Heat transfer from extended surfaces subject to variable heat transfer coefficient

The present article investigates the effect of locally variable heat transfer coefficient on the performance of extended surfaces (fins) subject to natural convection. Fins of different profiles have been investigated. The fin profiles presently considered are namely; straight and pin fin with rectangular (constant diameter), convex parabolic, triangular (conical) and concave parabolic profiles and radial fins with constant profile with different radius ratios. The local heat transfer coefficient was considered as function of the local temperature and has been obtained using the available correlations of natural convection for each pertinent extended surface considered. The performance of the fin has been expressed in terms of the fin efficiency. Comparisons between the present results for all fins considered and the results obtained for the corresponding fins subject to constant heat transfer coefficient along the fin are presented. Comparisons, i.e. showed an excellent agreement with the experimental results available in the literature. Results show that there is a considerable deviation between the fin efficiency calculated based on constant heat transfer coefficient and that calculated based on variable heat transfer coefficient and this deviation increases with the dimensionless parameter m.     

Effects of stretching/shrinking on the thermal performance of a fully wetted convective-radiative longitudinal fin of exponential profile

The present investigation focuses on the thermal performance of a fully wet stretching/shrinking longitudinal fin of exponential profile coated with a mechanism like a conveyer belt. The modeled equation is non-dimensionalized and solved by applying the Runge-Kutta-Fehlberg(RKF) method. The effects of parameters such as the wet parameter, the fin shape parameter, and the stretching/shrinking parameter on the heat transfer and thermal characteristics of the fin are graphically analyzed and discus...     

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.     

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     

Periodic heat transfer in the fins with variable thermal parameters

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Effect of variable ambient temperature on fin efficiency in a two-dimensional flow passage

The fin efficiency in a heat exchanger element that is a simplification of one row in a tube-and-fin heat exchanger was theoretically examined within wide ranges of the affecting variables: the conventional fin efficiency and the isothermal effectiveness of the heat exchanger. These variables are suggested for use also in the further studies. An analytical solution can be found for the case of a constant heat transfer coefficient. The ambient temperature variation alone decreases the fin efficiency less than 4%. The local heat transfer coefficient obtained from the numerical fluid flow simulations is strongly affected by the fin properties because the thermal boundary conditions for the fluid flow changes. On a poorly conducting fin surface the heat transfer coefficient in front of the fin base is much larger than on an isothermal fin because the heat flux is increasing in the flow direction. At low fin efficiencies this compensates for the decrease in fin efficiency due to ambient temperature variation.     

Double-diffusive natural convection in inclined finned triangular porous enclosures in the presence of heat generation/absorption effects

The problem of double-diffusive convection in inclined finned triangular porous enclosures for various thermal and concentration boundary conditions and in the presence of heat source or sink was studied. The finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of the governing parameters, namely the dimensionless time parameter, the inclination angle, Darcy number, heat generation/absorption parameter, the buoyancy parameter and the Rayleigh number on the streamlines, temperature and concentration contours as well as selected velocity component in the x-direction, local and average Nusselt numbers and local and average Sherwood number at the heated and concentrated wall for various values of the aspect ratio and the position of the fin were considered. The present results are validated by favorable comparisons with previously published results. All the results of the problem were presented in graphical and tabular forms and discussed.     

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.     

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     

Natural convection heat transfer from a thin rectangular fin with a line source at the base — a finite difference solution

This paper presents an analysis of the problem of a thin fin of finite thermal conductivity, with an isothermal line source at the base, dissipating heat to the surrounding air by natural convection. The horizontal surface to which the fin is attached is adiabatic so that heat is dissipated only through the fin. The temperature and velocity distributions in the field, the temperature profile in the fin, local Nusselt numbers along the fin and the average heat transfer coefficient of the fin are obtained by solving the governing equations in the field and the heat transfer equation in the fin simultaneously, using an explicit unsteady Finite Difference formulation leading to the steady state result. Numerical experiments are performed to study the influence of parameters namely the fin height, temperature of the heating source and the fin material on the average heat transfer coefficient. Comparison is made with fins of infinite thermal conductivity and the vertical isothermal flat plate.     

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     

Quantitative infrared investigation of local heat transfer in a circular finned tube heat exchanger assembly

This work deals with the local heat transfer coefficient evaluation over the fin of the second row of a staggered circular finned tube heat exchanger assembly. The coefficient distribution is determined by using a transient technique and by calculating the energy balance during the fin cooling. The calculation model takes into account radiation with the surrounding and lateral heat conduction into the material. The method uses infrared measurements and integration between time bounds that depend on space. It is proposed to choose the integration bounds with an original criterion based on local heat transfer. Validation is performed on the reference case consisting in a thin plate in an aerodynamically and thermally developing channel flow. Then, distributions of Nusselt number on the circular fin are presented for several Reynolds numbers. The high resolution of the whole method and set-up allow detecting thermal imprints of developing horseshoe vortices. These imprints are analyzed by following their angular evolution around the tube.     

Determining local values of the heat transfer coefficient on a fin surface

The paper discusses methods of establishing the course of a boiling curve that base on measurements of temperature distribution on a fin surface. Two cases of a local correlation between the heat transfer coefficient and the wall superheat are considered. The first is the case of a smooth copper fin for which the boiling curve is defined using the power-law formula. It is essential to determine, however, how sensitive this method is to measurement errors. In the other case, the local values of the heat transfer coefficient are approximated by means of a power-law polynomial. The method efficiency is studied using the example of a fin surface modified with a laser beam.     

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.     

Performance analysis and optimization of radiating fins with a step change in thickness and variable thermal conductivity by homotopy perturbation method

Although tapered fins transfer more rate of heat per unit volume, they are not found in every practical application because of the difficulty in manufacturing and fabrications. Therefore, there is a scope to modify the geometry of a constant thickness fin in view of the less difficulty in manufacturing and fabrication as well as betterment of heat transfer rate per unit volume of the fin material. For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the homotopy perturbation method has been used to evaluate the temperature distribution within the straight radiating fins with a step change in thickness and variable thermal conductivity. The temperature profile has an abrupt change in the temperature gradient where the step change in thickness occurs and thermal conductivity parameter describing the variation of thermal conductivity has an important role on the temperature profile and the heat transfer rate. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found. The derived condition of optimality gives an open choice to the designer.     

Measurements of steady-state heat dissipation from miniaturized horizontally-based straight rectangular fin arrays

Experiments have been conducted to investigate the effects of miniaturizing the base plate dimensions of horizontally-based straight rectangular fin arrays on the steady state heat dissipation performance. The variation of the steady-state heat dissipation rates per unit base area and the average heat dissipation coefficients within a limited fin base excess temperature above the ambient temperature (from 20 to 50 °C) have been studied as integral aluminum alloy fin arrays were miniaturized by changing the ratio of the base width to length from 0.51 to 1.96 for two inter-fin spacing distances of 3 mm and 11 mm. The miniaturization process have been initiated from a square-based array of 49 × 49 mm (maximum base area of 24.51 × 10^–4m²) and terminated at a square-based array of 25 × 25 mm (minimum base area of 6.25 × 10^–4m²) with rectangular-based arrays of varying intermediate areas in between. Relevant non-dimensional parameters formulated by earlier similarity analyses for large fin arrays with comparable inter-fin-spacing distances and fin heights have been found inadequate for generalizing the results. Modifications to correlations proposed for large fin arrays have been made by including the effect of varying the value of the base width to length ratio parameter to correlate the data for miniaturized fin arrays. Two types of correlations for miniaturized horizontally-based straight rectangular fin arrays, one which used the inter-fin separation distance as the prime geometric parameter, and the other, which employed half the fin length, have been presented, on the basis of the experimental conditions of this investigation.An erratum to this article can be found at     

Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity

Correlation equations for optimum design of annular fins with temperature-dependent thermal conductivity are obtained in the present work. The nonlinear fin equation which is associated with variable thermal conductivity condition is solved by Adomian decomposition method that provides an analytical solution in the form of an infinite power series. 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 for a given thermal conductivity parameter describing the variation of the thermal conductivity. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rate. 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 with temperature-dependent thermal conductivity.     

A study on the correlation between the thermal contact conductance and effective factors in fin–tube heat exchangers with 9.52 mm tube

The thermal contact resistance is a principal parameter interfering with heat transfer in a fin–tube heat exchanger. However, the thermal contact resistance in the interface between tubes and fins has not been clearly investigated. The objective of the present study is to examine the thermal contact conductance for various fin–tube heat exchangers with tube diameter of 9.52 mm and to find a correlation between the thermal contact conductance and effective factors such as expansion ratio, fin type, fin spacing and hydrophilic coating. In this study, experiments have been conducted only to measure heat transfer rate between hot and cold water. To minimize heat loss to the ambient air by the natural convection fin–tube heat exchangers have been placed in an insulated vacuum chamber. Also, a numerical scheme has been employed to calculate the thermal contact conductance with the experimental data. As a result, a new correlation including the influences of expansion ratio, slit of fin and fin coating has been introduced, and the portion of each thermal resistance has been estimated in the fin–tube heat exchangers with 9.52 mm tube.     

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.     

Comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface

This paper presents the comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface in duct. Experiments were performed to investigate the effect of duct height on heat transfer enhancement of a surface affixed with arrays (7 × 7) of short rectangular plate fins of a co-angular and a co-rotating type pattern in the duct. An infrared imaging system with the camera of TVS 8000 was used to measure the temperature distributions to calculate the local heat transfer coefficients of the representative fin regions. Pressure drop and heat transfer experiments were performed for both types of fin pattern varying the duct to fin height ratio (H _d/H _f) of 2.0–5.0. The friction factor calculated from the pressure drop shows that friction factor decreases with increasing the duct to fin height ratio (H _d/H _f) regardless of fin pattern and this is expected because the larger friction occurs for smaller duct to fin height ratios. Detailed heat transfer distribution gives a clear picture of heat transfer characteristics of the overall surface as well as the influence of the duct height. In addition, different flow behavior and flow structure developed by both patterns were visualized by the smoke flow visualization technique.