Conjugate mixed convection-conduction heat transfer along a vertical cylindrical fin in non-newtonian fluids

By considering the interaction between conduction within the fin and convection to the fluid surrounding the fin, an analysis is presented to study the heat transfer characteristics of laminar mixed convection of a non-Newtonian fluid flow over a vertical cylindrical fin. Due to the compatibility conditions of heat flux and temperature at the surface of fin, the boundary layer equations of the fluid are coupled with the heat conduction equation of the fin and should be solved simultaneously. Of interest are the effects of transverse curvature parameter, bouyancy parameter, power-law viscosity index, generalized Prandtl number and conjugate convection-conduction parameter on the local heat transfer coefficient, local heat flux and temperature distribution of the fin. Comparison of the calculated results with available data sets in the open literature for a Newtonian fluid shows a very good performance of the present numerical procedure.     

Conjugate forced convection-conduction plate fin in power law fluids

The heat transfer characteristics of laminar, forced convection flow for power law fluids from a vertical plate fin are studied analytically based on the conjugate convection and conduction theory. The resulting boundary layer equations of fluids are coupled with the one-dimensional heat conduction equation of fin through interfacial conditions. Numerical results for the local heat flux, local heat transfer coefficient, and temperature distribution along the fin surface and overall heat transfer rate under the effects of the conjugate convection-conduction parameter, generalized Prandtl number and fluid flow index are illustrated. The results obtained of the non-Newtonian power law fluid are found to have trends similar to those of the Newtonian fluids.     

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.     

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.     

Performance of a Circular Fin in a Cylindrical Porous Enclosure

The problem of natural convection heat transfer from a vertical cylindrical fin to a saturated porous medium in a cylindrical enclosure is solved numerically. A conjugate conduction-convection analysis is accomplished by solving the equation of heat conduction in the fin together with the mass, momentum and energy balance equations in the porous medium. Numerical results are obtained by using ADI method. The effects of the conduction-convection ratio parameter, aspect ratio and Darcy number on local heat transfer coefficients and fin efficiency are discussed. Comparison of the local heat transfer coefficients and fin efficiency is shown with those for non-porous medium.     

Experimental study of the effects of structured surface geometry on water spray cooling performance in non-boiling regime

Experiments were conducted to study the effects of enhanced surfaces on heat transfer performance during water spray cooling in non-boiling regime. The surface enhancement is straight fin. The structures were machined on the top surface of heated copper blocks with a cross-sectional area of 10 mm×10 mm. The spray was performed using Unijet full cone nozzles with a volumetric flux of 0.044–0.053 m³/(m²·s) and a nozzle height of 17 mm. It is found that the heat transfer is obviously enhanced for straight fin surfaces relative to the flat surface. However, the increment decreases as the fin height increases. For flat surface and enhanced surfaces with a fin height of 0.1 mm and 0.2 mm, as the coolant flux increases, the heat flux increases as well. However, for finned surface with a height of 0.4 mm, the heat flux is not sensitive to the coolant volumetric flux. Changed film thickness and the form of water/surface interaction due to an enhanced surface structure (different fin height) are the main reasons for changing of the local heat transfer coefficient.     

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.     

Conjugate Heat Transfer for Free Convection along a Vertical Plate Fin

<正>In this study,a new and effective improved Semi-Analytic and Semi-Empirical formula f(Pr)= (0.749999437Pr~(1/2))/((0.609+1.221Pr~(1/2)+1.238Pr)~(1/4))has been proposed to solve a conjugate problem with free convection in the incompressible laminar boundary layer flow and heat conduction in a solid wall for the flow passing a flat plate fin. A combination of flat-plate flow and flat-plate fin heat conduction has been considered in the present study.Finite -difference solutions for the interface temperature profiles and the heat transfer rates have been presented over the entire thermo-fluid-dynamic field for Prandtl numbers from 0.001 to 10000.First,the similar flow field has been solved by the Runge-Kutta method and the shooting methods,then the correlation equation of the local heat transfer coefficient have been obtained.Finally,the empirical formula has been substituted into the fin temperature heat conduction calculation processes to obtain the iterative solutions of the conjugate problems.     

Conjugate heat transfer of mixed convection for viscoelastic fluid past a horizontal flat-plate fin

A conjugate mixed convection heat transfer problem of a second-grade viscoelastic fluid past a horizontal flat-plate fin has been studied. Governing equations include heat conduction equation of the fin, and continuity equation, momentum equation and energy equation of the fluid, have been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite difference method. Solutions of a stagnation flow (β = 1.0) at the fin tip and a flat-plate flow (β = 0) on the fin surface were obtained by a generalized Falkner–Skan flow derivation. These solutions have been used to iterate with the heat conduction equation of the fin to obtain distributions of the local convective heat transfer coefficient and the fin temperature. Ranges of dimensionless parameters, the Prandtl number (Pr), the elastic number (E), the free convection parameter (G) and the conduction–convection coefficient (N_cc) are from 0.1 to 100, 0.001 to 0.01, 0 to 1.5 and 0.05 to 2.0, respectively. The elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a horizontal flat-plate fin. In addition, same as results from Newtonian fluid flow and conduction analysis of a horizontal flat-plate fin, a better heat transfer has been obtained with a larger N_cc, G and Pr.     

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

The transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21012     

Conjugate heat transfer measurements with single-phase and water flow boiling in a single-side heated monoblock flow channel

Optimized and robust designs of one-side heated plasma-facing components and other heat flux removal components are dependent on conjugate heat transfer. In the present case, the conjugate heat transfer involved measuring the local distributions of the inside wall temperature and heat flux in a single-side heated monoblock flow channel with: (1) peripheral (radial and circumferential) heat transfer; and, (2) coupled internal turbulent, forced convective single-phase flow and flow boiling. For the first time, multi-dimensional boiling curves have been measured for a single-side heated monoblock flow channel. Using a thermal hydraulic diameter as the characteristic dimension in select correlations for the highest mass velocity (3.2 Mg/m² s), good agreement was obtained. At lower mass velocities, only the single-phase correlations agreed better with the data for the averaged net incident heat flux vs the inside channel wall temperature. Hence, additional correlation development and adaptation are needed for single-side heated monoblocks with peripheral heat transfer.     

Longitudinal heat conduction study of a uniform power density apparatus for the experimental determination of the heat transfer coefficient

A combined experimental and numerical analysis was performed to accurately evaluate the effect of longitudinal heat conduction along an aluminium test section on the local heat transfer coefficient (HTC) experimental determination. The test section contains a rectangular channel with fins typical of compact heat exchangers. The hydraulic diameter of the channel is around 2 mm. The fluid stream is heated by flat electrical resistances clamped to the outer walls of the test section. The test section contains four zones with different fin pads each, in order to be able to generate data for several geometries at the same time at exactly the same mass flow rate.It was found that longitudinal conduction can lead to a quite uneven distribution of the heat flux to the fluid at the beginning and end of each zone of the test section. Three phenomena were found to be the cause for the observed uneven heat distribution, i.e. the longitudinal gradient of temperature along the wall induced by the fluid temperature rise, the presence of heated and non-heated zones, and the stepwise non-uniformity of the HTC along the test section induced where the fin pad changes.The study has shown that the elementary data reduction methodology, assuming that the surface power density generated by the electrical resistance and the heat flux density reaching the fluid are equal and uniform along the channel, is too far from the reality at the beginning and end of each zone of the test section, especially at low mass flow rates.     

The condition requiring conjugate numerical method in study of heat transfer characteristics of tube bank fin heat exchanger

The overall heat transfer performance of a tube bank fin heat exchanger is very important for engineering applications. Developing a fin pattern with good heat transfer performance for tube bank fin heat exchanger needs more our intensive effort. There are two methods to obtain the heat transfer performances of a fin pattern, i.e., one is experimental method, and the other is numerical method. If numerical method is used, the thermal boundary condition on the fin surfaces is necessary. Generally, there are two ways to treat the thermal boundary, i.e., one is to treat fin surface with uniform temperature, and the other is to use a conjugate numerical method. The former is very easy to be applied in numerical method, but the latter needs more numerical effort. This paper reports the condition under which whether a conjugate numerical method or a numerical method just specifying uniform temperature thermal boundary condition should be used. It is found that such condition is the fin efficiency. When the fin efficiency is less than 0.8, a conjugate numerical method must be used. Otherwise, the numerical results obtained by applying an uniform temperature thermal boundary condition on the fin surfaces has only slightly differences with the results obtained by a conjugate numerical method. The reported results will provide a criterion for the researchers to choose a suitable numerical method in finding a fin pattern more efficiently and reliably.     

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.     

An experimental and theoretical investigation into the heat transfer of a finned water wall tube in a circulating fluidized bed boiler

Heat transfer improvement in a water wall tube with fins was investigated in a circulating fluidized bed (CFB) boiler. Experiments were first conducted in a 6 MWth CFB boiler then a model was developed to analyse and interpolate the results. Temperatures at some discrete points within the wall cross‐section of the tube were measured by burying 0.8 mm thermocouples within a tube. Experimental data showed an increase in heat absorption up to 45 per cent. A good agreement between measured and predicted values was noted. The distribution of temperature in the metal wall and of heat flux around the outer wall of a tube with longitudinal and lateral fins was analysed by numerical solution of a two‐dimensional heat conduction equation. Effects of bed‐to‐wall heat transfer coefficient, water‐to‐tube inside heat transfer coefficient, bed temperature, water temperature and thermal conductivity of the tube material on the heat flux around the water tube are discussed. The present work also examines the influence of the length of the longitudinal fin and the water tube thickness. Heat flux was highest at the tip of the longitudinal fin. It dropped, but increased again near the root of the lateral fin. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical investigation on conjugate heat transfer to supercritical CO2 in membrane helical coiled tube heat exchangers

ABSTRACT

Conjugate heat transfer to supercritical CO₂ in membrane helical coiled tube heat exchangers has been numerically investigated in the present study. The purpose is to provide detailed information on the conjugate heat transfer behavior for a better understanding of the abnormal heat transfer mechanism of supercritical fluid. It could be concluded that the supercritical fluid mass flux and vertical/horizontal placement would significantly affect the abnormal heat transfer phenomenon in the tube side. The flow field of supercritical fluid is affected by both the buoyancy and centrifugal force in the conjugate heat transfer process. The local wall temperature and heat transfer coefficient in the tube side would rise and fall periodically for the horizontal heat exchanger, but this phenomenon will gradually disappear with the increase of the mass flow rate or fluid temperature in the tube side. The dual effects of buoyancy force and centrifugal force lead to the deflection of the second flow direction for the vertical placement, which further results in the heat transfer deterioration region on the top-generatrix wall for the downward flow being larger than that for the upward flow.     

基于有限元方法的溴化锂降膜吸收传热传质的数值研究

吸收器是吸收式制冷系统的重要部件.溴化锂溶液的降膜吸收是吸收器中最常见的传质传热形式之一.通过对溴化锂溶液在降膜吸收过程中传质和传热特性的分析,使用基于有限元法的COMSOL Multiphysics软件,建立了溴化锂溶液和水蒸汽降膜吸收的物理数学模型,计算了液膜内部温度和质量分数的分布、界面处传质通量、界面处传热通量...     

循环流化床锅炉膜式水冷壁管与鳍片上的温度分布

研究了循环流化床锅炉膜式水冷壁管的传热，并通过采用二维传热分析方法，讨论了带有竖直鳍片和横向鳍片的水冷壁管上温度与热流分布。探讨了炉膛侧传热系数、水冷壁管水侧传热系数、水温、床温、水冷壁管材的导热率以及竖直鳍片部最高，然后逐渐下降，但在横向鳍处理的根部又会上升。为了验证传热分析的真实性，在1台6MWth循环流化床锅炉膜式水冷壁管的横裁面内安置了0.8mm的热电偶，测量子水管横截面上的一些点的温度。实际测量值符合得相当好。     

Frost behavior on a fin considering the heat conduction of heat exchanger fins

A mathematical model is proposed for predicting frost behavior on a heat exchanger fin under frosting conditions, taking into account fin heat conduction. The change in the three-dimensional airside airflow caused by frost growth is reflected in this model. The numerical estimates of frost thickness are consistent with experimental data, with an error of less than 10%. Due to fin heat conduction, frost thickness decreases exponentially toward the fin tip, while considerable frost growth occurs near the fin base. When a constant fin surface temperature is assumed, the predicted frost thickness was larger by more than 200% at maximum, and the heat flux by more than 10% on average, compared to results obtained with fin heat conduction taken into account. Therefore, fin heat conduction could be an essential factor in accurately predicting frost behavior. To improve prediction accuracy under the assumption of constant fin surface temperature, the equivalent temperature (for predicting frost behavior) is defined to be the temperature at which the heat transfer rate neglecting fin heat conduction is the same as the heat transfer rate with fin heat conduction taken into consideration. Finally, a correlation for predicting the equivalent temperature is suggested.     

An experimental study in determining the local heat transfer coefficients for the plate finned-tube heat exchangers

A three-dimensional inverse problem in determining the local heat transfer coefficients for the plate finned-tube heat exchangers utilizing the steepest descent method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in the present study based on the measured temperature distributions on fin surface by infrared thermography.Two different tube arrangements (i.e. in-line and staggered) with different fin pitch and air velocity are considered and the corresponding local heat transfer coefficients are to be determined. Results show that some interesting phenomena of the local heat transfer coefficients for the finned surface are found in the work and the averaged heat transfer coefficient of the staggered configuration is about 8–13% higher than that of the in-line configuration.