Forced convective heat transfer enhancement with perforated pin fins

Increasing miniaturization of high speed multi-functional electronics demands ever more stringent thermal management. The present work investigates experimentally and numerically the use of staggered perforated pin fins to enhance the rate of heat transfer in these devices. In particular, the effects of the number of perforations and the diameter of perforation on each pin are studied. The results show that the Nusselt number for the perforated pins is 45 % higher than that for the conventional solid pins and it increases with the number of perforation. Pressure drop with perforated pins is also reduced by 18 % when compared with that for solid pins. Perforations produce recirculations in the x–y as well as the x–z planes downstream of the pins which effectively increase convective heat transfer. However, thermal dissipation decreases significantly when the ratio of pin diameter to perforation diameter exceeds 0.375. This is due to both a reduction in the number of perforation per pin and the decrease in the axial heat conduction along the pin.     

Convective heat transfer and pressure loss in rectangular ducts with drop-shaped pin fins

It has been experimentally researched that convective heat transfer and pressure loss characteristics in rectangular channels with staggered arrays of drop-shaped pin fins in crossflow of air. The effects of arrangements of pin fins on heat transfer and resistance are discussed and the row-by-row variations of the mean Nusselt numbers are presented. By means of the heat/mass transfer analogy and the naphthalene sublimation technique, the heat transfer coefficients on pin fins and on endwall (base plate) of the channel have been achieved respectively. The total mean heat transfer coefficients of pin fin channels are calculated and the resistance coefficients are also investigated. The experimental results show that heat transfer of a channel with drop-shaped pin fins is higher than that with circular pin fins while the resistance of the former is much lower than that of the latter in the Reynolds number range from 900 to 9000. Received on 20 January 1997     

An experimental method for evaluating the heat transfer coefficient of liquid-cooled short pin fins using infrared thermography

The aim of this research is to evaluate the convective heat transfer coefficient of liquid cooled short pin fins by means of the infrared thermography. An experimental apparatus was set-up to analyze single, in-line and staggered array configurations of short pin fins. In this work the attention is focused on single pins having different shapes: circular, square, triangular and rhomboidal. The infrared thermography is used to indirectly measure the lateral pin temperature by observing the upper surface temperature of radially heated pins; these are placed in a test section chamber equipped with a Zinc Selenide infrared window. Flow visualizations by means of ink tracers are also carried out to relate the thermal behavior with the flow field. Regressions by the Zukauskas correlation were performed for each shape and new coefficients were carried out; a comparison among the different pin geometries underlines a better thermal exchange for the triangular and rhomboidal pins.     

Perturbation analysis for periodic heat transfer in radiating fins

A perturbation analysis is presented for periodic heat transfer in radiating fins of uniform thickness. The base temperature is assumed to oscillate around a mean value. The perturbation expansion is carried out in terms of dimensionless amplitude of the base temperature oscillation. The zero-order problem which is nonlinear, and corresponds to the steady state fin behaviour, is solved by quasilinearization. A method of complex combination is used to reduce both the first and the second order problems to two, coupled linear boundary value problems which are subsequently solved by a noniterative numerical scheme. The second-order term is composed of an oscillatory component with twice the frequency of base temperature oscillation and a time-independent term which causes a net change in the steady state values of temperature and heat transfer rate. Within the range of parameters used, the net effect is to decrease the mean temperature and increase the mean heat transfer rate. This is in constrast to the linear case of convecting fins where the mean values are unaffected by base temperature oscillations. Detailed numerical results are presented illustrating the effects of fin parameter N and dimensionless frequency B on temperature distribution, heat transfer rate, and time-average fin efficiency. The time-average fin efficiency is found to reduce significantly at low N and high B.

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Störungsanalyse für periodische Wärmeübertragung an Strahlungsrippen

Zusammenfassung Eine Störungsanalyse wird für periodische Wärmeübertragung in Strahlungsrippen gleicher Dicke vorgelegt. Die Fußtemperatur wird als um einen Mittelwert schwingend angenommen. Die Störungsentwicklung wird in Termen einer dimensionslosen Amplitude e dieser Schwingung angesetzt. Das Problem nullter Ordnung, das nichtlinear ist und dem stationären Verhalten der Rippe entspricht, wird durch Quasilinearisierung gelöst. Eine Methode der komplexen Kombination wird angewandt, um die Probleme erster und zweiter Ordnung auf zwei gekoppelte Grenzwertprobleme zu reduzieren, die nacheinander nach einem nichtiterativen Schema gelöst werden. Der Term zweiter Ordnung besteht aus einer Schwingungskomponente mit der doppelten Frequenz der Schwingung der Fußtemperatur und einem zeitunabhängigen Term, der eine Nettoänderung der stationären Werte der Temperatur und der Wärmeübertragung verursacht. Im verwendeten Bereich der Parameter tritt eine Abnahme der mittleren Temperatur und eine Zunahme der mittleren Wärmeübertragung auf. Das steht im Gegensatz zum linearen Fall der Konvektionsrippe, bei dem die Mittelwerte durch Schwingungen der Fußtemperatur nicht beeinflußt werden. Detaillierte numerische Ergebnisse zeigen die Einflüsse des Rippenparameters N und der dimensionslosen Frequenz B auf Temperatur Verteilung, Wärmeübertragung und zeitliches Mittel des Rippengütegrades. Dieses zeitliche Mittel nimmt merklich ab bei kleinem N und hohem B.

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Nomenclature b fin thickness - B dimensionless frequency, L²/ - E emissivity - f₀, f₁ functions of X - g₀, g₁, g₂ functions of X - h₀, h₁, h₂ functions of X - k thermal conductivity - L fin Length - N fin parameter, 2EL²T_bm/bk - q heat transfer rate - Q dimensionless heat transfer rate, qL/kbT_bm - t time - T temperature - T_b fin base temperature - T_S effective sink temperature - T_bm mean fin base temperature - x axial distance - X dimensionless axial distance, x/L - dimensionless amplitude of base temperature (s. Eq.2) - thermal diffusivity - instantaneous fin efficiency - time-average fin efficiency - _ss steady state fin efficiency - dimensionless temperature, T/T_bm - ₀ zero-order approximation - ₁ first-order approximation - ₂ second-order approximation - _2s steady component of ₂ - , ₁, ₂ constants - complex function of X - ₁ real part of - ₂ imaginary part of - complex function of X - ₁ real part of Y - ₂ imaginary part of - dimensionless time, t/L² - frequency of base temperature oscillation     

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.     

A rigorous analysis of simultaneous heat and mass transfer in the pasta drying process

This study presents a two dimensional analysis of coupled heat and mass transfer during the process of pasta drying. Velocity and temperature distributions of air flowing around the pasta are predicted in steady state condition. Using these profiles and the similarity between heat and mass boundary layers, local convective heat and mass transfer coefficients were determined on different points of pasta surface. By employing these values, the solution of coupled heat and mass transfer equations within the pasta object in unsteady state condition was obtained. Furthermore the effects of operating conditions such as velocity, temperature and relative humidity of air flow on drying rate of pasta were studied. Sensitivity analysis results show that the effects of air temperature and relative humidity on the rate of drying are more important than the effect of air velocity. Finally, the results obtained from this analysis were compared with the experimental data reported in the literatures and a good agreement was observed while, no adjustable parameter is used in the presented model.     

A tube-by-tube reduction method for simultaneous heat and mass transfer characteristics for plain fin-and-tube heat exchangers in dehumidifying conditions

This study proposed a new method, namely a tube-by-tube reduction method to analyze the performance of fin-and-tube heat exchangers having plain fin configuration under dehumidifying conditions. The mass transfer coefficients which seldom reported in the open literature, are also presented. For fully wet conditions, it is found that the reduced results for both sensible heat transfer performance and the mass transfer performance by the present method are insensitive to change of inlet humidity. Unlike those tested in fully dry condition, the sensible heat transfer performance under dehumidification is comparatively independent of fin pitch. The ratio of the heat transfer characteristic to mass transfer characteristic (h_c,o/h_d,o C_p,a) is in the range of 0.6~1.0, and the ratio is insensitive to change of fin spacing at low Reynolds number. However, a slight drop of the ratio of (h_c,o/h_d,o C_p,a) is seen with the decrease of fin spacing when the Reynolds number is sufficient high. This is associated with the more pronounced influence due to condensate removal by the vapor shear. Correlations are proposed to describe the heat and mass performance for the present plate fin configurations. These correlations can describe 89% of the Chilton Colburn j-factor of the heat transfer (j_h) within 15% and can correlate 81% of the Chilton Colburn j-factor of the mass transfer (j_m) within 20%.     

Periodic heat transfer in the fins with variable thermal parameters

ＰＥＲＩＯＤＩＣＨＥＡＴＴＲＡＮＳＦＥＲＩＮＴＨＥＦＩＮＳＷＩＴＨＶＡＲＩＡＢＬＥＴＨＥＲＭＡＬＰＡＲＡＭＥＴＥＲＳ￥ＹａｎｇＸｉａｎｇｘｉａｎｇ（杨翔翔）;ＨｅＨｏｎｇｚｈｏｕ（何宏舟）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｃｈａｎｉｃａｌＥｎｇｉｎｅｅｒ...     

A closed form solution for periodic heat transfer in annular fins

A closed form solution is presented for an annular fin of a constant cross-sectional area subjected to a periodic base heat flux. The solution involves Bessel functions with complex arguments. Closed form expressions for real and imaginary parts of Bessel functions K₀, I₀ and I₁ are developed. The solution of the temperature distribution, instantaneous and time-average efficiencies depends on the amplitudeA and frequencyB, of the base heat flux as well as on the fin parameterm. The effect of these parameters on the amplitude and phase angle of the temperature as well as on the efficiency are discussed. A qualitative analysis of fins of similar and different geometries subjected to different periodic boundary conditions is presented.Es wird eine geschlossene Lösung für eine ringförmige Rippe mit einer konstanten Querschnittsfläche dargestellt, der an der Basis ein periodischer Wärmestrom zugeführt wird. Die Lösung wird mit Hilfe von Bessel-Funktionen mit komplexen Argumenten erhalten. Es werden geschlossene Ausdrücke für Real- und Imaginärteile der Bessel-Funktionen K₀, I₀ und I₁ entwickelt. Die Lösung für die Temperaturverteilung und für die momentanen und die zeitlich gemittelten Wirkungsgrade hängen sowohl von der AmplitudeA und der FrequenzB des Wärmestroms an der Basis, als auch von dem Rippenparameterm ab. Der Einfluß dieser Parameter auf die Amplitude und Phase der Temperatur sowie den Wirkungsgrad wird untersucht. Eine qualitative Berechnung von Rippen ähnlicher und verschiedener Geometrien, die verschiedenen periodischen Randbedingungen ausgesetzt werden, wird dargestellt.     

A study on heat transfer of the optimization in circular fins of parabolic profile with variable thermal parameters

Circular fins are used extensively in heat exchange devices to increase the heat transfer. For economic purposes, the traditional approach to the optimization of fins consists of minimizing the comsumption (investment) of fin material for the excution of a specified heat transfer task. The minimum weight cooling fin has optional profile to be a concave parabola. Therefore, the optimum geometric dimensions of circular fins of parabolic profile with variable thermal parameters are studied. The effect of the two pertinent physical parameters-thermal conductivity variation parameter α and the index of the heat transfer coefficient variationm upon the optimum geometric dimensions is also studied. The results pressented can be used as the design guideline for engineering practice.     

Flow and heat transfer between plates with longitudinal fins

Laminar, fully developed flow and heat transfer between parallel plates with longitudinal fins are analyzed. A modified eigenfunction expansion and point-match method gives highly accurate results. The resistance productf Re and Nusselt numbers for bothH1 andH2 problems are determined as a function of fin length and spacing. It is possible to decrease both size and weight of the heat exchanger by the addition of fins.     

Finite element method solution of simultaneous two-dimensional heat and mass transfer in laminar film flow

A finite element solution is given for the coupled heat and mass transfer taking place when a vapour with considerable heat of absorption is absorbed into a laminar film flow. Convection and diffusion parallel and perpendicular to the direction of flow are taken into account. Temperature and mass fraction profiles across the film are given as well as results in film flow direction for several values of the Peclet number. Comparison with a solution based on one-dimensional flow and diffusion perpendicular to the flow, shows that deviations from this case by our two-dimensional solution increase for decreasing Peclet number.     

Experimental investigation in heat transfer of triangular and pin fin arrays

The experiments were conducted with triangular and pin fin array at constant heat flux. Nu is determined as a function of Re_max at Pr=0.7 for both sets of experiments. For each fin array, an equation is obtained to determine Nu as a function of Re_max using experimental results. These regressions are accurate within the accuracy of the measurements (±15) at Re_max ranging between 100 and 700. Received on 22 December 1997     

A Taguchi approach for determination of optimum design parameters for a heat exchanger having circular-cross sectional pin fins

The present work submits an investigation about the optimal values of design parameters and performance analysis for a heat exchanger having cylindrical pin fins positioned in a rectangular channel. The experiments covered the following range: Reynolds number 13,500–42,000, the clearance ratio (C/H) 0, 0.33 and 1, the interfin spacing ratio (S _y /D) 1.208, 1.944 and 3.417. In the experimentation, Taguchi method was employed, and Nusselt number and friction factor were considered as performance parameters. 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 goals were optimized together, considering the priority of goals, and the optimum results were found to be Reynolds number of 42,000, fin height of 50 mm and pitch of 3.417. The performance analysis also was made under a constant pumping power constraint, and the results showed that the use of cylindrical pin fins may lead to an advantage on the basis of heat transfer enhancement.     

Quasi-linear heat and mass transfer

Flow, Turbulence and Combustion - From the assumption that the heat flux (mass flux with respect to the mass-average velocity) vector is an isotropic function of the temperature (mass-fraction)...     

Multi‐objective optimization of a rotating cooling channel with staggered pin‐fins for heat transfer augmentation

A rotating channel with staggered pin‐fins is formulated numerically and optimized for performance (heat transfer/required pumping power) using a Kriging meta‐model and hybrid multi‐objective evolutionary algorithm. Two design variables related to cooling channel height, pin diameter, and spacing between the pins are selected for optimization, and two‐objective functions related to the heat transfer and friction loss are employed. A design of experiment is performed, and 20 designs are generated by Latin hypercube sampling. The objective function values are evaluated using a Reynolds‐averaged Navier–Stokes solver, and a Kriging model is constructed to obtain a Pareto‐optimal front through a multi‐objective evolutionary algorithm. Rotation in a cooling channel with staggered pin‐fins induces Coriolis force that causes a heat transfer discrepancy between the trailing (pressure) and leading (suction) surfaces, with a higher Nusselt number on the trailing surface. The tradeoff between the two competing objective functions is determined, and the distribution of the Pareto‐optimal solutions in the design space is discussed through k‐means clustering. In the optimal designs, with a decrease in spacing between the pins, heat transfer is enhanced whereas friction loss is increased. Copyright © 2011 John Wiley & Sons, Ltd.