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.     

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.     

Single-Phase Cryogenic Flow and Heat Transfer Through Microscale Pin Fin Heat Sinks

Single-phase heat transfer and pressure drop of liquid nitrogen in microscale heat sinks are studied experimentally in this paper. Effects of geometrical variations are characterized on the thermofluidic performance of staggered microscale pin fin heat sinks. Pitch-to-diameter ratio and aspect ratio of the micro pin fins are varied. The pin fins have square shape with 200 or 400 μm width and are oriented at 45 degrees to the flow direction. Thermal performance of the heat sinks is evaluated for Reynolds numbers (based on pin fin hydraulic diameter) from 108 to 570. Results are presented in a nondimensional form in terms of friction factor, Nusselt number, and Reynolds number and are compared with the predictions of existing correlations in the literature for micro pin fin heat sinks. Comparison of flow and heat transfer performance of the micro pin fin heat sinks reveals that at a particular critical Reynolds number of ～250, pin fin heat sinks with the same aspect ratio but larger pitch ratio show a transition in both friction factor and Nusselt number. In order to better characterize this transition, visualization experiments were performed with the Fluorinert PF5060 using an infrared camera. At the critical Reynolds number, for the larger pitch ratio pin fin heat sink, surface thermal intensity profiles suggest periodic flapping of the flow behind the pin fins at a Strouhal number of 0.227.     

Forced convective heat transfer across a pin fin micro heat sink

This paper investigates heat transfer and pressure drop phenomena over a bank of micro pin fins. A simplified expression for the total thermal resistance has been derived, discussed and experimentally validated. Geometrical and thermo-hydraulic parameters affecting the total thermal resistance have been discussed. It has been found that very low thermal resistances are achievable using a pin fin heat sink. The thermal resistance values are comparable with the data obtained in microchannel convective flows. In many cases, the increase in the flow temperature results in a convection thermal resistance, which is considerably smaller than the total thermal resistance.     

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.     

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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.     

Quick design of truncated pin fins of hyperbolic profile for heat-sink applications by using shortened power series

A heat sink normally consists of a substrate on which a bundle of pin fins made of a highly conducting metal like aluminum or copper is attached. Its performance can be qualified by the space they occupy in relation to the thermal resistance they provide, which requires the solution of the quasi one-dimensional heat conduction equation in the geometry of interest. This technical brief reports exact and approximate analytical procedures for the truncated pin fin of hyperbolic profile. The exact solution involves rather intricate Bessel functions, whereas the approximation is based on easily computable power series. Compared to the exact figures, simple, truncated power series having between five and eight terms yield results of excellent quality for practical combinations of the two controlling parameters: the thermal length mL and the coordinate ratio W. Results are presented for the two variables of interest in thermal design: the fin tip temperature (a local quantity) and the fin thermal efficiency (a global quality ratio).     

Simple correlation equations for optimum design of annular fins with uniform thickness

Simple correlation equations for optimum design of annular fins with uniform cross section are obtained in the present work. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rates. 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. 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 of uniform thickness.     

Thermal Enhancement from Pin Fins by Using Elliptical Perforations with Different Inclination Angles

Many of the proposed methods introduce the perforated fin with the straight direction to improve the thermal performance of the heat sink. The innovative form of the perforated fin (with inclination angles) was considered. Present rectangular pin fins consist of elliptical perforations with two models and two cases. The signum function is used for modeling the opposite and the mutable approach of the heat transfer area. To find the general solution, the degenerate hypergeometric equation was used as a new derivative method and then solved by Kummer's series. Two validation methods (previous work and Ansys 16.0‐Steady State Thermal) are considered. The strong agreement of the validation results (0.31% to 0.52%) lends to the reliability of the presented model. It was found that use of the perforated fin leads to decreased thermal resistance and improvement in the thermal performance of the pin fin by enhancing the heat transfer and increasing Nusselt number. Also, the increase of the inclination angle, size, and number of perforations can be used to optimize the present model by maximizing the heat transfer area and minimizing both the weight and length of the pin fins.     

Heat transfer and flow characteristics of offset fins in the low-Reynolds-number region

The characteristics of heat exchangers with offset-type plate fins for space stations are studied for Reynolds numbers less than 300 based on the hydraulic diameter. A three-dimensional analysis is carried out to study the effects of the following parameters on the heat transfer and the flow characteristics: (a) the thermal boundary layer developing on the bottom plate and on the fins on the plate, (b) the aspect ratio (height/pitch) of the cross section of the flow passage, the fin thickness, the fin length in the direction of the flow, the thermal conductivity of the fluid and the fins, and the Prandtl number of the fluid. The results obtained are as follows. (1) The heat-transfer coefficient on the fin surface is characterized by the thermal-conductivity ratio of fluid to fin material. When the thermal conductivity of the fin material approaches that of the fluid, the heat-transfer coefficient on the fin surface becomes low. (2) The optimum condition of the aspect ratio depends on the value of the thermal-conductivity ratio between the fluid and the fins. (3) When the aspect ratio becomes large or small, the friction factor of offset fins approaches that of fully developed duct flow with the same aspect ratio as the Reynolds number decreases. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(4): 249–261, 1997     

Efficiency of the Horizontal Single Pin Fin Subjected to Free Convection and Radiation Heat Transfer

In this communication, the results of numerical calculations of the heat transfer coefficient and temperature distribution along the horizontal single pin fin in still ambient air, as well as the fin efficiency, are presented and compared with classical analytical results in the case of the constant heat transfer coefficient fin theory. The measured temperature distributions along the two low carbon steel pin fins having a length-to-diameter ratio of 35—one covered with the polished nickel and the other painted mat black—agree very well with the numerical results and are higher than the classical results. The analytically calculated fin efficiency does not differ significantly from the results of the numerical calculations if they are compared for the same dimensionless fin parameter in which the heat transfer coefficient is determined for the fin base temperature. More extended numerical calculations showed that beyond the fin parameter of five, the analytical results of the fin efficiency are higher than the numerical results by no more than about 1%. The largest difference between the classical and numerical fin base efficiencies is about 3.5%, and it was observed at a fin parameter of about 1, where the length of the pin fin has the optimal value based on the classical theory.     

The heat transfer characteristics of liquid cooling heat sink with micro pin fins

This paper numerically and experimentally investigated the liquid cooling efficiency of heat sinks containing micro pin fins. Aluminum prototypes of heat sink with micro pin fin were fabricated to explore the flow and thermal performance. The main geometry parameters included the diameter of micro pin fin and porosity of fin array. The effects of the geometrical parameters and pressure drop on the heat transfer performance of the heat sink were studied. In the experiments, the heat flux from base of heat sink was set as 300 kW/m². The pressure drop between the inlet and the outlet of heat sink was set < 3000 Pa. Numerical simulations with similar flow and thermal conditions were conducted to estimate the flow patterns, the effective thermal resistance. It was found that the effective thermal resistance would reach an optimum value for various pressure drops. It was also noted that the effective thermal resistance was not sensitive to porosity for sparsely packed pin fins.     

Impact of convective tip condition on the transient thermal behavior of wet porous convective radiative exponential profiled inclined longitudinal fin structures subject to heat generation

A convective-radiative fully wet porous inclined longitudinal fin of exponential profile is the focus of the current work. The thermal behavior of the fin under unsteady conditions has been analyzed for adiabatic and convective boundary conditions. The exponential fin and its counterpart inverted exponential fin are simultaneously investigated by considering temperature-relevant thermal conductivity and heat generation. The modeled governing equation upon nondimensionalization reduces to a partial differential equation which is computed by employing the finite difference approach. The impact of relevant parameters like the convective parameter, radiative parameter, wet porous parameter, dimensionless time, exponential index, dimensionless ambient temperature, generation number, thermal conductivity parameter, and angle of inclination on thermal characteristics of exponential and inverted exponential fin structures with adiabatic and convective boundary restrictions have been examined. One of the main outcomes was that the inverted exponential fin with an adiabatic tip gives rise to the highest thermal curve, and the tapered exponential fin with a convective tip resulted in the lowest thermal curve.     

Effectiveness of Composite Fins Under Maximum Heat Dissipation

This paper is devoted to the determination of the effectiveness and the optimization of two-dimensional (2-D), longitudinal rectangular composite fins under convective conditions through the concept of relative inverse thermal admittance. The influence of composite layer thickness and the composite and fin thermal conductivity ratio on the optimum geometry is determined. Effectiveness is used as the fundamental parameter to prove that the fin is fulfilling the objective of increasing heat dissipation. Once the optimum thickness has been obtained, the Biot number and the effectiveness are easily calculated. The optimization process is carried out through universal graphs in which the range of parameters covers most of the practical cases a designer will find and ensuring fins operate as a real dissipation device.     

A dimensionless analysis of heat and mass transport in an adsorber with thin fins; uniform pressure approach

A numerical study on heat and mass transfer in an annular adsorbent bed assisted with radial fins for an isobaric adsorption process is performed. A uniform pressure approach is employed to determine the changes of temperature and adsorbate concentration profiles in the adsorbent bed. The governing equations which are heat transfer equation for the adsorbent bed, mass balance equation for the adsorbent particle, and conduction heat transfer equation for the thin fin are non-dimensionalized in order to reduce number of governing parameters. The number of governing parameters is reduced to four as Kutateladze number, thermal diffusivity ratio, dimensionless fin coefficient and dimensionless parameter of Γ which compares mass diffusion in the adsorbent particle to heat transfer through the adsorbent bed. Temperature and adsorbate concentration contours are plotted for different values of defined dimensionless parameters to discuss heat and mass transfer rate in the bed. The average dimensionless temperature and average adsorbate concentration throughout the adsorption process are also presented to compare heat and mass transfer rate of different cases. The values of dimensionless fin coefficient, Γ number and thermal diffusivity ratio are changed from 0.01 to 100, 1 to 10^− 5 and 0.01 to 100, respectively; while the values of Kutateladze number are 1 and 100. The obtained results revealed that heat transfer rate in an adsorbent bed can be enhanced by the fin when the values of thermal diffusivity ratio and fin coefficient are low (i.e., α^? = 0.01, Λ = 0.01). Furthermore, the use of fin in an adsorbent bed with low values of Γ number (i.e. Γ = 10^− 5) does not increase heat transfer rate, significantly.     

Two-dimensional thermal analysis of a polygonal fin with two tubes on a square pitch

The boundary element method (BEM) has been used to investigate the two-dimensional temperature distribution and the flow of heat from a polygonal fin with two tubes on a square pitch. This numerical method is shown to be convergent, stable and consistent. The resultant heat flows from the fin and the tubes are presented in the form of fin performance ratios. The values of the two-dimensional fin performance ratios are almost identical to those obtained for a single radial rectangular fin of equivalent surface area. The one-dimensional fin performance indicators, fin performance ratio or fin efficiency can be used to predict the heat flows. However, the two-dimensional temperature distributions have revealed the existence of conductive paths between the two tubes depending upon the fin dimensions, the values of the heat transfer and material thermal conductivity, and the magnitude of the temperature differences between the two tubes and the surrounding air.     

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     

吸附式制冷系统传热传质过程的数值模拟

建立了沸石－水吸附式制冷系统吸附床在非第一类边界条件时的二维传热传质模型。考虑了工质对的吸附特性对脱附过程的影响,讨论了肋片数量、肋片物性参数,吸附床的有效导热系数,接触热阻等参数对脱附时间的影响。结果表明,增加肋片可以改善吸附床的性能,其中肋片的数量和接触热阻的影响较大,肋片的物性参数影响不大。     

Thermal performance measurement of heat sinks with confined impinging jet by infrared thermography

In this paper, the thermal performance of heat sinks with confined impingement cooling is measured by infrared thermography. The effects of the impinging Reynolds number, the width and the height of the fins, the distance between the nozzle and the tip of the fins, and the type of the heat sinks on the thermal resistance are investigated. The results show that increasing the Reynolds number of the impinging jet reduces the thermal resistance of the heat sinks consistently. However, the reduction of the thermal resistance decreases gradually with the increase of the Reynolds number. The thermal resistance can be decreased by increasing the fin width combined with an appropriate Reynolds number. Increasing the fin height to enlarge the area of heat transfer also decreases the thermal resistance, but the effects are less conspicuous than those on altering the fin width. An appropriate impinging distance with minimum thermal resistance can be found at a specific Reynolds number, and the optimal impinging distance increases as the Reynolds number increases. Generally speaking, the thermal performance of the pin–fin heat sinks is superior to that of the plate–fin heat sinks because the pin–fin heat sinks consist of smaller volumes but greater exposure surfaces.     

Analysis of heat transfer through Bi-convection fins

Heat transfer through fins subject to two different convective media is modeled and analyzed analytically in this work. The terminology “Bi-convection fin” is used to refer to this kind of fins. Five different cases are analyzed: Case A: Bi-convection thickness-wise Bi-metallic fins; Case B: Bi-convection span-wise rectangular fins; Case C: Bi-convection longitudinal-wise fins; Case D: Bi-convection perimeter-wise fins with uniform cross-section; and Case E: Bi-convection perimeter-wise permeable fins. Closed form solutions for the fin temperature and heat transfer rate are obtained. It is found that Heat transfer through Bi-convection fins may be minimized for certain designs such as those belonging to cases A, B, D and E. On the other hand, it may be maximized as for those belonging to case C at specific values of fin indices and convection heat transfer coefficients ratio. Finally, the heat transfer through Bi-convection fins is found to increase as their effective thermal conductivity, cross-sectional area, fin indices and the difference between the base and the effective free stream temperatures increase.