Constructal design of Y-shaped assembly of fins

This work relies on constructal design to perform the geometric optimization of the Y-shaped assembly of fins. It is shown numerically that the global thermal resistance of the Y-shaped assembly of fins can be minimized by geometric optimization subject to total volume and fin material constraints. A triple optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly, an internal optimal ratio of plate-fin thicknesses and an optimal angle between the tributary branches and the horizontal. Parametric study was performed to show the behavior of the minimized global thermal resistance. The results also show that the optimized Y-shaped structure performs better than the optimized T-shaped one.     

Constructal entransy dissipation rate minimization of a disc

Disc cooling problem is optimized by taking entransy dissipation rate minimization as optimization objective. The non-dimensional mean temperature difference of the disc cooling model with radial high conducting fins inserted is deduced. The effects of the fin geometry, the fin aspect ratio, the ratio between the high conductivity and low conductivity, the relative amount of high conductivity material and the number of high conducting fins on the entransy dissipation rate of disc cooling are analyzed. The optimization results show that the high conducting fin should be extended to the centre of circle as the heat transfer effect of the high conducting fins is improved, and there exists an optimal fin aspect ratio corresponding to minimum entransy dissipation rate for different high conducting effects of the fin, and the number of high conducting fins has a slight effect on the entransy dissipation rate. Comparison with those for maximum temperature difference minimization shows that the constructs based on entransy dissipation rate minimization are different from those based on maximum temperature difference minimization, but the optimal constructal shape changing potentials of the number of fins and the relative amount of high conductivity material are similar.     

Optimization of heat sink geometries for impingement air-cooling of LSI packages

This paper describes the use of our previous study's prediction procedures for calculating thermal resistance and pressure drop. The procedures are used in the optimization of heat sink geometries for impingement air-cooling of LSI packages. Two types of heat sinks are considered: ones with longitudinal fins and ones with pin fins. We optimized the heat sink geometries by evaluating 16 parameters simultaneously. The parameters included fin thickness, spacing, and height. For the longitudinal fins, the optimal fin thicknesses were found to be between 0.12 and 0.15 mm, depending on which of the four types of fans were used. For pin fins, the optimal pin diameters were between 0.39 and 0.40 mm. Under constant pumping power, the optimal thermal resistance of the longitudinal fins was about 60% that of the pin fins. For both types of heat sinks, the optimal thermal resistance for four off-the-shelf fans was only slightly (maximum about 1%) higher than the theoretical optimum for the same pumping power. When manufacturing cost performance is considered, the most economical fin thickness and diameter are about 5 to 10 times higher than the optimal values calculated without respect for manufacturing costs. These values almost correspond to the actual limits of extrusion and press heat-sink manufacturing processes. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 138–151, 1999     

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.     

An analysis of entropy generation through a circular duct with different shaped longitudinal fins for laminar flow

The present study focuses on the entropy generation analysis in a circular duct with internal longitudinal fins of different shape for laminar flow. Three different fin shapes are chosen for the analysis: Thin, triangular and V-shaped fins. Calculations are performed for various dimensionless lengths and number of fins, dimensionless temperature difference and fin angle for triangular and V-shaped fins. It is found that the number of fins and dimensionless length of the fins for both thin fins and triangular fins, and the fin angle for triangular and V-shaped fins have significant effect on both entropy generation and pumping power. Further, both entropy generation and pumping power also are influenced by dimensionless temperature difference.     

最大热阻最小化的环形高导热通道三维体点导热最优构形的解析解法

基于构形理论,采用解析解法,以最大温差最小为优化目标,对基于环形高导热通道和圆柱形单元体的三维“体-点”导热模型进行构形优化,得到无量纲最大热阻最小的三维圆柱体最优构形.结果表明:增大高、低导热材料导热系数比、高导热材料占比和单元体数目均有助于提高圆柱形构造体的导热性能,但当单元体数目较大时,圆柱形构造体的导热性能改善...     

Geometric optimization of morphing fins coupled with a semicircular heat generating body: A numerical investigation on the basis of Bejan's theory

The objective of the present work is to optimize, by means of constructal design associated with exhaustive search and genetic algorithm, the geometry of morphing T-shaped fins that remove heat from a semicircular basement. The fins are bathed by a steady stream with constant ambient temperature and convective heat transfer. The semicircular body that serves as a basement for the T-shaped construct generates heat uniformly and it is perfectly insulated on the outer perimeter. It is shown numerically that the global thermal resistance can be minimized by geometric optimization subjected to constraints, namely, the basement area constraint, the T-shaped fins area fraction constraint and the auxiliary area fraction constraint, i.e. the ratio between the area that circumscribes the T-shaped fin and the basement area. The combination of the degrees of freedom values in the context of constructal design generated a search space with several “potential” local minima so that the classic technique, i.e. the exhaustive search, had to be substituted by the genetic algorithm method. In this context, the initial investigation regarding the degrees of freedom L₁/L₀ and t₁/t₀ was performed by means of the exhaustive search, while the parameters k_p, ϕ, λ and ψ have been studied by employing GA technique. First achieved results indicate that when the geometry is free to morph then the thermal performance is improved according to the constructal principle named by Bejan “optimal distribution of imperfections”. Finally, a comparative analysis between T-shaped constructs coupled with rectangular, trapezoidal and semicircular geometries has been carried out in terms of effectiveness in heat removal. The performance of the T-shaped morphing fin having semicircular basement (the case here treated) proved to be considerably superior than the other tested geometries.     

Constructal design of T–Y assembly of fins for an optimized heat removal

Constructal design has been applied to a large variety of problems in nature and engineering to optimize the architecture of animate and inanimate flow systems. This numerical work uses this method to seek for the best geometry of a T–Y assembly of fins, i.e., an assembly where there is a cavity between the two branches of the assembly of fins. The global thermal resistance of the assembly is minimized by geometric optimization subject to the following constraints: the total volume, the volume of fin-material, and the volume of the cavity. Parametric study was performed to show the behavior of the twice minimized global thermal resistance. The results show that smaller cavity volume and larger fins volume improve the performance of the assembly of fins. The twice minimized global thermal resistance of the assembly and its corresponding optimal configurations calculated for the studied parameters were correlated by power laws.     

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In this study, fully developed laminar flow and convective heat transfer in an internally finned tube heat exchanger are investigated numerically. The flow is assumed to be both hydrodynamically and thermally developed with uniform outside wall temperature. Parameters of the thickness, length, and number of fins and thermal conductivity ratio between fin and working fluid are varied to obtain the friction factor as well as Nusselt number. The results show that the heat transfer improves significantly if more fins are used; however, the pressure drop turns out to be large in this heat exchanger. In addition, it is found that the emergence of closed-loop isotherms between the areas of two neighboring fins leads to heat transfer enhancement in the internally finned tube. When the fin number is smaller than 14, there appears a maximum Nusselt number at about 0.8 of the dimensionless fin length. Finally, an experiment is conducted to verify the numerical results.     

Optimum dimensions of convecting–radiating fins:: Part I — longitudinal fins

The optimum dimensions of convective radiating extended surfaces or fins have been determined. Several fin shapes, profiles, have been analyzed including those treated by Gardner (Trans. ASME 69 (8) (1945) 621–631). Consideration is given to radiating fins and convective–radiating fins. In addition the cases of non-zero temperature sink, and the influence of the temperature dependent thermal conductivity and emissivity have been investigated. The results are generalized by expressing the fin’s optimum thickness, height, and heat dissipation in dimensionless form. They are presented graphically and in polynomial form the latter being particularly useful for computerized calculations.     

Heat exchanger design: Optimal thickness (under natural convective conditions) of vertical rectangular fins protruding upwards from a horizontal rectangular base

Steady-state rates of heat transfer from an array of vertical, rectangular polished duralumin fins under natural convective conditions have been measured. The horizontal base, which was manufactured of the same material, was kept at the uniform temperature of either 20·0 (±0·2)°C or 40·0 (±0·2)°C above the local air temperature of 20 (±0·2)°C.

The optimal thickness of the fins in this array, corresponding to a maximum rate of heat dissipation, was deduced. For a base of width 190 mm and length 500 mm, the optimal thickness for fins of 60 mm protrusion rose from 2·0 mm to 4·5 mm when the fin separation was increased from 20 mm to 60 mm. This optimal fin thickness was almost invariant with respect to the change of the considered base temperature.     

Thermal performance and efficiency of convective–radiative T-shaped fins with temperature dependent thermal conductivity,heat transfer coefficient and surface emissivity

This paper analytically investigates the thermal performance of convective–radiative T-shape fin with simultaneous variation of thermal conductivity, heat transfer coefficient and surface emissivity with temperature. Unlike some other fin studies, the sink temperatures for convection and radiation are assumed to be non-zero. This model is a more realistic representation of fins in actual engineering practice. The collection of graphs provided should facilitate design and performance evaluation of T-shaped fins.     

Optimal Design of Constructal T-Shaped Fin Under Partially Wet Condition for Enhanced Thermal Performance: An Analytical Approach

Abstract

In refrigeration and air conditioning systems, the fin surface may become dry, fully wet or partially wet depending upon the psychometric, thermo-physical and geometric parameters. The current work is intended to determine the length of the dry portion, temperature distribution, performance and optimum design parameters of a T-shaped fin under partially wet condition. Temperature dependent thermal conductivity of the fin material is taken and the humidity ratio of saturated air is considered to vary linearly with the corresponding fin surface temperature. Considering these the governing equation of T-shaped fin becomes nonlinear and it has been solved analytically by using Homotopy Perturbation Method. The point of separation between the dry and wet portions of a T-shaped fin may be located either in the stem or flange part and hence, two cases having different governing equations and boundary conditions are analyzed in the current study. For the optimization study, Lagrange multiplier technique is employed and the results are obtained by maximizing the heat transfer rate for a constant fin volume. Further, a comparative study is presented between insulated and convective fin tip conditions.     

Forced-convective steady-state heat transfers from shrouded vertical fin arrays,aligned parallel to an undisturbed air-stream

An experimental investigation of the steady-state rates of heat loss from an array of vertical rectangular fins of 3 mm thickness and 250 mm length, when in the presence of an almost adiabatic horizontal shroud, situated adjacent to and above the horizontal fin tips, is reported. With the fin's horizontal base at a uniform temperature of 40 ± 0·1° C above that of the ambient environment, the optimal fin separation—corresponding to the maximum rate of heat loss—is deduced. As the ratio of the shroud height above the vertical fins to the fin height decreases from unity to zero, this optimal value decreases by approximately 17%.The frictional characteristics of the air flow through the fin array have also been studied in the Reynolds number range of 4·0 × 10⁴ to 2·0 × 10⁵. Large streamwise pressure drops and high heat-transfer rates resulted when the fins were closely spaced and no clearance gap was present above the vertical fins. In reasing the shroud clearance resulted in smaller overall pressure drops and decreasing heat-transfer rates from the heat exchanger.     

Experimental investigation of thermal resistance of a heat sink with hexagonal fins

In the present work, the effects of the heights, widths of the hexagonal fins, streamwise and spanwise distances between fins and flow velocity on thermal resistance and pressure drop characteristics were investigated using Taguchi experimental design method. Also the temperature distribution within the selected pin fins was determined. Thermal resistance and dimensionless pressure drop were considered as performance statistics. L₁₈(2¹*3⁷) orthogonal array was selected as an experimental plan for the five parameters mentioned above. While the optimum parameters were determined, due to the goals (above aims) more than one being, the trade-off among goals was considered. First of all, each goal was optimized, separately. Then, all the goals were optimized together, considering the priority of the goals, and the optimum results were found to be fin width of 14 mm, fin height of 150 mm, spanwise distance between fins of 20 mm, streamwise distance between fins of 10 mm and flow velocity of 4 m/s.     

基于恒截面流道矩形单元体的积耗散率最小传质构形优化

以质量积耗散率最小为优化目标,对恒截面高渗透率通道的矩形单元体传质构形问题进行了分析和优化,得到结构体内平均传质效果最好的结构外形。结果表明:对于单元体和各级构造体,其平均传质压差均为最大传质压差的2/3。因为高渗透率材料中质流率密度符合线性分布,所以基于积耗散率最小与最大压差最小的最优构形完全一致。所得最优构形同时使得传质能力和传质安全性最好。     

Multidisciplinary optimization of a pin-fin radial heat sink for LED lighting applications

In this study, the cooling performance and mass of a pin-fin radial heat sink were optimized. A radial heat sink with pin fins was examined numerically to obtain a lighter heat sink while maintaining a similar cooling performance to that of a plate-fin heat sink investigated in a previous study. Both natural convection and radiation heat transfer were considered. Experiments were performed to validate the numerical model. The average temperature and mass of the heat sink for various types of fin arrays were compared to determine an appropriate reference configuration. The effects of various geometric parameters on the thermal resistance and mass of the heat sink were investigated; these indicated that the system was sensitive to the number of fin arrays, as well as the length of the long and middle fins. Multidisciplinary optimization was carried out using the three design variables to minimize the thermal resistance and mass simultaneously, and Pareto fronts were obtained with various weighting factors. A design for the optimum radial heat sink is proposed, which reduces the mass by more than 30% while maintaining a similar cooling performance to that of a plate-fin heat sink.     

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.     

Numerical analysis of heat removal enhancement with extended surfaces

The problem of heat removal is a major issue in modern industry. The reasons for researching in this field are both to increase the performances of the target systems and to reduce the damages that high temperatures can cause. The present trend in high-tech production processes is to seek better performances by means of smaller devices. Aiming at this, it becomes necessary that all the components of the system examined are designed to supply the best possible performance. This paper faces the problem of optimising fins to enhance heat removal. The analysis so conjugates geometrical and thermo-fluid mechanical aspects. The starting point of this activity was a research, based on the Bejan’s Constructal Theory, which focused on heat removal enhancement from high temperature surfaces through T-shaped fins. Initially, the same system was here numerically investigated using a CFD code. The performances computed were very similar to the reference ones. This validation allowed to apply the method to new configurations, so to develop systems further on optimised, able to remove higher thermal fluxes in the same processes. Y-shaped profiles were consequently examined, obtained by varying the angle between the two arms of the original T. The idea of performance optimisation as proposed in the reference work, was initially based on the maximisation of the dimensionless thermal conductance. This was here widened to a new definition taking into account thermal efficiency as another parameter of evaluation. It was, in fact, observed that the width reduction, typical of Y-shaped profiles with respect to T-shaped ones, enhance efficiency significantly.This new approach to heat removal optimisation suggested the realisation of arrays with multiple Y-shaped fins. Each array had the same width of the corresponding optimised T-shaped fin. This choice allowed immediate comparisons, so to evaluate the actual performance enhancements typical of multiple-fin configurations, with respect to previous configurations.     

Measurement of performance of plate-fin heat sinks with cross flow cooling

This work assesses the performance of plate-fin heat sinks in a cross flow. The effects of the Reynolds number of the cooling air, the fin height and the fin width on the thermal resistance and the pressure drop of heat sinks are considered. Experimental results indicate that increasing the Reynolds number can reduce the thermal resistance of the heat sink. However, the reduction of the thermal resistance tends to become smaller as the Reynolds number increases. Additionally, enhancement of heat transfer by the heat sink is limited when the Reynolds number reaches a particular value. Therefore, a preferred Reynolds number can be chosen to reduce the pumping power. For a given fin width, the thermal performance of the heat sink with the highest fins exceeds that of the others, because the former has the largest heat transfer area. For a given fin height, the optimal fin width in terms of thermal performance increases with Reynolds number. As the fins become wider, the flow passages in the heat sink become constricted. As the fins become narrower, the heat transfer area of the heat sink declines. Both conditions reduce the heat transfer of the heat sink. Furthermore, different fin widths are required at different Reynolds numbers to minimize the thermal resistance.