Performance analysis of extended surfaces subjected to fouling

 The time dependent performance of extended surfaces subjected to fouling is addressed in this work. Where fins are used for augmenting boiling heat transfer, the interaction of local values of temperature excess, fouling resistance and surface characteristics of the deposit can be quite complex. Taking typical asymptotic fouling growth parameters from literature for reverse solubility salts, three kinds of fin geometry are analysed – rectangular, triangular and annular. For various values of the fin parameter mL, the temperature distribution and variation of fouling resistance are obtained as a function of time. To interpret the performance of a fouled fin, a new term `cleanliness efficiency' is introduced. The necessity of choosing an optimal value of mL for the fin is also highlighted here. It is shown that for all three fin configurations, cleanliness efficiency differs little, thus simplifying the geometry dependence. The approach set out in this work will help in the design of finned heat exchangers subjected to fouling and thereby minimise their overdesign. Received on 12 July 2000     

Thermal Analysis of Natural Convection Porous Fins

This work introduces a simple method of analysis to study the performance of porous fins in a natural convection environment. The method is based on using energy balance and Darcy’s model to formulate the heat transfer equation. The thermal performance of porous fins is then studied for three types of fins: long fin, finite-length fin with insulated tip and a finite-length fin with tip exposed to a known convection coefficient. It is found from the analysis that the effect of different design and operating parameters such as: Ra number, Da number, thermal conductivity ratio, Kr and length thickness ratio on the temperature distribution along the fin is grouped into one newly defined parameter called S_H. The effect of the variation of S_H on the porous fin thermal performance is established. The effect of varying the fin length and thermal conductivity ratio on the heat transfer rate from the fin is investigated and compared with that for a solid fin at certain conditions. It is found that the heat transfer rate from porous fin could exceed that of a solid fin. It is also found that increasing the fin length and effective thermal conductivity enhances the heat transfer from the fin up certain limit, where a further increase in these parameters adds no improvement to the fin performance. On Leave from Jordan University of Science and Technology, Irbid-Jordan     

Optimization of annular fins on a horizontal tube

A combination of uniform-thickness annular fins evenly spaced on a tube is a common extended-surface heat exchanger configuration. An analytical model is developed and is verified by comparing total heat transfer predicted by the model to available experimental data. A direct-pattern search technique is applied to the model to optimize the fin/ tube geometry. Optimum dimensions and spacing of fins are established to provide the maximum free convection heat transfer from a fin/tube combination. The optimum arrangement is dependent on fin thermal conductivity, tube diameter, volume of fin material per unit length of tube, and temperature difference between the tube and the surrounding air. Calculated results indicate that a fin in the optimum fin/tube system is shorter and thicker than an isolated fin optimized for minimum material (with no consideration of the effects of fin spacing).     

Decomposition method for thermal design analysis of vertical straight fins under condensation of quiescent and flowing steam

An analytical model is developed for the temperature distribution in vertical rectangular fins, subject to condensation of saturated steam under laminar free or forced convection. Both the thermal conductivity of the fin material and the thermophysical properties involved in the heat transfer process are assumed to be functions of temperature. A generalized analysis is carried out for both convection conditions, based on a decomposition method. An optimization scheme is also presented to facilitate the actual design calculations. The results obtained from the analysis reveal significant variation of fin performance with respect to the design constants under optimum conditions.     

Efficiency and optimisation of fin with temperature-dependent thermal conductivity: a simplified solution

An analytical simplified solution is proposed for temperature distribution and fin efficiency, when thermal conductivity is temperature dependent. An optimal linearization technique is used to solve the nonlinear equation. Based on classical solution, some accurate results are obtained and presented with thermal conductivity parameter and fin parameter. Arithmetic mean temperature is less precise than an equivalent thermal conductivity. Optimal thickness for rectangular fin is derived.     

Transient heat transfer in a functionally graded convecting longitudinal fin

The study investigates the transient thermal performance of a constant area longitudinal fin made of a functionally graded material. Such a fin offers advantages that are not attainable with a traditional fin made of a homogeneous material. A numerical approach has been used to study the transient response of the fin with a step change in its base temperature. The fin is assumed to have an adiabatic tip. Three types of variations in the thermal conductivity with the longitudinal distance along the fin are considered: (a) linear, (b) quadratic, and (c) exponential. New analytical solutions for the steady state performance of the fin are derived in terms of the Bessel functions for cases (a) and (c) and in terms of the Legendre functions for case (b). These solutions provide a check on the accuracy of the transient numerical predictions for large times. The thermal performance of the fin is governed by the classical fin parameter, N _c, and the fin thermal conductivity grading parameter, a. Results are presented for the transient temperature distribution, base heat flow, convective heat loss, the energy stored in the fin and the fin efficiency for representative values of N _c and a. It is found that the transient, as well the steady state performance of the fin, is significantly affected by the functional grading of the fin material. The results presented are not only of fundamental interest but can also be used to design a functionally graded fin with the desirable steady and transient thermal characteristics.     

An experimental investigation on performance of rectangular fins on a horizontal base in free convection heat transfer

This paper reports an experimental study of free convection heat transfer from rectangular fin-arrays on a horizontal base. An experimental set-up was constructed and calibrated, 15 sets of fin-arrays and a base plate without fins were tested in atmosphere. Fin height was varied from 6 mm to 26 mm, fin spacing was varied from 6.2 mm to 83 mm. The base-to-ambient temperature difference was also varied independently and systematically with the power supply to heater ranging from 8 W to 50 W. Fin length and fin thicknesses were fixed at 100 mm and 3 mm, respectively. The experimental program was conducted so as to clearly delineate the separate roles of fin height, fin spacing and base-to-ambient temperature difference. It was found that for a given base-to-ambient temperature difference the convection heat transfer rate from fin-arrays takes on a maximum value as a function of fin spacing and fin height. For a given base-to-ambient temperature difference the enhancement of the convection heat transfer rate of fin-arrays relative to that for base plate without fins is strongly dependent on the fin spacing to fin height ratio and number of fins. A correlation was also presented relating the convection heat transfer rate of fin-arrays relative to that for base plate without fins with the relevant non-dimensional parameters. Received on 7 August 1997     

Boiling on a straight pin fin with variable thermal conductivity

This work theoretically investigated the thermal performance and stability characteristics of a straight pin fin subject to boiling considering a temperature-dependent thermal conductivity of fin, k=k _sat(1+b(T−T _sat)). Steady-state temperature distribution and the associated fin base heat flow were for the first time analytically found, whose stability characteristics were evaluated by linear stability analysis. A positive temperature coefficient b will raise both the fin's temperature and base heat flow. The corresponding stability for stable fin boiling was enhanced. A negative b results in an opposite trend. The use of a mean thermal conductivity in fin boiling calculations is discussed. Received on 3 November 1997     

Performance evaluation and optimization of semi-dimpled slit fin

In this paper, the semi-dimpled slit fin is proposed and the characteristics of heat transfer and fluid flow are analyzed based on the orthogonal experiment design method. A serial studies on the effects of fin pitch, arrangement of semi-dimple, dimple radius on heat transfer and flow characteristics of semi-dimpled slit fin are investigated. The computational results show fin pitch (Fp) has significantly effected on the performance of heat transfer and fluid flow, the influence of arrangement of semi-dimple, the dimple radius (R) and the opening direction of semi-dimples dwindle. At the same time, compared to the general semi-dimpled slit fin, the heat transfer coefficient and JF factors of the optimized fin increase by 10.7–25.1 and 2.6–7.7 %, respectively. When Re ≤ 1,521, the overall performance of slit fin is better than that of optimized fin; while Re > 1,521, the overall performance of optimized fin is better than that of slit fin. Finally, the performance evaluation plot of enhanced heat transfer of heat exchanger is applied to analyze the optimized fin, it can be seen that optimization fin have better heat transfer performance under the same power consumption.     

Unsteady thermal response of a porous fin under the influence of natural convection and radiation

In this study, the effects of transient thermal performance of a rectangular porous fin in the presence of radiation and natural convection heat transfer are considered. The porous fin allows the flow to infiltrate through it and solid–fluid interaction takes place. This study is performed using Darcy’s model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered, namely, long fin, finite length fin with insulated tip and finite length fin with tip exposed. The effects of the porosity parameter S_h, radiation parameter G and the temperature ratio C_T on the dimensionless transient temperature distribution and heat transfer rate are discussed.     

Periodic heat transfer in the fins with variable thermal parameters

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Analysis of heat transfer in a partially wet radial fin assembly during dehumidification

This paper presents the analysis of heat transfer in a partially wet annular fin assembly during the process of dehumidification. In past studies, both fully dry and fully wet fins have been analyzed. New analytical formulation leading to a closed-form solution has been developed for a partially wet fin, which is most common in dehumidifier coil operation during air conditioning. The parameters that influenced the heat transfer rate in the finned tube structure are ratio of fin and wall thermal conductivities, ratio of fin thickness to fin pitch, ratio of wall thickness to fin pitch, ratio of fin length to fin pitch, cold fluid Biot number, ambient Biot number, the relative humidity and dry bulb temperature of the incoming air, and the cold fluid temperature inside the coil. Calculations were carried out to study the performance of the heat exchanger. The computed results included the temperature distribution in the wall and the fin and the fin efficiency.     

Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.     

Optimum fin spacing of rectangular fins on a vertical base in free convection heat transfer

The steady-state natural convection heat transfer from aluminum vertical rectangular fins extending perpendicularly from vertical rectangular base was investigated experimentally. Thirty different fin configurations were tested. Experiments were performed for fin lengths of 250 and 340 mm. Fin thickness was kept fixed at 3 mm. Fin height and fin spacing were varied from 5 to 25 mm and 5.75 to 85.5 mm, respectively. Five heat inputs ranging from 25 to 125 W were supplied for all fin configurations, hence; the base-to-ambient temperature differences were measured in order to evaluate the heat transfer rates from fin arrays. The results of experiments have shown that the convective heat transfer rate from fin arrays depends on geometric parameters and base-to-ambient temperature difference. The separate roles of fin height, fin spacing and base-to-ambient temperature difference were investigated. It was found that, for a given base-to-ambient temperature difference, the convective heat transfer rate from fin arrays takes on a maximum value as a function of fin spacing and fin height and an optimum fin spacing value which maximizes the convective heat transfer rate from the fin array is available for every fin height. These measurements were to extend data obtained earlier from aluminum fin-arrays using the same experimental system and method (Yüncü and Güvenç in Heat Mass Transfer 37:409–416, 2001). Data collated from earlier and present work cover the range of fin spacing from 4.5 to 85.5 mm. The fin length range was from 100 to 340 mm, the fin height from 5 to 25 mm and the number of fins per array 3 to 34. The range of base-to-ambient temperature difference was quite extensive, from 30 to 150 K. These results indicate that the optimum fin spacing is between 6.1 and 11.9 mm, for the fin arrays employed in the earlier and present work. A scale analysis is performed in order to estimate the order-of-magnitude of optimum fin spacing at a given fin length and base-to-ambient temperature difference. From the scale analysis, correlations to evaluate the optimum fin spacing value and the corresponding maximum convective heat transfer rate at a given fin length and base-to-ambient temperature difference were obtained.     

An engineering procedure for air side performance evaluation of flat tube heat exchangers with louvered fins

An accurate evaluation of possible air side heat transfer surface geometries is a prerequisite for optimal heat exchanger design. Aiming for practical engineering applicability a simplified and transparent analytical procedure for the assessment of louvered fin and flat tube heat exchanger geometries and the calculation of fin parameters that enable maximal performance for given boundary conditions has been developed. The proposed method comprises determining fins temperature profiles and effective heat transfer temperature difference, introduction of a relative heat transfer surface area, as well as the utilization of recent experimentally obtained heat transfer correlations confirmed for the observed range of boundary conditions. The proposed methodology is validated through comparison with experimental and numerical results of other authors.     

An experimental investigation on performance of fins on a horizontal base in free convection heat transfer

 Natural convection heat transfer in rectangular fin-arrays mounted on a vertical base was investigated experimentally. An experimental set-up was constructed and calibrated to test 15 different fin configurations. Fin length and fin thickness were kept fixed at 100 and 3 mm respectively, while fin spacing was varied from 4.5 to 58.75 mm and fin height was varied from 5 to 25 mm. Base-to-ambient temperature difference was also varied through a calibrated wattmeter ranging from 10 to 50 W. The results showed that fin spacing is the most significant parameter in the performance of fin arrays; and for every fin height, for a given base-to-ambient temperature difference, there exists an optimum value for the fin spacing for which the heat transfer rate from the fin array is maximized. It was seen that higher heat transfer enhancement are obtained with vertically oriented bases than with horizontally oriented bases for fin arrays of the same geometry. Received on 16 February 2000     

A fluid–structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness

Research on fish locomotion has made extensive progress towards a better understanding of how fish control their flexible body and fin for propulsion and maneuvering. Although the biologically flexible fish fins are believed to be one of the most important features to achieve optimal swimming performance, due to the limitations of the existing numerical modeling tool, studies on a deformable fin with a non-uniformly distributed stiffness are rare. In this work, we present a fully coupled fluid–structure interaction solver which can cope with the dynamic interplay between flexible aquatic animal and the ambient medium. In this tool, the fluid is resolved by solving Navier–Stokes equations based on the finite volume method with a multi-block grid system. The solid dynamics is solved by a nonlinear finite element method. A sophisticated improved IQN-ILS coupling algorithm is employed to stabilize solution and accelerate convergence. To demonstrate the capability of the developed Fluid–Structure-Interaction solver, we investigated the effect of five different stiffness distributions on the propulsive performance of a caudal peduncle-fin model. It is shown that with a non-uniformly distributed stiffness along the surface of the caudal fin, we are able to replicate similar real fish fin deformation. Consistent with the experimental observations, our numerical results also indicate that the fin with a cupping stiffness profile generates the largest thrust and efficiency whereas a heterocercal flexible fin yields the least propulsion performance but has the best maneuverability.     

Shape optimization for the minimum volume of pin fins in simultaneous heat and mass transfer environments

A methodology for determining the optimum pin fin profile is introduced to minimize the fin volume for a constrained heat transfer rate under dehumidifying surface conditions. In this methodology, the mass transfer is evaluated using the polynomial variation of humidity ratio with temperature. A scheme is developed for solving the optimum conditions derived as a function of unknown temperature-dependent parameter and tip temperature under both the fully and partially wet surface conditions. The effect of psychrometric properties of the surrounding air on the optimum wet fin profile has been examined. The analysis presented in this study is pertinent to the dry, fully wet, and partially wet surface conditions. In every case study of optimum wet fins, the excess temperature at the tip vanishes with respect to the surrounding temperature. A non-linear temperature distribution in the optimum wet fin has been identified.     

Thermal analysis of annular fins with temperature-dependent thermal properties

The thermal analysis of the annular rectangular profile fins with variable thermal properties is investigated by using the homotopy analysis method （HAM）. The thermal conductivity and heat transfer coefficient are assumed to vary with a linear and power-law function of temperature, respectively. The effects of the thermal-geometric fin parameter and the thermal conductivity parameter variations on the temperature distribution and fin efficiency are investigated for different heat transfer modes. Results from the HAM are compared with numerical results of the finite difference method （FDM）. It can be seen that the variation of dimensionless parameters has a significant effect on the temperature distribution and fin efficiency.