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.     

Multiobjective thermo‐economic and thermodynamics optimization of a plate–fin heat exchanger

In the present work, a multiobjective heat transfer search (MOHTS) algorithm is proposed and investigated for thermo‐economic and thermodynamic optimization of a plate–fin heat exchanger (PFHX). Heat exchanger effectiveness and total annual cost (TAC) are considered as thermo‐economic objective functions. Similarly, entropy generation rate and heat exchanger effectiveness are considered as thermodynamic objective functions. Six design variables including flow length of cold and hot streams, no flow length, fin height, fin pitch, and fin offset length are considered as decision variables. Effectiveness and accuracy of the proposed algorithm are evaluated by analyzing application examples of a PFHX. The results obtained using the proposed algorithm for thermo‐economic considerations are compared with the available results of NSGA‐II and TLBO in the literature. Results show that 3.56% to 10.29% reductions in TAC with 0.48% to 0.81% higher effectiveness are observed using the proposed approach compared to TLBO and NSGA‐II approaches. Additionally, the distribution of each design variable in its allowable range is also shown for thermo‐economic consideration to identify the level of conflict on objective functions. The sensitivity analyses of design variables on the objective functions value are also performed in detail.     

Laminar free convection underneath a downward facing inclined hot fin array

A combined theoretical, experimental and numerical study was conducted to investigate the problem of laminar free convection underneath a hot isothermal and inclined fin array. The influence of inclination on the location where the flow stagnates, and splits, was examined. Heat transfer rates were calculated for different fin array geometries and temperatures. The results show that for small inclination angles the cooling rate is essentially constant. Beyond a certain angle, the tilting of the fin array enhances substantially the heat transfer rate. Sensitivity analyses indicate that the heat transfer coefficient increases at higher fin temperatures and larger fin spacing, but is of a lesser sensitivity to fin height changes. Additionally, it was discovered that the array optimal fin spacing do not depend on the inclination angle. In the theoretical part, a semi empirical model was developed for the heat transfer coefficient of horizontal and slightly inclined arrays that have large fin spacing. In effect it constitutes the necessary modeling addition to the previously developed model for moderately and tightly spaced fins of slightly tilted arrays. Together, they provide analytical expressions for the heat transfer coefficient of slightly inclined arrays, for any fin spacing.     

Heat transfer from a horizontal fin array by natural convection and radiation—A conjugate analysis

The problem of natural convection heat transfer from a horizontal fin array is theoretically formulated by treating the adjacent internal fins as two-fin enclosures. A conjugate analysis is carried out in which the mass, momentum and energy balance equations for the fluid in the two-fin enclosure are solved together with the heat conduction equations in both the fins. The numerical solutions by using alternating direction implicit (ADI) method yield steady state temperature and velocity fields in the fluid, and temperatures along the fins. Each end fin of the array is exposed to limited enclosure on one side and to infinite fluid medium on the other side. Hence a separate analysis is carried out for the problem of end fin exposed to infinite fluid medium with appropriate boundary conditions. From the numerical results, the heat fluxes from the fins and the base of the two-fin enclosure, and the heat flux from the end fin are calculated. Making use of the heat fluxes the total heat transfer rate and average heat transfer coefficient for a fin array are estimated. Heat transfer by radiation is also considered in the analysis. The results obtained for a four-fin array are compared with the experimental data available in literature, which show good agreement. Numerical results are obtained to study the effectiveness for different values of fin heights, emissivities, number of fins in a fixed base, fin base temperature and fin spacing. The numerical results are subjected to non-linear regression and equations are obtained for heat fluxes from the two-fin enclosure and single fin as functions of Rayleigh number, aspect ratio and fin emissivity. Also regression equations are obtained to readily calculate the average Nusselt number, heat transfer rate and effectiveness for a fin array.     

Heat transfer from a vertical fin array by laminar natural convection and radiation—A quasi‐3D approach

A quasi‐3D numerical model is developed to study the problem of laminar natural convection and radiation heat transfer from a vertical fin array. An enclosure is formed by two adjacent vertical fins and vertical base in the fin array. Results obtained from this enclosure are used to predict heat transfer rate from a vertical fin array. All the governing equations related to fluid in the enclosure, together with the heat conduction equation in both fins are solved by using the Alternating Direction Implicit (ADI) method for getting the temperatures along the height of the fin and the temperature of the fluid in the enclosure. Separate analysis is carried out to calculate the heat transfer rates from the end fins in the fin array. A numerical study has been carried out for the effect of fin height, fin spacing, fin array base temperature, and fin emissivity on total heat transfer rates and effectiveness of the fin array. The numerical results obtained for an eight‐fin array show good agreement with the available experimental data. Results show that the fin spacing is the most significant parameter and there exists an optimum value for the fin spacing for which the heat transfer rate from the fin array is maximum. Correlations are presented for predicting the total heat transfer rate, average Nusselt number, and effectiveness of the fin array. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20360     

An experimental investigation of heat transfer in pin fin array

Detailed heat transfer measurements were performed by using 178 thermocouples in a channel with pin fin array. Local heat transfer coefficients and local heat transfer enhancement coefficients were obtained for eight Reynolds numbers ranging from 2000 to 100,000 on the endwall of the channel. The endwall boundary conditions for heat transfer investigation are heating the bottom endwall and heating symmetrically the bottom and top endwalls with constant heat flux. The mechanism of heat transfer enhancement with pin fin array has been discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(7): 533–541, 2001     

Second law analysis for optimal thermal design of radial fin geometry by convection

This paper presents a second law analysis for the optimal geometry of fin array by forced convection. The analytical analysis involves the achievement of a balance between the entropy generation due to heat transfer and entropy generation due to fluid friction. In the design of a thermal system, it is important to minimize thermal irreversibilities because the optimal geometry will be found when the entropy generation rate is minimized. In this paper, the entropy generation rate is discussed and optimum thickness for fin array is determined on the basis of entropy generation minimization subjected to the global constraint. In addition, the influence of cost parameters on the optimum thickness of fin array is also considered and presented in graphical form. It has been found that the increase in cross flow fluid velocity will enhance the heat transfer rate that will reduce the heat transfer irreversibility.     

Performance study on plain fin filled with catalyst in a plate fin heat exchanger for hydrogen liquefaction

In order to develop the correlations of the fin performances of the catalyst filled plate fin heat exchanger (CFPFHE) for hydrogen liquefaction, a numerical model of the plain fin filled with catalyst at 30–80 K is established. The effects of temperature, the structural parameters of the fin and catalyst layer and the operating condition on the fin performances of the fin channel are analyzed and discussed. The results show that the temperature distribution patterns and fin performances at 30–40 K and above 40 K have obvious differences. The results above 40 K can be characterized by that at 70–80 K. The sensitivity analysis shows that the distributions of sensitivity at 70–80 K and 30–40 K are similar. The heat transfer and ortho-para hydrogen conversion performances are mainly affected by the structural parameters of the fin and the operating condition, while the flow performance is mainly affected by the structural parameters of the catalyst layer. The correlations of the flow and heat transfer performances at 70–80 K and 30–40 K are obtained by fitting the data points on the response surface with more than 97% of the fitting degrees and within ±15% of the deviations. Meanwhile, the correlations of the ortho-para hydrogen conversion performance show that the mass space velocities at 70–80 K and 30–40 K should be lower than 1.25 and 7.50 kg m^?3 s^?1 respectively to reach the standard of the ortho-para hydrogen conversion. The correlations of the fin performances can be used as the basis of optimization design of the CFPFHE.     

Performance and optimum design analysis of an absorber plate fin using recto-trapezoidal profile

This paper establishes a new profile, viz. recto-trapezoidal (RT) of an absorber plate fin on the basis of ease of fabrication as well as augmentation of heat transfer rate per unit fin volume. An analytical model has been developed for evaluating the thermal performance and optimum dimensions of an absorber plate fin using this typical profile. The present study is equally suitable for an absorber plate fin having a rectangular, trapezoidal or triangular profile also with consideration of their respective geometrical parameters. The optimization of the RT profile has been cast in a generalized form either by maximizing heat transfer rate for a given fin volume or by minimizing fin volume for a given heat transfer duty. From the optimum design analysis, significant results have been noticed when an additional constraint is imposed with the fin volume. Under this design condition, it may also be highlighted that for an optimal circumstance, the heat transfer rate through a RT profile absorber plate fin is greater than a trapezoidal or triangular profile for the same fin volume. However, this observation may be restricted to the limited values of fin volume only. The optimum design analysis for the RT profiled absorber plate fin has also been studied under the different design constants. Finally, for the variation of all the design variables, optimum design curves have been generated for a wide range of thermo-geometric parameters.     

Optimal fin geometry based on exergoeconomic analysis for a pin-fin array with application to electronics cooling

Exergoeconomic analysis for a pin-fin array involves the achievement of a balance between the entropy generation due to heat transfer and pressure drop, while considering the unit cost of entropy generation. This process yields the optimum fin operation parameters based on minimum cost. In this study, analytical equations are presented considering the cost of operation for a pin-fin array. The solution of these equations would give the optimum fin diameter and length that result in a fin array with minimum operational cost. In addition, the influence of important fin thermal, physical, geometrical and cost parameters on the optimum diameter and length is presented in graphical form for quick calculations and easy interpretation. The presented results are subjected to the constraint that L/D is of the order of 1 or greater than 1. A case is also presented to demonstrate the use of the model for conditions typically found in cooling of electronic components.     

Numerical study of the fin efficiency and a modified fin efficiency formula for flat tube bank fin heat exchanger

In this paper, a three-dimensional numerical heat transfer analysis has been performed in order to obtain the temperature distribution and the fin efficiency using the experimentally determined local heat transfer coefficients from the naphthalene sublimation technique and heat and mass transfer analogy. The influences of the fin material, fin thickness, and transversal tube pitch on the fin efficiency are studied for flat tube bank fin heat exchangers. The fin efficiency, obtained by a numerical method using the averaged heat transfer coefficient, is compared with that using the local heat transfer coefficient. The reliability of the generally used formula for fin efficiency is tested also, and then a modified fin efficiency formula with a new equivalent fin height is provided. The results show that the difference between the fin efficiency obtained by the numerical method using the local heat transfer coefficient and the fin efficiency using the averaged heat transfer coefficient is small, but the fin efficiency obtained by the generally used formula is lower than that obtained by the numerical method using the local heat transfer coefficient; the fin efficiency obtained by the modified formula matches very well with the fin efficiency obtained by the numerical method using the local heat transfer coefficient. The modified formula for the fin efficiency calculation is more reliable, and it can be applied directly to the design of a flat tube bank fin heat exchanger and also will be useful in engineering applications.     

Optimized heat transfer fin design for a metal-hydride hydrogen storage container

This paper presents a heat transfer fin optimization for a LaNi₅ hydrogen storage container. In this simplified approach, a one-dimension fin model is proposed in order to avoid geometrical restrictions and constrains associated to a particular technological solution. Therefore, the presented model can be utilized as a general framework for the development of containers with inner fins.     

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.     

Pool boiling heat transfer on horizontal rectangular fin array in saturated FC-72

The flow patterns and pool boiling heat transfer performance of copper rectangular fin array surfaces immersed in saturated FC-72 were experimentally investigated. The effects of the geometry parameters (fin spacing and fin length) on boiling performance were also examined. The test surfaces were manufactured on a copper block with a base area of 10 mm × 10 mm with three fin spacing (0.5 mm, 1.0 mm and 2.0 mm) and four fin lengths (0.5 mm, 1.0 mm, 2.0 mm and 4.0 mm). All experiments were performed in the saturated state at 1 atmospheric condition. A plain surface was used as the reference standard and compared with the finned surfaces. The photographic images showed different boiling flow patterns among the test surfaces at various heat fluxes. The test results indicated that closer and higher fins yielded a greater flow resistance that against the bubble/vapor lift-off in the adjacent fins. Moreover, as the heat flux approached to critical heat flux (CHF), numerous vapor mushrooms periodically appeared and extruded from the perimeter of the fin array, causing dry-out in the center of the fin array. Closer and higher fins provide more heat transfer. The results also showed that overall heat transfer coefficient decayed rapidly as the fin spacing decreased or the fin length increased. The maximum value of CHF on the base area was 9.8 × 10⁵ W m⁻² for the test surface with a 0.5 mm fin spacing and a 4.0 mm fin length, which has a value five times greater than that of the plain surface.     

Thermal optimization of tapered pin fin exposed to nonuniform surface heat transfer coefficient

In the present work, thermal analysis and design optimization of tapered pin fin subjected to variable surface heat transfer coefficient have been numerically carried out. It is well known that heat is transferred through the fin by conduction along its length and dissipated from the fin surface via natural convection to the ambient. The thermal analysis and the optimum dimension were carried out using finite element (FE) modeling software ANSYS-17.2. The thermal performance of the tapered pin fin has been studied over a wide range of physical dimensions. In addition, the effect of base to tip surface heat transfer coefficient ratio (ε) on the fin performance is evaluated. It was found that the effect of variable heat transfer coefficient has a significant impact on the fin efficiency. The rate of increase of fin efficiency was lower in the low as well as in high range of ε, meanwhile, it was steeper in the intermediate range of ε. It was also observed that the optimal values of the heat dissipation were higher for lower values of ε at the same conditions.     

Effect of flow bypass on the performance of a shrouded longitudinal fin array

Theoretical and experimental studies were carried out to investigate the effects of duct velocity, fin density and tip-to-shroud clearance on the flow bypass and its impact on the pressure drop across a longitudinal aluminum fin array and its thermal performance. The clearance was varied parametrically, starting with the fully shrouded case and variations of the channel height giving partially shrouded configuration of different clearance ratios were also carried out. The flow bypass was found to increase with increasing fin density and insensitive to the air flow rate. This effect of fin density decreased as the clearance increased. The calculated total pressure was greatly affected by fin density. For fully-shrouded fin array, with H_f/S equals to 8 and 12.72, the pressure drop increased by a factor of 4.3 and 20 of that with H_f/S equals to 3.4, respectively. The total pressure drop and the average convective heat transfer coefficients corresponding to the fully and partially shrouded tested fin array of H_f/S = 3.4 were compared. Going from fully to partially shrouded one of the largest clearance ratio (C/H_f = 0.89), the total pressure drop is reduced by about 50%. For clearance ratios equal to 0.36, 0.56, and 0.89, the average heat transfer coefficients were reduced by about 12, 17, and 30% of that for the fully shrouded configuration at Re_D of about 3 × 10³. That percentage reduction in heat transfer coefficients are decreased with the increase of air flow rate.     

Electrohydrodynamic enhancement of heat transfer in vertical fin array using computational fluid dynamics technique

Electrohydrodynamic enhanced heat transfer of the natural convection inside an enclosure with a vertical fin array is numerically investigated via a computational fluid dynamics technique. The parameters considered in a numerical modeling are supplied voltage, Rayleigh number, inclined angle, number of electrodes, electrode arrangement, number of fins, and fin length. The results reveal that the flow and heat transfer enhancements are significantly dependent on the number and position of electrodes around the fins. Moreover, the heat transfer coefficient is substantially improved by the electric field especially at the large number of fins and the long fin length.     

Thermal-hydraulic performance of novel louvered fin using flat tube cross-flow heat exchanger

Experimental studies were conducted to investigate the air-side heat transfer and pressure drop characteristics of a novel louvered fins and flat tube heat exchangers. A series of tests were conducted for 9 heat exchangers with different fin space and fin length, at a constant tube-side water flow rate of 2.8 m³/h. The air side thermal performance data were analyzed using the effectiveness-NTU method. Results were presented as plot of Colburn j factor and friction factor f against the Reynolds number in the range of 500–6500. The characteristics of the heat transfer and pressure drop of different fin space and fin length were analyzed and compared. In addition, the curves of the heat transfer coefficients vs. pumping power per unit heat transfer area were plotted. Finally, the area optimization factor was used to evaluate the thermal hydraulic performance of the louvered fins with differential geometries. The results showed that the j and f factors increase with the decrease of the fin space and fin length, and the fin space has more obvious effect on the thermal hydraulic characteristics of the novel louvered fins.     

Boiling on plate fin and annular fin

This paper for the first time theoretically investigated the heat transfer performance and associated stability characteristics of a plate fin or an annular fin subject to boiling. Stability analysis reveals that in both cases, the N, F, TN and FTN modes are stable; while in the T or FT modes, the operation remains stable only if the fin length is less than some critical value. Plate fin is potentially useful in constant heat flux applications. On the basis of the same fin's base area and volume, the annular fin can deliver more heat and provide wider operational range of base superheat.     

Thermodynamic optimization of cross flow plate-fin heat exchanger using a particle swarm optimization algorithm

This study explores the use of particle swarm optimization (PSO) algorithm for thermodynamic optimization of a cross flow plate-fin heat exchanger. Minimization of total number of entropy generation units for specific heat duty requirement under given space restrictions, minimization of total volume, and minimization of total annual cost are considered as objective functions and are treated individually. Based on the applications, heat exchanger length, fin frequency, numbers of fin layers, lance length of fin, fin height and fin thickness or different flow length of the heat exchanger are considered for optimization. Heat duty requirement constraint is included in the procedure. Two application examples are also presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using PSO are validated by comparing with those obtained by using genetic algorithm (GA). Parametric analysis is also carried out to demonstrate the effect of heat exchanger dimensions on the optimum solution. The effect of variation of PSO parameters on convergence and optimum value of the objective has also been presented.