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.     

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.     

Enhanced boiling heat transfer using radial fins

A numerical bifurcation analysis is carried out in order to determine the solution structure of radial fins subjected to multi-boiling heat transfer mode. One-dimensional conduction is employed throughout the thermal analysis. The fluid heat transfer coefficient is temperature dependent on the three regimes of phase-change of the fluid. Six fin profiles, defined in the text, are considered. Multiplicity structure is obtained to determine different types of bifurcation diagrams, which describe the dependence of a state variable of the system like the temperature or the heat dissipation on the fin design parameters, conduction–convection parameter (CCP) or base temperature difference (ΔT). Specifically, the effects of ΔT, CCP and Biot number are analyzed. The results are presented graphically, showing the significant behavioral features of the heat rejection mechanism.

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Formulation of nanofluids for natural convective heat transfer applications

The paper is concerned about formulation of aqueous based nanofluids and its application under natural convective heat transfer conditions. Titanium dioxide nanoparticles are dispersed in distilled water through electrostatic stabilization mechanisms and with the aid of a high shear mixing homogenizer. Nanofluids formulated in such a way are found very stable and are used to investigate their heat transfer behaviour under the natural convection conditions. The preliminary results are presented in this paper. Both transient and steady heat transfer coefficients are measured and the results show a systematic decrease in the natural convective heat transfer coefficient with increasing particle concentration. This is in contradiction to the initial expectation. Possible reasons for the observations are discussed.     

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.     

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.     

Unsteady natural convective flow past a moving vertical cylinder with heat and mass transfer

Transient natural convection boundary layer flow of an incompressible viscous fluid past an impulsively moving semi- infinite vertical cylinder is considered. The temperature and concentration of the cylinder surface are taken to be uniform. The unsteady, nonlinear and coupled governing equations of the flow are solved using an implicit finite difference scheme. The finite difference scheme is unconditionally stable and accurate. Numerical results are presented with various sets of parameters for both air and water. Transient effects of velocity, temperature and concentration profiles are analyzed. Local and average skin friction, rates of heat and mass transfer are shown graphically. Received on 1 November 1999     

Hydromagnetic convective heat transfer in vertical pipes

In the present analysis, we consider the effect of radial magnetic field on the steady flow produced by the combined free and forced convection in an annulus between two coaxial vertical cylinders. A numerical solution of the problem is obtained by using Runge-Kutta-Merson method. For Rayleigh number Ra<0, that is, when the temperature of the pipes decreases as their height increases, the velocity increases with |Ra|. However, it reduces as the Hartmann number M increases. On the other hand, when Ra>0, there occurs back flow controlled by the effect of the magnetic field. Further, the influence of Rayleigh number and Hartmann number on the temperature is also discussed.Nomenclature c _p specific heat at constant pressure - g acceleration due to gravity - H _r applied magnetic field - H _z induced magnetic field - p pressure - T temperature of the fluid - T ₁, T ₂ temperatures of the inner and outer cylinders at z=0 - U _z velocity - coefficient of volume expansion - density - _w reference density - coefficient of viscosity - _e magnetic permeability - _e electrical conductivity - thermal conductivity - _m magnetic diffusivity     

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     

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.     

Characterization of convective heat transfer in channels of small cross section using digital interferometry

Forced convection in channels of small cross sectional dimensions has been recommended as an effective heat removal method for electronic components and packages. Many of the experimental results reported in the literature on the heat transfer performance of small-cross section channels are of contradicting nature, even though some generally agreeing results are also found. One of the probable reasons for the deviations, as suggested by investigators, is the intrusive nature of measurement techniques, which interferes with the flow field. Hence a non intrusive measurement technique is preferable for temperature measurement in small channels. The present work is aimed at developing an interferometric method for convective heat transfer measurement in a liquid medium flowing through channels of small cross sectional dimensions, with hydraulic diameters ranging from 12 to 3 mm and characterizing the nature of fluid flow and heat transfer in these channels. Mach–Zehnder interferometric arrangement is used to obtain the temperature distributions in water flowing through the channels, which are further analyzed digitally to obtain the local heat transfer coefficients and Nusselt numbers. The results are compared and contrasted with classical results for channel flow and heat transfer, and attempt has been made to interpret the variations and deviations observed. The experimental study has been performed under different fluid velocities in the laminar flow regime, and under various wall heat fluxes corresponding to the heat dissipation range expected in microelectronic devices. Parametric variations for the heat transfer performance have been obtained and correlated using the experimental results.     

A generalized variational formulation for convective heat transfer

The Scope of this paper is to develop the basic equations for a variational formulation which can be used to solve problems related to convection and/or diffusion dominated flows. The formulation is based on the introduction of a generalized quantity defined as the hear displacement. The governing equation is expressed in terms of this quantity and a variational formulation is developed which leads to a system of equations similar in form to Lagrange's equations of mechanics. These equations can be used for obtaining approximate solutions, though they are of particular interest for application of the finite element method. As an example of the formulation two finite element models are derived for solving convectiondiffusion boundary value problems. The performance of the two models is investigated and numerical results are given for different cases of convection and diffusion with two types of boundary conditions. The applications of the developed formulations are not limited to convection-diffusion problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation.     

Studies on convective heat transfer through helical coils

An experimental investigation on steady state convection heat transfer from vertical helical coiled tubes in water was performed for laminar flow regime. Three coils with curvature ratios as 0.0757, 0.064, 0.055 and range of Prandtl number from 3.81 to 4.8, Reynolds number from 3,166 to 9,658 were considered in this work. The heat transfer data were generated from 30 experiments conducted at constant water bath temperature (60 °C) for different cold water flow rates in helical coils. For the first time, an innovative approach of correlating Nusselt number with ‘M’ number is proposed which is not available in the literature and the developed correlations are found to be in good agreement with the work of earlier researchers. Thus, dimensionless number ‘M’ was found to be significant to characterize the hydrodynamics of fluid flow and heat transfer correlations in helical coils. Several other correlations based on experimental data are developed. To cover wide range of industrial applications, suitable generalized correlations based on extended parameters beyond the range of present experimental work are also developed. All these correlations are developed by using least-squares power law fit and multiple-regression analysis of MATLAB software. Correlations so developed were compared with published correlations and were found to be in good agreement. Comparison of heat transfer coefficients, friction factor and Nusselt number for different geometrical conditions is presented in this paper.     

Periodic heat transfer in the fins with variable thermal parameters

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Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure

 A collocated, non-orthogonal grid based finite volume technique has been applied for investigating the two dimensional natural convective flow and heat transfer around a heated cylinder kept in a square enclosure. The effects of different enclosure wall thermal boundary conditions, fluid Prandtl number and the ratio between enclosure and cylinder dimensions (aspect ratio) upon the flow and thermal features, have been systematically studied. It is observed that the patterns of recirculatory flow and thermal stratification in the fluid are significantly modified, if any of these parameters is varied. The overall heat transfer rates are also affected due to the changes in the flow and temperature patterns. The study presents useful observations regarding the variation of local Nusselt number along each wall, for the different cases considered. Received on 2 August 2000 / Published online: 29 November 2001