height, fin spacing and base-to-ambient temperature difference were investigated. It was found that, for a given base-to-ambient temperature difference, the convective heat transfer rate from fin arrays takes on a maximum value as a function of fin spacing and fin height and an optimum fin spacing value which maximizes the convective heat transfer rate from the fin array is available for every fin height. These measurements were to extend data obtained earlier from aluminum fin-arrays using the same experimental system and method (Yüncü and Güvenç in Heat Mass Transfer 37:409–416, 2001). Data collated from earlier and present work cover the range of fin spacing from 4.5 to 85.5 mm. The fin length range was from 100 to 340 mm, the fin height from 5 to 25 mm and the number of fins per array 3 to 34. The range of base-to-ambient temperature difference was quite extensive, from 30 to 150 K. These results indicate that the optimum fin spacing is between 6.1 and 11.9 mm, for the fin arrays employed in the earlier and present work. A scale analysis is performed in order to estimate the order-of-magnitude of optimum fin spacing at a given fin length and base-to-ambient temperature difference. From the scale analysis, correlations to evaluate the optimum fin spacing value and the corresponding maximum convective heat transfer rate at a given fin length and base-to-ambient temperature difference were obtained.     

The optimal dimensions of convective-radiating circular fins

The optimal dimensions of convective-radiating circular fins with variable profile, heat-transfer coefficient and thermal conductivity, as well as internal heat generation are obtained. A profile of the form y=(w/2) [1+(r _o/r) ⁿ ] is studied, while variation of thermal conductivity is of the form k=k _o[1+ɛ((T−T _∞)/ (T _b−T _∞)) ^m ]. The heat-transfer coefficient is assumed to vary according to a power law with distance from the bore, expressed as h=K[(r−r _o)/(r _e−r _o)]^λ. The results for λ=0 to λ=1.9, and −0.4≤ɛ≤0.4, have been expressed by suitable dimensionless parameters. A correlation for the optimal dimensions of a constant and variable profile fins is presented in terms of reduced heat-transfer rate. It is found that a (quadratic) hyperbolic circular fin with n=2 gives an optimum performance. The effect of radiation on the fin performance is found to be considerable for fins operating at higher base temperatures, whereas the effect of variable thermal conductivity on the optimal dimensions is negligible for the variable profile fin. It is also observed, in general, that the optimal fin length and the optimal fin base thickness are greater when compared to constant fin thickness. Received on 22 February 1999     

Heat transfer from extended surfaces subject to variable heat transfer coefficient

The present article investigates the effect of locally variable heat transfer coefficient on the performance of extended surfaces (fins) subject to natural convection. Fins of different profiles have been investigated. The fin profiles presently considered are namely; straight and pin fin with rectangular (constant diameter), convex parabolic, triangular (conical) and concave parabolic profiles and radial fins with constant profile with different radius ratios. The local heat transfer coefficient was considered as function of the local temperature and has been obtained using the available correlations of natural convection for each pertinent extended surface considered. The performance of the fin has been expressed in terms of the fin efficiency. Comparisons between the present results for all fins considered and the results obtained for the corresponding fins subject to constant heat transfer coefficient along the fin are presented. Comparisons, i.e. showed an excellent agreement with the experimental results available in the literature. Results show that there is a considerable deviation between the fin efficiency calculated based on constant heat transfer coefficient and that calculated based on variable heat transfer coefficient and this deviation increases with the dimensionless parameter m.     

Heat transfer from convecting-radiating fins of different profile shapes

A finite difference method is used to predict the performance of convecting-radiating fins of rectangular, trapezoidal, triangular, and concave parabolic shapes. The analysis assumes one-dimensional, steady conduction in the fin and neglects radiative exchange between adjacent fins and between the fin and its primary surface. For the range of thermal and geometrical parameters investigated, the variation of heat transfer rate and the fin efficiency with other profile shapes was found to be within 11 percent of the rectangular shape. The effect of profile shape is most pronounced when the Biot number,Bi, and radiation number,N _r, are small compared to unity. Because of several limiting assumptions, the results would be used only for preliminary analysis and design particularly when a fin assembly is involved rather than an individual fin.     

Shape optimization for the minimum volume of pin fins in simultaneous heat and mass transfer environments

A methodology for determining the optimum pin fin profile is introduced to minimize the fin volume for a constrained heat transfer rate under dehumidifying surface conditions. In this methodology, the mass transfer is evaluated using the polynomial variation of humidity ratio with temperature. A scheme is developed for solving the optimum conditions derived as a function of unknown temperature-dependent parameter and tip temperature under both the fully and partially wet surface conditions. The effect of psychrometric properties of the surrounding air on the optimum wet fin profile has been examined. The analysis presented in this study is pertinent to the dry, fully wet, and partially wet surface conditions. In every case study of optimum wet fins, the excess temperature at the tip vanishes with respect to the surrounding temperature. A non-linear temperature distribution in the optimum wet fin has been identified.     

Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity

Correlation equations for optimum design of annular fins with temperature-dependent thermal conductivity are obtained in the present work. The nonlinear fin equation which is associated with variable thermal conductivity condition is solved by Adomian decomposition method that provides an analytical solution in the form of an infinite power series. 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 for a given thermal conductivity parameter describing the variation of the thermal conductivity. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rate. 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 with temperature-dependent thermal conductivity.     

Experimental study of convective heat transfer from a rotating finned tube in transverse air flow

 The convective heat transfer from fins to air has been evaluated using rotating annular fins subjected to an air flow parallel to the fins. The fin cooling is studied using infrared thermography. The thermal balance in a fin during its cooling process allows us to obtain the heat transfer coefficient from the temperature time evolution of the fin. Moreover, Particle Image Velocimetry allows us to obtain the flow field in the mid-plane between two fins. The influence of the fin spacing on the convective heat transfer is studied for various velocities of the superposed air flow and various fin rotational speeds. These tests were carried out for air flow Reynolds numbers (based on the shaft diameter and the velocity of the superposed air flow) between 2550 and 18200 and rotational Reynolds numbers (based on the shaft diameter and the peripheral speed) between 800 and 2.9 × 10⁴, for different fin spacings. Received: 14 May 1999/Accepted: 8 October 1999     

A note on the heat transfer in convective fins

In this paper a generalized approach to the problem of heat transfer through convective fins is given. The proper dimensionless variables, which specify the general problem are identified, and upper bounds of the values of the dimensionless number N_r defined as “the ratio of the heat transferred by the fin to that of the corresponding bare surface” are derived. It was shwon that these limiting values of the N_r are 1/√B₁ and √2/B₁ for longitudinal fins and spines respectively, where B₁ is the Biot number hb/k, while for annular fins of constant thickness and hyperbolic profile, N_r? K(β)/√B_i, where K(β) is a number determined by the profile of the fin and the ratio β=x₂/x₁ of the outside to the inside radii. It was also shown that for longitudinal fins and spinces the possible adverse insulating effect by the use of the fin is avoided, if one selects the value of √hA/KC < 1, which is a rather stricter criterion than the one reported in the literature, namely that of hA/kC < 1 [2–5]. An example is given to show how one may utilize the appropriate value of N_r and the fin effectiveness e, to obtain the dimensions of the fin.     

Effects of stretching/shrinking on the thermal performance of a fully wetted convective-radiative longitudinal fin of exponential profile

The present investigation focuses on the thermal performance of a fully wet stretching/shrinking longitudinal fin of exponential profile coated with a mechanism like a conveyer belt. The modeled equation is non-dimensionalized and solved by applying the Runge-Kutta-Fehlberg(RKF) method. The effects of parameters such as the wet parameter, the fin shape parameter, and the stretching/shrinking parameter on the heat transfer and thermal characteristics of the fin are graphically analyzed and discus...     

Thermal analysis of annular fins with temperature-dependent thermal properties

The thermal analysis of the annular rectangular profile fins with variable thermal properties is investigated by using the homotopy analysis method （HAM）. The thermal conductivity and heat transfer coefficient are assumed to vary with a linear and power-law function of temperature, respectively. The effects of the thermal-geometric fin parameter and the thermal conductivity parameter variations on the temperature distribution and fin efficiency are investigated for different heat transfer modes. Results from the HAM are compared with numerical results of the finite difference method （FDM）. It can be seen that the variation of dimensionless parameters has a significant effect on the temperature distribution and fin efficiency.     

Thermal Analysis of Natural Convection Porous Fins

This work introduces a simple method of analysis to study the performance of porous fins in a natural convection environment. The method is based on using energy balance and Darcy’s model to formulate the heat transfer equation. The thermal performance of porous fins is then studied for three types of fins: long fin, finite-length fin with insulated tip and a finite-length fin with tip exposed to a known convection coefficient. It is found from the analysis that the effect of different design and operating parameters such as: Ra number, Da number, thermal conductivity ratio, Kr and length thickness ratio on the temperature distribution along the fin is grouped into one newly defined parameter called S_H. The effect of the variation of S_H on the porous fin thermal performance is established. The effect of varying the fin length and thermal conductivity ratio on the heat transfer rate from the fin is investigated and compared with that for a solid fin at certain conditions. It is found that the heat transfer rate from porous fin could exceed that of a solid fin. It is also found that increasing the fin length and effective thermal conductivity enhances the heat transfer from the fin up certain limit, where a further increase in these parameters adds no improvement to the fin performance. On Leave from Jordan University of Science and Technology, Irbid-Jordan     

An experimental investigation on the airside performance of fin-and-tube heat exchangers having sinusoidal wave fins

The heat transfer and friction characteristics of the heat exchangers having sinusoidal wave fins were experimentally investigated. Twenty-nine samples having different waffle heights (1.5 and 2.0 mm), fin pitches (1.3–1.7 mm) and tube rows (1–3) were tested. Focus was given to the effect of waffle configuration (herringbone or sinusoidal) on the heat transfer and friction characteristics. Results show that the sinusoidal wave geometry provides higher heat transfer coefficients and friction factors than the herringbone wave geometry, and the difference increases as the number of row increases. The j/f ratios of the herringbone wave geometry, however, are larger than those of the sinusoidal wave geometry. Compared with the herringbone wave geometry, the sinusoidal wave geometry yielded a weak row effect, which suggests a superior heat transfer performance at the fully developed flow region for the sinusoidal wave geometry. Possible reasoning is provided considering the flow characteristics in wavy channels. Within the present geometric variations, the effect of waffle height on the heat transfer coefficient was not prominent. The effect of fin pitch was also negligible. Existing correlations highly overpredicted both the heat transfer coefficients and friction factors. A new correlation was developed based on the present data.