Heat Conduction In Fins Research Articles

Discrete effects on the source term for the lattice Boltzmann modelling of one-dimensional reaction–diffusion equations

This work presents a detailed numerical analysis of one-dimensional, time-dependent (linear) reaction–diffusion type equations modelled with the lattice Boltzmann method (LBM), using the two-relaxation-time (TRT) scheme, for the D1Q3 lattice. The interest behind this study is twofold. First, because it applies to the description of many engineering problems, such as the mass transport in membranes, the heat conduction in fins, or the population growth in biological systems. Second, because this study also permits understanding the general effect of solution-dependent sources in LBM, where this problem offers a simple, yet non-trivial, canonical groundwork. Without recurring to perturbative techniques, such as the Chapman-Enskog expansion, we exactly derive the macroscopic numerical scheme that is solved by the LBM-TRT model with a solution-dependent source and show that it obeys a four-level explicit finite difference structure. In the steady-state limit, this scheme reduces to a second-order finite difference approximation of the stationary reaction–diffusion equation that, due to artefacts from the source term discretization, may operate with an effective diffusion coefficient of negative value, although still remaining stable. Such a surprising result is demonstrated through an exact stability analysis that proves the unconditional stability of the LBM-TRT model with a solution-dependent source, in line with the already proven source-less pure diffusion case (Lin et al., 2021). This proof enlarges the confidence over the LBM-TRT model robustness also for the (linear) reaction–diffusion problem class. Finally, a truncation error analysis is performed to disclose the structure of the leading order errors. From this knowledge, two strategies are proposed to improve the scheme accuracy from second- to fourth-order. One exclusively based on the tuning of the LBM-TRT scheme free-parameters, namely the two relaxation rates and the lattice weight coefficient, and the other based on the redefinition of the structure of the relaxation rates, where the leading order truncation error is absorbed into one of the relaxation rates, liberating the other to improve additional features of the scheme. Numerical tests presented in the last part of the work support the ensemble of theoretical findings.

Average Wall Radiative Heat Transfer Characteristic of Isothermal Radiative Medium in Inner Straight Fin Tubes

Abstract Wall radiative heat transfer in inner straight fin tubes is very complex considering the coupling of heat conduction in fins and radiative heat transfer of medium with solid surfaces, influenced by a number of factors such as fin parameters, radiative properties and run conditions. The method of simulation is very inconvenient to design the heat exchanger involving the enhancement of inner straight fins on wall radiative heat transfer in tube, such as ascension pipe heat exchanger and radiant syngas cooler. In this study, a simplified method is used. The average radiative heat transfer between radiative medium and solid surfaces is first studied by simulation with fins supposed have a constant temperature. Then an approximate correlation of this radiative heat transfer coefficient is proposed using the traditional radiative heat transfer calculation method with a view coefficient, which has a little error within 15%. A calculation method of average wall radiative heat transfer coefficient is further derived based on fin theory with an average temperature of fin surface used to consider the varying of the temperature along the fin when the conductivity of fins is finite. Using the predicting method proposed, a method for design calculation of fins in tubes to optimize wall radiative heat transfer is also given with three dimensionless numbers of π/n, 2H/D, and nt/πD representing the structural properties of fins defined. Three cases of (ks = 43 W/(m•K), ɛw = 0.7, Tg = 1073.15 K, Tw = 573.15 K, D = 0.66 m, κD = 1.32), (ks = 162 W/(m•K), ɛw = 0.7, Tg = 1073.15 K, Tw = 573.15 K, D = 0.66 m, κD = 1.32) and (ks = 43 W/(m•K), ɛw = 0.3, Tg = 973.15 K, Tw = 673.15 K, D = 0.66 m, κD = 0.66) are analyzed in detail based on the design calculation method. It is verified that the radiative heat transfer could be enhanced twice by introducing fins. Under the same h0, conductivity and emissivity are two important factors that should be considered to choose the material for fins. The microfins or the special treatments on the tube wall are a best choice for the fin material having a relatively small conductivity.

Numerical simulation of non-Fourier heat conduction in fins by lattice Boltzmann method

The addition of fin to the surface of microelectronic elements is a very effective way to enhance their heat transfer rate. Since the heat generation of the microelectronic elements is very fast, the Fourier law is no longer valid and the non-Fourier effect must be considered when designing a fin. Cattaneo – Vernotte model (CV model) is the most common model that is used to describe the non-Fourier effect in heat conduction. The mathematical expression of the CV model is essentially a wave equation. The lattice Boltzmann method (LBM) can be used to solve the wave equation in the CV heat conduction problem. In this paper, LBM is used to solve the non-Fourier heat conduction in a fin under periodic boundary conditions. Effects of relaxation time, shape and the frequency of the base temperature oscillations on heat transfer efficiency are analyzed.

An appropriate analysis for optimum design of wet fins based on modified 1-D and 2-D approaches

The analysis of thin fins has generally been done by considering one-dimensional (1-D) heat conduction in fins. The condition for 1-D heat conduction for dry surfaces has been reported by many researchers. However, in the case of refrigeration and air conditioning applications, fin surface becomes wet due to the condensation of moisture on the surfaces. For the wet surface, no analysis has so far been conducted with considering two-dimensional (2-D) heat conduction in a fin. The present paper aims to determine analytically the temperature distribution for 2-D heat conduction in wet fins. Modified one-dimensional method is proposed appropriately for the solution of the two-dimensional heat conduction in the fin based on a trapezoidal rule. From the results, it can be highlighted that the modified 1-D model matches closely with the 2-D model. It has also been observed that under any design condition, 1-D classical model does not have capacity to predict the accurate result for thermal performance and local optimization parameters. In any range of Bi, modified 1-D model determines the heat transfer exactly with that by the 2-D model. This investigation also shows that there is no such condition found for the global optimization: the heat transfer rate and the fin efficiency always increase with Bi which may be extremely important aspect in a practical design to be selected Bi in an application. On the other hand, it can be demonstrated that this design condition for optimization has never been studied in the literature of fin heat transfer before.

Investigation Performance of Heat Exchanger on Thermoacoustic Heat Engine for Harvesting a Waste Heat

A green technology of acoustic of fluid-structure interactions become an emerging technology today, a call thermoacoustic heat engine. Thermoacoutics heat engine systems convert the energy on a harvesting from a waste heat energy and convert to an electrical energy. That component of devices a call a hot heat exchangers. This paper study was focused on a new design of thermoacoustics heat exchanger and investigation of its performance in terms of thermal analysis. A conceptual design was produced with three designs of hot heat exchangers, which are wire-type, finger-type and star-type. Commercial code ANSYS-CFX software are used on the evaluation, the heat exchanger’s designs were simulated with two thermal conditions which are steady state and transient heat conduction. Materialselection from copper and aluminium a chosen to look-out the engagement between theoretical and numerical study. There are three inlet temperatures that are assumed will be supplied by constant waste heat which are 200°C, 350°C and 500°C.The star-type design has the highest value of heat conduction through a fin heat conduction with copper as a material which is 32.84W. Star-type hot heat exchanger recorded the fastest time to distribute temperature compared to wiretype and fingertype heat exchanger. Result shown the combination between star-type design and copper material will produce a good agreement to design a hot heat exchanger.

Inverse Hyperbolic Heat Conduction in Fins with Arbitrary Profiles

This study aims to estimate unknown base temperature distribution in different non-Fourier fins. The Cattaneo–Vernotte (CV) heat model is used to predict the heat conduction behavior in these fins. This inverse problem is solved by the function-estimation version of the Adjoint conjugate gradient method (ACGM) based on boundary temperature measurements. The ACGM includes direct, sensitivity, and adjoint problems. For each of these problems, a one-dimensional general formulation of the non-Fourier model for longitudinal fins with arbitrary profile is driven and solved by an implicit finite difference method. In this study, three different profiles are considered: triangular, convex parabolic, and concave parabolic. For each of them, two different base temperature distributions are estimated using an inverse method. Moreover, the effects of sensor positions at the fin tip and a specific place in-between are considered on the base temperature estimation. A close agreement between the exact values and the estimated results is found, confirming the validity and accuracy of the proposed method. The results show that the ACGM is an accurate and stable method to determine the thermal boundary conditions in different non-Fourier fin problems.

Conjugate heat transfer for free convection along a vertical plate fin

In this study, a new and effective improved Semi-Analytic and Semi-Empirical formula f(Pr)= {ie337-1} 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.

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.

Prediction of heat exchanger capacity by thermal network method (Influence of thermal conduction in fins on capacity of a condenser)

AbstractThis paper describes the influence of heat flow from high‐temperature refrigerant to low‐temperature refrigerant through fins by thermal conduction. To estimate that influence, we applied a thermal network method that can consider refrigerant quality distribution in the heat exchanger. At the same time, for verifying the estimation, an experiment was performed with a two‐row, two‐pass heat exchanger. Prediction shows that the heat transfer capacity of a condenser is reduced by 3% for a simple two‐row, two‐pass heat exchanger by heat conduction in fins. Comparison of experimental results and predicted results proves that the prediction error was within 1% for condenser capacity. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(2): 101–114, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20184

3D numerical simulation on fluid flow and heat transfer characteristics in multistage heat exchanger with slit fins

In this paper, a numerical investigation is performed for three-stage heat exchangers with plain plate fins and slit fins respectively, with a three-dimensional laminar conjugated model. The tubes are arranged in a staggered way, and heat conduction in fins is considered. In order to save the computer resource and speed up the numerical simulation, the numerical modeling is carried out stage by stage. In order to avoid the large pressure drop penalty in enhancing heat transfer, a slit fin is presented with the strip arrangement of “front coarse and rear dense” along the flow direction. The numerical simulation shows that, compared to the plain plate fin heat exchanger, the increase in the heat transfer in the slit fin heat exchanger is higher than that of the pressure drop, which proves the excellent performance of this slit fin. The fluid flow and heat transfer performance along the stages is also provided.

Prediction of Capacity of a Heat Exchanger by Thermal Network Method (Influence of Thermal Conduction in Fins on Capacity of a Condenser)

This paper presents an influence of heat flow from high temperature refrigerant to low temperature refrigerant through fins by thermal conduction. For estimating the influence, we applied thermal network method that can consider refrigerant quality distribution in the heat exchanger. At a same time, for verifying the estimation, an experiment was performed with 2 row-2 pass heat exchanger. Prediction shows that heat transfer capacity of a condenser is reduced by 3% for a simple 2 row-2 pass heat exchanger by heat conduction in fins. By comparison between the experimental results and the predicted results, it was proved that predicting error was within 1% for condenser capacity.

Detection of cavities in Helmholtz-type equations using the boundary element method

Helmholtz-type equations arise naturally in many physical applications related to wave propagation, vibration phenomena and heat transfer. These equations are often used to describe the vibration of a structure, the acoustic cavity problem, the radiation wave, the scattering of a wave and heat conduction in fins. In this paper, the numerical recovery of a single and two circular cavities in Helmholtz-type equations from boundary data is investigated. The boundary element method (BEM), in conjunction with a constrained least-squares minimisation, is used to solve this inverse geometric problem. The accuracy and stability of the proposed numerical method with respect to the distance between the cavities and the outer boundary of the solution domain, the location and size of the cavities, and the distance between the cavities are also analysed. Unique and stable numerical solutions are obtained.

Transient multiboiling in a pin fin with temperature dependent thermal conductivity

Transient heat conduction in fins undergoing different kinds of convective processes (film, transition, nucleated boiling and natural convection) as in multiboiling processes take place, is a strongly non-linear problem because of the abrupt changes in the heat transfer coefficient that occur at certain temperatures. Transient equations for the thermal fields and fluxes are solved simultaneously, giving the time constant of the process; the stationary solution is compared with the numerical or experimental values of other authors. Temperature dependencies of the heat transfer coefficient and the thermal conductivity is assumed due to the large interval of temperatures occurring. Network Simulation Method is used for the numerical solution, which gives simultaneously thermal field of temperatures and heat fluxes.

Computer programs for temperature in fins and slab bodies with the method of Green's functions

AbstractHeat conduction in fins and slab bodies, a traditional undergraduate topic, is treated with the Green's function (GF) method. A variety of boundary conditions and heating conditions are included. Computer programs are described which are designed to improve student learning of the GF method. The programs are available from the author. © 2004 Wiley Periodicals, Inc. Comput Appl Eng Educ 12: 189–197, 2004; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20010

Effect on noncondensable gas on laminar film condensation along a vertical plate fin

Abstract Laminar film condensation along a vertical plate fin in the presence of a noncondensable gas is numerically investigated. In the present analysis, the gas mass fraction and temperature at the liquid–vapor interface is regarded as the spatial variation along the fin surface. Governing boundary layer equations together with their corresponding boundary conditions for the condensation system and the one-dimensional fin heat conduction equation with its negligible tip leakage are cast into dimensionless forms. The resulting system of equations is solved by using the central finite-difference approximation for the fin and local nonsimilarity method for boundary layer equations. Results show that the fin efficiency decreases with increasing the thermal resistance ratio of fin-to-liquid Nc, and relatively small amounts of the noncondensable gas in the bulk of the vapor have a significant effect on the fin efficiency for small values of Nc. In addition, the interface temperature is not equal to the fin temperature along the vertical fin, and the local heat transfer coefficient is not uniform, either.

Heat Transfer and Flow Characteristics of Offset Fins in Low-Reynolds-Number Region. Effect of Thermal Conductivity of Fins.

The effects of thermal conductivity of fins on the heat-transfer characteristics of offset fins in low-Reynolds-number region are studied. Three-dimensional forced convection flow is solved numerically considering heat conduction in fins, and the results are compared with experimental results. It was found that : (1) heat-transfer coefficient on SUS fins in water is less than that on aluminum fins. This is caused by the fact that the thermal boundary layer which developed on the bottom surface relaxes the temperature gradient in the fluid perpendicular to the fin surface, as well as by the fact that the heat conduction characteristics of SUS fins is poor. (2) Analytical results of pressure drop and heat-transfer coefficients agree very well with those obtained by experiment, which shows the validity of the present analyses.