Performance analysis and optimization of absorber plates of different geometry for a flat-plate solar collector: a comparative study

This paper presents a comparative study on the performance and optimization of several profile shapes namely, rectangular, trapezoidal and rectangular profile with a step change in local thickness (RPSLT). This analysis concentrates on the performance and optimization of RPSLT. A modification has been suggested for the analysis of RPSLT absorber plate that was observed by Hollands and Stedman [Solar Energy 49 (1992) 493]. The result indicates that there is optimum fin efficiency of trapezoidal profile for constant plate volume. The RPSLT profile of absorber plate is superior to other profiles because of higher performance and less difficulties in fabrication.     

Minimum Mass Design of Radiating Radial Fin of Trapezoidal Profile

This article presents the optimum design of a radiating radial fin of trapezoidal profile. Optimum parameters for rectangular and triangular profiles are given in the form of simple correlations. Using these, the base thickness and the length of the fin can be easily determined from the given data of heat dissipation, thermal conductivity, emittance, base radius, base temperature, and environment temperature.     

Performance analysis and optimization of a thermally non-symmetric annular fin

Considering thermally non-symmetric convective boundary conditions, optimum dimensions of an annular fin which has a rectangular cross-section are investigated. Two-dimensional heat diffusion equation is solved analytically to obtain temperature distribution and heat transfer rate. In this work, fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rates. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found employing NCONF routine in the IMSL Library. The derived condition of optimality gives an open choice to the designer.     

Analytic method for thermal performance and optimization of an absorber plate fin having variable thermal conductivity and overall loss coefficient

The absorber of a collector receives solar energy which is delivered to the transport medium to be carried away as useful energy. During this process, temperature of the absorber plate increases and therefore, thermophysical parameters engaged to determine the thermal performance of an absorber plate varies with temperature of the plate. The present study demonstrates analytically to determine the performance of an absorber plate fin with temperature dependent both thermal conductivity and overall heat loss coefficient. The decomposition method is proposed for the solution methodology. An optimum design analysis has also been carried out. A comparative study has been executed among the present results and that of existed in the published work, and a notable difference in results has been found. Finally, unlike published work, dependency parameters on the performances and optimum design have been highlighted.     

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.     

Performance and optimization analysis of a constructal T-shaped fin subject to variable thermal conductivity and convective heat transfer coefficient

In the present study, an exercise has been devoted to establish an analytical model for thermal performance and optimization of a constructal fin subject to variable thermal conductivity of fin material and convective heat transfer coefficient over the fin surface. For the adaptation of these considerations, the governing energy equation for the stem as well as the flange becomes nonlinear. A new analytical scheme based on the Adomian decomposition method has been established for the solution process. As the present study is an analytic, it can be extended to the analysis for determining the optimum dimensions of fins satisfying either the maximization of rate of heat transfer for a given fin volume or the minimization of fin volume for a desired heat transfer rate. From the results, it can be highlighted that the present model predicts the fin performance always an under value in comparison with that the published results whereas the optimum heat transfer rate determined by using the present analysis gives an over value. The effect of different geometric and thermophysical parameters on both the fin performance and optimization has been studied. For a comparative study, the present and published results are executed for a wide range of thermogeometric parameters.     

Performance and optimization analysis of SRC profile fins subject to simultaneous heat and mass transfer

Fin material near the tip of a uniform cross sectional (UC) fin does not participate actively in transferring heat. This effect may seem to have progressed much with the increase in fin length. A uniform cross sectional fin with a step reduction in local cross section (SRC) not only increases the effective utilization of fin material near the tip but also it promotes the ease of fabrication. In this study, an effort has been devoted to determine analytically the overall fin performance of both longitudinal and pin fins of SRC profile under fully dry, partially wet and fully wet conditions. The effect of various design and psychometric parameters on the fin performance of SRC fins has been investigated and compared it is with the corresponding UC fin. A scheme for optimizing SRC fins has also been demonstrated in the present work. From the result, it can be highlighted that the optimum values of Biot number and aspect ratio of SRC fins increase with the increase in relative humidity for the same fin volume. In comparison with the UC fin for the identical fin volume, the SRC fin transfers more rate of heat and consequently, this difference in heat transfer rate increases slowly with the relative humidity.     

A method to reduce the flow depth of a plate heat exchanger without a loss of heat transfer performance

With the aim of improving heat exchanger compactness, this study investigates how the optimum configuration of an air–liquid plate heat exchanger changes as the heat exchanger depth decreases. In this respect, optimization of an air–liquid plate heat exchanger with a given frontal area and a given depth is achieved. The optimum fin pitch and plate pitch are obtained to maximize the heat transfer rate based on heat transfer and pressure loss correlations in finned channels. Then, the focus of this study is placed on how the optimum channel configuration changes when the heat exchanger depth decreases for compactness. The results illustrate that the heat transfer performance can remain unchanged if the geometric parameters, such as the plate thickness, the plate pitch, the fin thickness, and the fin pitch, are reduced proportionally to the square root of the flow depth reduction given that the flow remains laminar. This finding is arranged into a simple scaling rule to obtain the configuration of a more compact heat exchanger from an existing configuration. In addition, the scaling arguments are extended to practical situations where the fin thickness and the plate thickness are not properly reduced following the scaling rule due to limitations on available material thicknesses.     

Numerical and experimental study of a solar equipped with offset rectangular plate fin absorber plate

A mathematical model that allows the determination of the thermal performances of the single-pass solar air collector with offset rectangular plate fin absorber plate is developed. The model can predict the temperature profile of all the components of the collector and of the air stream in the channel duct. Into the latter are introduced the offset rectangular plate fins, which increase the thermal heat transfer between the absorber plate and the fluid. The offset rectangular plate fins, mounted in a staggered pattern, are oriented parallel to the fluid flow and are soldered to the underside of the absorber plate. They are characterized by high heat transfer area per unit volume and generate the low pressure losses. The experimental results of the air stream temperature will be compared with the results obtained by the theoretical model suggested.     

Effects of fin shapes on heat transfer in microchannel heat sinks

In the present study, compact water cooling of high‐density, high‐speed, very‐large‐scale integrated (VLSI) circuits with the help of microchannel heat exchangers were investigated analytically. This study also presents the result of mathematical analysis based on the modified Bessel function of laminar fluid flow and heat transfer through combined conduction and convection in a microchannel heat sink with triangular extensions. The main purpose of this paper is to find the dimensions of a heat sink that give the least thermal resistance between the fluid and the heat sink, and the results are compared with that of rectangular fins. It is seen that the triangular heat sink requires less substrate material as compared to rectangular fins, and the heat transfer rate per unit volume has been almost doubled by using triangular heat sinks. It is also found that the effectiveness of the triangular fin is higher than that of the rectangular fin. Therefore, the triangular heat sink has the ability to dissipate large amounts of heat with relatively less temperature rise for the same fin volume. Alternatively, triangular heat sinks may thus be more cost effective to use for cooling ultra‐high speed VLSI circuits than rectangular heat sinks.     

An analytical prediction for performance and optimization of an annular fin assembly of trapezoidal profile under dehumidifying conditions

The present study demonstrates an analysis analytically to determine the performances and optimum design of wet annular fin assemblies of the trapezoidal profile. The Frobenius power series method is adopted as an analytical tool to solve the governing differential equation of the above type of wet fin assemblies. The performance parameters, namely, the surface efficiency and augmentation factor are determined. The present model has also ability to predict the performances of a wet fin assembly of triangular fin geometry for the selection of the very small value of the tip thickness. As the present study establishes an analytical model, it can be easily employed in determination of an optimum design condition. Both the performance and optimization study have been made by two approaches of the analysis described based on the handling of the psychrometric properties at the tip as a function of temperatures. Finally, it can be highlighted that the performances and optimum conditions of a wet fin assembly are not only dependent upon the psychrometric properties of air but also dependent upon the approach selected for calculating the energy transferred by the mechanism of mass transfer.     

Performance analysis of finned tube and unbaffled shell-and-tube heat exchangers

This work considers an optimum design problem for the different constraints involved in the designing of a shell-and-tube heat exchanger consisting of longitudinally finned tubes. A Matlab simulation has been employed using the Kern's method of design of extended surface heat exchanger to determine the behavior on varying the values of the constraints and studying the overall behavior of the heat exchanger with their variation for both cases of triangular and square pitch arrangements, along with the values of pressure drop. It was found out that an optimum fin height existed for particular values of shell and tube diameters when the heat transfer rate was the maximum. Moreover it was found out that the optimum fin height increased linearly with the increase in tube outer diameter. Further studies were also performed with the variation of other important heat exchanger design features and their effects were studied on the behavior of overall performance of the shell-and-tube heat exchanger. The results were thereby summarized which would proclaim to the best performance of the heat exchanger and therefore capable of giving a good idea to the designer about the dimensional characteristics to be used for designing of a particular shell and tube heat exchanger.     

Thermal performance enhancement of solar air heaters,by a fan-blown absorber plate with rectangular fins

The aim of this study is to provide a remedy for the low thermophysical properties of air, which is used as a fluid of transfer in solar collectors. A fully developed flow needs to be created by the use of staggered fin rows soldered under the absorber plate. The fluid flow undergoes contractions followed by expansions, which creates a fully developed turbulent flow, and increases the thermal heat transfer between the absorber plate and the air. The fins increase the heat transfer surface, from which an appreciable improvement of the thermal heat performance of solar air heaters has been found in comparison to those of solar air heaters with a plane absorber. In this work we have tested the influence of the dimension of the fins and the influence of the space between consecutive fin rows mounted in staggered rows.     

Performance analysis and optimization of elliptic fins circumscribing a circular tube

The performance of elliptic disc fins has been analyzed using a semi-analytical technique. It has been shown that the efficiency of such fins can also be predicted very closely using the sector method. However, the equivalent annulus method is not suitable for this fin geometry. A method for the optimum design of fins, using a constraint of either fin volume or rate of heat dissipation has also been suggested. Optimum elliptical fins dissipate heat at a higher rate compared to an annular fin when space restriction exists on both sides of the fin. Even when the restriction is on one side only, the performance of elliptical fin is comparable to that of eccentric annular fin for a wide parametric range.     

Optimum design of a longitudinal fin array with convection and radiation heat transfer using a genetic algorithm

In the present work, the optimization of a longitudinal fin array is investigated. Heat is transferred by conduction along the fins and dissipated from the fin surface via natural convection to the ambient and radiation to other fin surfaces and surrounding. The aim of the optimization is to find the optimum geometry and the number of fins in such a way that the rate of heat transfer from the array is maximized. A modified genetic algorithm is used to maximize the objective function which is defined as the net heat rate from the fin surface for a given length. The fin profile is represented by B-spline curves, where the shape of fin is determined by the positions of a set of control points. The effects of the base temperature, the fin length and the height of array on the optimum geometry and on the number of fins are investigated by comparing the results obtained for several test cases. In addition, the contributions of convective heat transfer and radiative heat transfer in net heat transfer are studied for these cases. The enhancement of heat transfer due to the optimum fin geometry is examined by comparing the results obtained for the optimum fin profile with those with conventional profiles.     

A model on the basis of analytics for computing maximum heat transfer in porous fins

This study presents an analytical work on the performance and optimum design analysis of porous fin of various profiles operating in convection environment. Straight fins of four different profiles, namely, rectangular, convex parabolic and two exponential types are considered for the present investigation. An analytical technique based on the Adomian decomposition method is proposed for the solution methodology as the governing energy equations of porous fins for all the profiles are non-linear. A comparative study has been carried out among the results obtained from the porous and solid fins, and an appreciable difference has been noticed for a range of design conditions. Finally, the result shows that the heat transfer rate in an exponential profile with negative power factor is much higher than the rectangular profile but slightly higher than the convex profile. On the other hand, the fin performance is observed to be better for exponential profiles with positive power factor than other three profiles. A significant increase in heat transfer through porous fins occurs for any geometric fin compared to that of solid fins for a low porosity and high flow parameter.     

Influence of Shape,Number, and Position of Horizontal Minifins on Thermal-Hydraulic Performance of Minichannel Heat Sink Using Nanofluid

In the first part of present study, an experimental setup with constant heat flux is used to investigate the thermal performance of the water inside a horizontal triangular pin fin channel. For the sake of validation of the computational fluid dynamics (CFD) study, a simulation is conducted according to the geometry and operating conditions of the experimental work. The numerical model consists of a study that has been established based on the geometrical parameters and operating conditions similar to the experimental work. The influence of four different cross sections of minifins (shaped as square, trapezoidal, triangular, and sinusoidal) and of number of triangular minifins (1, 3, 5, 7, and 9) and their positions (in the regions of entrance, central, and terminal) on the heat transfer rate and pressure drop in a minifin minichannel heat sink are numerically investigated by a two-dimensional CFD model. The coolant is Cu–water nanofluid at a volumetric concentration of 2%. The results demonstrated that the sinusoidal minifin minichannel heat sink has the highest convective heat transfer coefficient in comparison with other shapes, while the trapezoidal minifin minichannel showed the highest thermal resistance. The highest pressure drop was observed for the triangular minifin inside minichannel. By increasing the number of fins, thermal resistance considerably decreased. Likewise, at the central and entrance positions, respectively, the highest Nusselt number and friction factor inside the minichannel was observed. This study can provide useful guidelines for the design of the cooling devices.     

Development of Colburn j Factor and Fanning Friction Factor Correlations for Compact Surfaces of the Triangular Perforated Fins Using CFD

The necessity of increased heat transfer surface area has resulted in the development of compact heat exchangers, which are widely used in the aerospace and automobile industries. Hence perforations are made on triangular plain fins to study the effects on the heat transfer coefficient. A numerical model has been developed for the perforated fin of a triangular plate fin heat exchanger. Perforated fin performance has been analyzed with the help of computational fluid dynamics (CFD) by changing the various parameters of the fin. The Colburn j factor and the Fanning friction factor are calculated for different Reynolds numbers. The values of the Colburn j factor and the Fanning friction factor are validated for known geometric fins with available data in the literature and extended to triangular perforated fins. The correlations have been developed between Reynolds number, Colburn j factor, and Fanning friction factor by taking into account fin height, fin thickness, and fin spacing. The present numerical analysis is carried out for air media.     

省煤器矩形肋的优化模型

针对电站锅炉省煤器所用扩展受热面存在传热能力低、占用空间大等问题,对矩形肋进行了优化设计并建立了优化模型,即在矩形肋重量一定条件下,如何利用无量纲方程对矩形肋尺寸进行寻优,以获取最大传热量的理论方法。深入考虑了矩形肋传热效果的2个重要影响因素——烟风速度和污染系数,论证了矩形肋的优化对省煤器增加传热量降低造价具有很重要的作用。另外,优化图表为肋管的热力特性设计提供了参考。     

Thermo-Hydraulic Performance Enhancement of Finned Elliptical Tube Heat Exchangers by Utilizing Innovative Dimple Turbulators

Abstract

As a new type of fin structure in finned tube heat exchangers, dimple turbulators exhibit excellent potential for thermo-hydraulic performance enhancement. A three-dimensional numerical simulation study was conducted to investigate the influences of five kinds of innovative concave dimple turbulators (CDTs), namely – elliptical dimple, conical frustum dimple, trapezoidal prism dimple, leeward triangular dimple and upward triangular dimple (UwTD) on the thermo-hydraulic performance enhancement in a plate fin-and-elliptical tube (PFET) heat exchanger, where CDTs are textured on the fin surface transversely between the elliptical tubes. The computational results are analyzed by considering the performance evaluation criterion for the PFET heat exchangers with different types of CDT shapes. The present investigation demonstrates that the heat transfer enhancement is intimately pertained to ejection with longitudinal counter-rotating flow, strengthened secondary flow and vortex structures at the downstream rim of CDT. A parametric study on the CDTs indicated that the UwTD vortex turbulators give better thermo-hydraulic performance under the present conditions. The numerical simulation results illustrated different secondary flow structures and heat transfer characteristics of the CDTs with various shapes, which disclosed the influential mechanisms of differently shaped dimple turbulators on the heat transfer augmentation in PFET heat exchangers.