Fin Heat Transfer Modeling and Its Impact on Predictions of Efficiency and Condensation in Gas-Fired Boilers

In conventional and high-efficiency boilers it is important to understand where water from the products of combustion may condense onto the heat exchanger surface. The usual fin modeling approach is inadequate because it predicts no circumferential preference for condensation, whereas spatial effects have been observed. Two alternative approaches for modeling fin heat transfer are explored: one method is based on a generalization of observed trends in local convective heat transfer coefficients, and the other on a semiempirically motivated variation in convective flow temperature. Temperature distribution and fin efficiency predictions are compared to the conventional fin modeling approach. The alternative fin heat transfer models described in this study both predict more extensive condensation on the portion of the fin within the wake of the tube. Furthermore, both models predict fin efficiencies below those obtained using an assumption of constant heat transfer coefficient and convective temperature.     

Experimental study of convective heat transfer on a finned rotating cylinder

In this study, the local convective heat transfer from a rotating finned cylinder to the surrounding air was evaluated using an infrared thermographic experimental set up. Solving the inverse conduction heat transfer problem allows the local convective heat transfer coefficient to be identified. We used the specification function method, along with spatio-temporal regularization, to develop a model of local convective heat transfer in order to take lateral conduction and 2D geometry into account. This model was tested using rotational Reynolds numbers (based on the cylinder diameter and the peripheral speed) between 4300 and 17 900. The local heat transfer on the fin surface was analyzed to determine the influence of the rotational Reynolds number and the influence of the height and spacing of the fins. In this paper, we propose an efficiency definition that allows the optimal geometrical configuration of the finned cylinder to be identified for the given operating conditions.     

Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity

A hybrid numerical technique which combines the differential transformation and finite difference method is utilized to investigate the annular fin with temperature-dependent thermal conductivity. The exposed surfaces of the fin dissipate heat to the surroundings by convection and radiation. The influences of the convective heat transfer coefficient, absorptivity, emissivity and thermal conductivity parameter on the temperature distribution are examined. The results show that the convective heat transfer plays a dominant role for heat dissipation under the convection–radiation condition. The optimum radii ratio of fin which maximizes the heat transfer rate and fin efficiency is also discussed.     

Thermal distribution analysis of rectangular fin considering multiboiling heat transfer modes

In this investigation, a numerical method is used to compute the thermal distribution analysis of a rectangular fin with surface emissivity and internal heat generation. Here, the thermal conductivity, heat generation, emissivity at the surface, and coefficient of heat transfer depend on temperature linearly. The role of four distinct multiboiling heat transfer modes such as laminar film boiling (condensation), laminar convection, turbulent convection, and nucleate boiling are discussed in detail and the corresponding outcomes are displayed graphically. Isolated (insulated) and convective tip boundary conditions for the fin tip are employed in this study. The solution is obtained using shooting technique involving Runge Kutta Fehlberg method. It is emphasized that the thermal distribution shows a diminishing trend for the convective tip condition compared to the insulated tip. In addition to this, it is illustrated that laminar film boiling and laminar convection are two effective modes of heat transfer in comparison with turbulent convection and nucleate boiling for a finned surface in boiling liquids. The study on fin efficiency shows that fin efficiency increases with the increase in internal heat generation number.     

Performance analysis and optimization of straight taper fins with variable heat transfer coefficient

In the present paper, the thermal analysis and optimization of straight taper fins has been addressed. With the help of the Frobenius expanding series the temperature profiles of longitudinal fin, spine and annular fin have been determined analytically through a unified approach. Simplifying assumptions like length of arc idealization and insulated fin tip condition have been relaxed and a linear variation of the convective heat transfer coefficient along the fin surface has been taken into account. The thermal performance of all the three types of fin has been studied over a wide range of thermo-geometric parameters. It has been observed that the variable heat transfer coefficient has a strong influence over the fin efficiency. Finally, a generalized methodology has been pointed out for the optimum design of straight taper fins. A graphical representation of optimal fin parameters as a function of heat duty has also been provided.     

Predicting the thermal performance characteristics of staggered vertical pin fin array heat sinks under combined mode radiation and mixed convection with impinging flow

A theoretical and experimental study was carried out investigating the influence of thermal radiation on the thermal performance of a pin fin array heat sink with the purpose of developing accurate predictive capability for such situations, and to determine the particular design parameters and environmental conditions under which thermal radiation might be advantageous to the thermal performance. Several different types of experimental tests were run with the corresponding physical parameter variations including the emissivity of the heat sink, elevated ambient air temperature, the temperature of a visible hot surface, and its radiation configuration factor. A theoretical model, validated by experimental data, which includes the capability of predicting the influence of thermal radiation on the thermal performance of a pin fin array heat sink, was developed by introducing an effective radiation heat transfer coefficient that was added to the convective heat transfer coefficient.     

Optimization of a Thermally Asymmetric Convective and Radiating Annular Fin

In this study, convective and radiating annular fins of rectangular profile under thermally asymmetric conditions are examined using an analytical method. For the fin base condition, it is assumed that heat transfer from the fluid to the inside surface of the pipe is equal to the heat transfer through the fin base. The temperature distribution along the fin height at the fin tip is presented to demonstrate the effects of the thermally asymmetric condition. The heat loss and fin tip radius for fixed fin height are optimized as a function of the fin top convection characteristic number. Also, for fixed fin volume, the heat loss and fin dimensions are optimized based on the top, bottom, and tip convection characteristic numbers, radiation characteristic numbers, fin base radius, and fin volume. The fin effectiveness as a function of the top convection characteristic number and annular fin length are also presented.     

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.     

Local heat transfer measurements of plate finned-tube heat exchangers by infrared thermography

An experimental study is performed using an infrared thermovision to monitor temperature distribution over a plate-fin surface inside the plate finned-tube heat exchangers. The differentiation of the temperature function is derived to determine the local convective heat transfer coefficients on the tested fin, using a local element lumped conduction equation included the convective effect on the boundaries with experimental data. It is disclosed that the infrared thermography is capable of rapidly detecting location and extent of transition and separation regions of the boundary layer over the whole surface of the tested models. Through the comparison of the test results on the strategy region of the in-line and staggered arrangements, it is more easy to understand or interpret the detailed dynamic phenomena of flow existed in the heat exchangers. In addition, the experimental results demonstrate that the averaged heat transfer coefficient of staggered configuration is 14-32% higher than that of in-lined configuration     

Methodology for Estimation of Local Convective Heat Transfer Coefficient for Vapor Condensation

This paper aims to present an effective two-dimensional inverse heat conduction technique and an experimental design for accurately estimating the local convective heat transfer coefficient of vapor condensation over a conical surface, given temperature measurements at some interior locations. The functional form for the heat transfer coefficient is not known a priori. The method uses a sequential procedure together with Beck's function specification approach. Solution accuracy and the effects of experimental errors are examined using simulated temperature data. It is concluded that a good estimation of space-variable heat transfer coefficient can be made from the knowledge of transient temperature recordings using the proposed inverse heat conduction problem method. The method is also used in a series of numerical experiments to provide the optimum experimental design for condensation heat transfer investigation.     

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.     

Natural convective heat transfer in square enclosures heated from below

The paper deals with the results of an experimental and numerical study of free convective heat transfer in a square enclosure characterized by a discrete heater located on the lower wall and cooled from the lateral walls.The study analysed how the heat transfer develops inside the cavity at the increasing of the heat source length.The experimental data are obtained by measuring the temperature distribution in the air layer by real-time and double-exposure holographic interferometry while the commercial finite volumes code Fluent 6.0 is used for the numerical study. Convection has been studied for Rayleigh number from 10³ to 10⁶. Different convective forms are obtained depending on Ra and on the heat source length.The local Nusselt number is evaluated on the heat source surface and it shows a symmetrical form raising near the heat source borders. Graphs of the local Nusselt number on the heat source and of the average Nusselt number at several Ra are finally presented.     

Convective‐radiative fins with simultaneous variation of thermal conductivity,heat transfer coefficient,and surface emissivity with temperature

This paper is a numerical study of thermal performance of a convective‐radiative fin with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. The convective heat transfer is assumed to be a power function of the local temperature between the fin and the ambient which allows simulation of different convection mechanisms such as natural convection (laminar and turbulent), boiling, etc. The thermal conductivity and the surface emissivity are treated as linear functions of the local temperature between the fin and the ambient which provide a satisfactory representation of the thermal property variations of most fin materials. The thermal performance is governed by seven parameters, namely, convection–conduction parameter Nc, radiation–conduction parameter Nr, thermal conductivity parameter A, emissivity parameter B, the exponent n associated with convective heat transfer coefficient, and the two temperature ratios, θ_a and θ_s, that characterize the temperatures of convection and radiation sinks. The effect of these parameters on the temperature distribution and fin heat transfer rate are illustrated and the results interpreted in physical terms. Compared with the constant properties model, the fin heat transfer rate can be underestimated or overestimated considerably depending on the values of the governing parameters. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20408     

Prediction of heat transfer coefficient on the fin inside one-tube plate finned-tube heat exchangers

The finite difference method in conjunction with the least-squares scheme and the experimental temperature data is proposed to predict the average heat transfer coefficient and the fin efficiency on the fin inside one-tube plate finned-tube heat exchangers for various air speeds and the temperature difference between the ambient temperature and the tube temperature. Previous works showed that the heat transfer coefficient on this rectangular fin is very non-uniform. Thus the whole plate fin is divided into several sub-fin regions in order to predict the average heat transfer coefficient and the fin efficiency on the fin from the knowledge of the fin temperature recordings at several selected measurement locations. The results show that the surface heat flux and the heat transfer coefficient on the upstream region of the fin can be markedly higher than those on the downstream region. The fin temperature distributions depart from the ideal isothermal situation and the fin temperature decreases more rapidly away from the circular center, when the frontal air speed increases. The average heat transfer coefficient on the fin increases with the air speed and the temperature difference between the ambient temperature and the tube temperature. This implies that the effect of the temperature difference between the tube temperature and the ambient temperature is not negligent.     

Thermal transport analysis in parallel-plate channel filled with open-celled metallic foams

Forced convective heat transfer in highly porous, open-celled metallic foams sandwiched between two infinite parallel plates is analytically modeled using the Brinkman-Darcy and two-equation models. With uniform heat flux, closed-form solutions for fully developed flow and heat transfer are obtained. Nusselt number with explicit expression is derived and the analytical results are verified by existing experimental data. To examine the effect of axial heat conduction neglected in the analytical modeling, numerical simulations, which are verified by the analytical solution, are performed. A modified fin analysis method with improved predicting accuracy compared with the conventional fin analysis method by introducing equivalent foam temperature is also put forward. The predictions obtained with the analytical model, the numerical simulation and the modified fin analysis method are compared with each other, and their pros and cons are discussed. Finally, a systematic parametric study is conducted on heat transfer in parallel-plate channels filled with metallic foams, with useful suggestions for practical designs obtained.     

A simple design of fins for boiling heat transfer

This study presents the thermal characteristics of a fin with excavation at base when various types of boiling occur simultaneously at adjacent locations on its surface experimentally and analytically. The heat transfer coefficient of each boiling mode is taken as a power function of wall superheat. Continuity of temperature and the heat transfer rate at the intersection of the two different modes on fin surface are employed to obtain the one-dimensional temperature distribution and total heat transfer of the excavated fin. Both heating and cooling cases are investigated in the analysis. Compared with solid pin fins, the proposed fins can extend the operating condition to a higher temperature of the heat transfer surface. In addition, the experimental data compare favorably with the analytical results.     

The Characteristic Temperature in the Definition of Heat Transfer Coefficient on the Fin Side Surface in Tube Bank Fin Heat Exchanger

The characteristic temperature in the definition of the fin side surface heat transfer coefficient of two tube bank fin heat exchangers is investigated in detail. The results reveal that if the average temperature of the fin side fluid is used in the definition of the fin side surface coefficient, a small discrepancy between the numerical and experimental results is obtained. The results not only give a technical definition of the characteristic temperature of the fin side surface heat transfer coefficient, but also imply that the discrepancy between experimental and numerical results may come from incorrect use of the characteristic temperature.     

Numerical analysis of natural convection heat transfer from rectangular shrouded fin arrays on a horizontal surface

The main aim of this investigation is to discover the effects of clearance parameters on the steady-state heat transfer. In order to solve the three-dimensional elliptic governing equations, a finite volume based CFD code was used. The clearance gap between fin tips and shroud, the base and fin temperatures and the size and configuration of the finned surfaces were varied during the parametric study. The numerical results have been compared to existing experimental values from the literature and the comparison shows a good agreement. It is found that the heat transfer coefficient increases with the increase in the clearance parameter and it approaches to the value of heat transfer coefficient obtained for unshrouded fin arrays.     

Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium

The problem of conjugate natural convection about a vertical cylindrical fin with uniform lateral mass flux in a fluid-saturated porous medium has been studied numerically. Solutions based on the third level of truncation are obtained by the local nonsimilarity method. The effects of the surface mass flux, the conjugate convection-conduction parameter, and the surface curvature on fin temperature distribution, local heat transfer coefficient, local heat flux, average heat transfer coefficient, and total heat transfer rate are presented. A comparison with finite-difference solutions for the case of constant wall temperature was made, and found in a good agreement.