Thermal analysis of natural convection and radiation in porous fins

In this study, the effects of radiation and convection heat transfer in porous media are considered. The geometry considered is that of a rectangular profile fin. 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 viz. long fin, finite length fin with insulated tip and finite length fin with tip exposed. The theory section addresses the derived governing equation. The effects of the porosity parameter S_h, radiation parameter G and temperature ratio C_T on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation.     

Constructal design of longitudinally finned tubes cooled by forced convection

The constructal design method is used in the present study to find the configuration of longitudinally finned tubes cooled by forced convection. The finned tubes are arranged in parallel inside a fixed two‐dimensional domain. Two degrees of freedom inside the domain are considered for the design. The first degree of freedom is the tube‐to‐tube spacing, and the second is the length of the longitudinal fin. For both these degrees of freedom, a three‐fin position inside the domain is considered. The fin is placed in the front, back, and front and back of the tube in the first, second, and third positions, respectively. Maximization of the heat flow density (heat transfer/volume) from the finned tubes to the cold cross flow is the objective function of the present study. For the three fin positions, the constant pressure difference between the upstream and the downstream drives the cross flow. The dimensionless continuity, momentum, and energy equations for two dimensional, steady, and incompressible flows are solved by discretizing it according to the finite volume method. The thermal condition of the fins and the tubes is constant surface temperature. The dimensionless pressure drop known as Bejan number is varied in the range of 10³ ≤ Be ≤ 10⁵. The fin length is changed from L_f = 0 (unfinned tube) to L_f = 0.2, 0.4, and 0.4. The tubes are cooled by air (Prandtl number = 0.71). The results illustrated that for the considered Bejan numbers and fin positions, the spacing between the unfinned and the finned tubes can be adjusted to optimal spacing such that the heat flow from the tubes to the coolant is maximum.     

Book Review Corner

The optimum dimensions of rectangular longitudinal radiating fins with radiant interaction between the fin and its base are determined. The basic assumptions are one-dimensional heat conduction and ideal black-surface radiation. The governing differential equation is formulated by means of dimensionless variables and is solved using a variable-step Runge-Kutta [1, 2] algorithm, with local extrapolation [3], in order to carry out the required minimization procedure. The optimum thickness, height, and percent contribution of the fin heat dissipation are presented in dimensionless form in several diagrams that give insight into the operational characteristics of the heat rejection mechanism. It has been found that the results are strongly affected by the surface Biot number B_r = hrR/k. Several examples that highlight design criteria with regard to the selection of the material, amount of heat rejected, and tube and fin base temperature are given. A comparison of our results with those existing in the literature shows some significant differences that are discussed.     

Heat transfer enhancement of finned-tube heat exchanger using nozzle- and diffuser-shaped fins instead of straight fins

In this paper, a new method has been used to improve the heat transfer rate in the finned-tube heat exchanger with nozzle- and diffuser-shaped arrangement. For this study, the effect of several parameters was studied numerically. For the computational fluid dynamics simulation, the continuity, momentum, and energy equations were solved by the finite volume method using the standard k–ԑ model. The rate of heat transfer increases with the decreasing of fin bend radius (15 < R_fb < 20) for both nozzle-shaped fin and diffuser-shaped fin. By increasing of side temperature (600 < T_side < 900) and side Reynolds number (2000 < Re_side < 5000) the heat transfer rate increased for both nozzle- and diffuser-shaped fins. Results showed that a nozzle-shaped fin with a fin bend radius of 15 mm under the condition of Re_in = 20,000, T_side = 900 K, and Re_side = 3400 has a higher effect on heat transfer in comparison with the other types of fins. The maximum heat transfer rate was almost 39% and 35% for the nozzle-shaped fin with a bend radius of 15 mm and diffuser-shaped fin with a bend radius of 15 mm compared with the simple tube, respectively. Finally, correlational equations have been suggested to forecast the average Nu number as functions of various parameters of the tube equipped with different types of outer fins involving nozzle- and diffuser-shaped.     

Experimental and numerical investigation of thermal -hydraulic performance in wavy fin-and-flat tube heat exchangers

To the more deeply understand the enhancement heat transfer mechanism and optimization design for wavy fin-and-flat tube heat exchangers, three-dimensional numerical simulations and experimental investigation of air flow and heat transfer characteristics over the wavy fin heat exchangers are presented in this study. The numerical simulation results compared with the wind tunnel test data, the results show that the numerical simulation results are in good with the test. The experimental results show that, in the range of Re = 1000–5500, the standard k-ε mode (SST) is more suitable to predict the air flow and heat transfer of wavy fin. The waviness amplitude has the distinct effect on the heat transfer and pressure drop of wavy fin, while the wavy fin profile (Triangular, Sinusoidal and Triangular round corner) has little effect on the heat transfer performance. In additional, the enhancement heat transfer mechanism of wavy fin is explained in view of field synergy principle. Reduction the synergy angle between velocity and temperature gradient will induce to the heat transfer coefficients increase of wavy fin.     

Analytical solutions of the 1-D heat conduction problem for a single fin with temperature dependent heat transfer coefficient - II. Recurrent direct solution

The recurrent direct solution of the 1-D heat conduction problem for a single straight fin and spine with power-law-type temperature dependent heat transfer coefficient has been derived using inversion of the closed-form solution obtained in the first part of the study. The expression with improving convergence to calculate accurately the dimensionless temperature excess T_e at the fin tip for a given values of the fin parameter N and exponent n in heat transfer equation has been obtained by a linearization method. Equation for the temperature excess distribution throughout the fin has also been derived. The obtained formula for T_e allows to calculate the fin base thermal conductance and augmentation factor. Obtained expressions are seen to be simple and convenient for the engineering design of the fins and finned surfaces.     

Model of a total momentum filtered energy selective electron heat pump affected by heat leakage and its performance characteristics

A total momentum filtered energy selective electron (ESE) heat pump model with heat leakage is established in this paper. The analytical expressions of heating load and coefficient of performance (COP) for both the total momentum filtered (k_r-filtered) ESE heat pump and the conventionally filtered (k_x-filtered) ESE heat pump in which the electrons are transmitted according to the momentum in the direction of transport only are derived, respectively. The optimal performance of the k_r-filtered ESE heat pump is analyzed by using the theory of finite time thermodynamics (FTT). The optimal regions of COP and heating load for the k_r-filtered heat pump are obtained. By comparing the performance of the k_r-filtered device with that of the k_x-filtered device, it is found that the heating load performance and the COP versus heating load characteristic curves of the k_r-filtered heat pump are totally different from those of the k_x-filtered device; and the maximum COP and maximum heating load of the k_r-filtered device are generally higher than those of the k_x-filtered device. The influences of heat leakage, resonance width, hot reservoir temperature and chemical potential on the performance of the total momentum filtered ESE heat pump are further analyzed by numerical calculations. The obtained results can provide some theoretical guidelines for the design of practical electron systems such as solid-state thermionic heat pump devices.     

Heat transfer of nanofluids in the mini-rectangular fin heat sinks

In the present study, the heat transfer characteristics of nanofluids cooling in the mini-rectangular fin heat sink are studied. The heat sinks with three different channel heights are fabricated from the aluminum by the wire electrical discharge machine with the length, width and base thickness of 110, 60, and 2 mm, respectively. The nanofluids are the mixture of de-ionized water and nanoscale TiO₂ particles. The results obtained from the nanofluids cooling in mini-rectangular fin heat sink are compared with those from the de-ionized water cooling method. Effects of the inlet temperature of nanofluids, nanofluid Reynolds number, and heat flux on the heat transfer characteristics of mini-rectangular fin heat sink are considered. It is found that average heat transfer rates for nanofluids as coolant are higher than those for the de-ionized water as coolant. The results of this study are of technological importance for the efficient design of cooling systems of electronic devices to enhance cooling performance.     

Numerical estimation of pressure drop and heat transfer characteristics in annular‐finned channel heat exchangers with different channel configurations

In this numerical investigation, three‐dimensional analysis has been used to study the effect of finned channels configuration of (circular, square, and triangular shape) and fin spacing with four rows in staggered arrangements. The finite volume method with k‐ ω turbulent model is applied to estimate the heat transfer and flow characteristics. The results illustrate that the development of the boundary layer between the fins surfaces is credited to the finned channels configuration, fin spacing, and Reynolds number. Moreover, the results of pressure drop and heat transfer with various channel configuration and different fin spacings (1.6, 2, and 4 mm) are presented and validated with the available correlations. The triangular‐finned channel with 1.6 mm fin spacing offered higher heat transfer enhancement followed by square‐ and circular‐finned channels. A considerable agreement was observed when the current findings and the existing correlations were compared, with a maximum deviation of 15% for all the cases.     

Conjugate mixed convection heat transfer from a vertical rectangular fin

A numerical investigation of the heat transfer from a rectangular fin by combined forced and natural convection is presented. Results are given for buoyancy parameters in the range of $\text{0 ?}\text{Gr/Re}{}^2\text{? 2}$ and convection - conduction parameters in the range of $\text{0 ? √}\text{Re k}{}_{\mathrm{f}}\text{L/k}{}_{\mathrm{s}}\text{b}\text{? 10}$. The results are compared with the conventional fin theory and it is found that concerning the fin efficiency, the latter produces acceptable results although it is not strictly correct.     

Heat transfer enhancement in cubical enclosures with vertical fins

Natural convection of air in a cubical enclosure with a thick partition fitted vertically on the hot wall is numerically investigated for Rayleigh numbers of 10³–10⁶. A three dimensional convective circulation is generated, in which the cold flow sweeps the fin faces and the hot wall, with low flow blockage. The combined contributions of these faces cause heat transfer enhancements over 40% at high Rayleigh numbers and thermal conductivity ratios (R_k). These enhancements significantly exceed the ones obtained with horizontal fins. Even low R_k values cause heat transfer enhancements, except at Ra = 10⁴.     

A thermal nonequilibrium model to natural convection inside non-Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

This article displays a numerical investigation on natural convection within non-Darcy porous layer surrounded by two horizontal surfaces having sinusoidal temperature profiles with difference in phase and wave number. The Darcy–Brinkman–Forchheimer model and local thermal nonequilibrium condition have been employed. Simulations have been performed for wide ranges of inertia coefficient (10^–4 ≤ Fs/Pr* ≤ 10^–2), thermal conductivity ratio (0.1 ≤ K _r ≤ 100), phase difference (0 ≤ β ≤ π), modified Rayleigh number (200 ≤ Ra* ≤ 1000), wavelength (3 ≤ k ≤ 12), and nondimensional heat transfer coefficient (0.1 ≤ H ≤ 100). Results demonstrate that Nusselt number highly relies on Fs/Pr*, K _r, β, Ra*, and k as compared to H. A considerable enhancement in fluid, solid, and overall Nusselt numbers has been observed with diminishing Fs/Pr* and β and increasing k, K _r, and H. The raising in β has a significant impact on Nu for smaller k and this effect is almost ignored when k > 12. The increase in Ra*, K _r, β, and H and decrease in Fs/Pr* and k acts to reduce the severity of nonequilibrium zone and increase the size of thermal equilibrium zone. The influence of H on nonequilibrium area is more evident than K _r.     

Investigation of heat transfer characteristics in plate-fin heat sink

The present study applies the inverse method in conjunction with the experimental temperature data to investigate the accuracy of the heat transfer coefficient on the fin in the plate-fin heat sink for various fin spacings. The commercial software is applied to solve the governing differential equations with the RNG k–? model in order to obtain the heat transfer and fluid flow characteristics. Under the assumption of the non-uniform heat transfer coefficient, the entire fin is divided into several sub-fin regions before performing the inverse scheme. The average heat transfer coefficient in each sub-fin region is assumed to be unknown. Later, the present inverse scheme in conjunction with the experimental temperature data is applied to determine the heat transfer coefficient and fin efficiency. In order to determine a more reliable heat transfer coefficient, a comparison between the present inverse and numerical results and those obtained from the existing correlations will be made. The numerical fin temperatures will also be compared with the experimental data.     

Numerical investigation of thermal enhancement of plate fin type heat exchanger with creases and holes in construction machinery

The present study aims to develop a new shape of plate fin heat exchanger by applying ceases and holes on the plate fin which is used in the construction machinery under the poor environment where the dust content is high and much extraneous materials are generated. In the present study, the louver fin heat exchanger, the plate fin heat exchanger and the heat exchanger of the shape newly proposed in this study were analyzed comparatively using three-dimensional numerical simulation. The fully developed airflow in the unit cell of heat exchangers considered was modeled with k–ω turbulence model using steady incompressible Reynolds-Averaged Navier–Stokes (RANS) equations. The calculated pressure drop and heat transfer capacity for the louver fin heat exchanger, the plate fin heat exchanger and the heat exchanger of the shape newly proposed in this study were assessed in terms of the Fanning friction factor (f factor) and Colburn j-factor (j factor) while the overall performance was estimated using the volume and area goodness factors.     

Effect of fin pitches on the air-side performance of crimped spiral fin-and-tube heat exchangers with a multipass parallel and counter cross-flow configuration

This study investigates the effect of fin pitches and fin materials on the air-side performance of crimped fin-and-tube heat exchangers in the range of high Reynolds numbers (4000–13000). The test samples are made from copper and aluminium with different fin pitches (f_p = 3.2, 4.2 and 6.2 mm). It is found that the proposed simple average effectiveness equation from the pure counter and parallel circuitry arrangement can well represent the effectiveness-NTU relationship for the current z-shape arrangement. The experimental results reveal that the fin pitch casts insignificant effect on the heat transfer characteristics (Colburn j factor). However, a detectable rise of the friction factor is seen when the fin pitch is increased to f_p = 6.2 mm. On the other hand, the effect of fin material on the airside performance is negligible.     

Optimum design of a radial heat sink under natural convection

We investigated natural convection heat transfer around a radial heat sink adapted for dissipating heat on a circular LED (light emitting diode) light and optimized heat sink. The numerical results were validated with experimental results and it showed a good agreement. To select the optimum reference model, three types of heat sinks (L, LM and LMS model) were compared. Parametric studies were performed to compare the effects of the number of fins, long fin length, middle fin length and heat flux on the thermal resistance and average heat transfer coefficient. Finally, multi-objective optimizations considering thermal performance and mass simultaneously were performed and Pareto front were conducted with various weighting factors. It was found that it was impossible to optimize both thermal performance and heat sink mass at the same time, and there existed an upper limit to the ratio of weighting factors (ω₁/ω₂).     

Study on performance comparison of different fin combinations of catalyst filled plate fin heat exchanger for hydrogen liquefaction

A mathematical model of catalyst filled plate fin heat exchanger (CFPFHE) is established to compare different fin models and analyze fin performance of different fin combinations. The results show that the single-layer fin model inadequately reflects the double-layers fin model from flow distribution and fin performance. The indexes of ortho-para hydrogen conversion (YY_pH2) of different fin combinations are all about 0.95, meeting the requirement of the CFPFHE. The plain_serrated fin has the best fin performance among four fin combinations. Compared with the plain_plain, the Colburn heat transfer factor (j factor) and thermal enhancement factor (TEF) of cool and hot sides of the plain_serrated fin are increased by 68.0～51.0% and 28.5～13.6%, 8.5～6.1% and 8.4%～6.1% at Re_hot = 500～1500, respectively. Further, the fin combinations of high-efficiency fin and plain respectively used in cool and hot sides have excellent overall fin performance, which provides a theoretical guidance for fin selection of the CFPFHE.     

Finite circular fin method for wavy fin-and-tube heat exchangers under fully and partially wet surface conditions

The present study proposes the finite circular fin method for analyzing the heat and mass transfer characteristics of wavy fin-and-tube heat exchangers under fully and partially wet surface conditions. The analysis is carried out by dividing the wavy fin-and-tube heat exchanger into many tiny segments. The tiny segments can be analyzed based on surface conditions, i.e. fully wet, fully dry or partially wet surface condition. From the experimental results, it is found that the heat and mass transfer characteristics are insensitive to the inlet relative humidity but the effect of relative humidity on mass transfer characteristic become more pronounced when the partially wet surface condition takes place. The heat transfer characteristic is independent of the fin spacing. Effect of fin spacing on mass transfer characteristic is small when fin spacing is larger than 2.5 mm. However, at smaller fin spacing, the mass transfer characteristic slightly decreases when the relative humidity increases. The ratios of h_c,o/h_d,oC_p,a are in the range of 0.6–1.2. Correlations are proposed to describe the heat and mass transfer characteristics. These correlations can describe 95.63% of the heat transfer characteristic within 15% and 95.14% of the mass transfer characteristic within 20%. Correspondingly, 94.68% of the ratios of h_c,o/h_d,oC_p,a are predicted by the proposed correlation within 20%.     

Numerical study of the heat sink with un-uniform fin width designs

The thermal performances of the heat sink with un-uniform fin width designs with an impingement cooling were investigated numerically. The governing equations are discretized by using a control-volume-based finite-difference method with a power-law scheme on an orthogonal non-uniform staggered grid. The coupling of the velocity and the pressure terms of momentum equations are solved by the SIMPLEC algorithm. The well-known k ? ε two-equations turbulence model is employed to describe the turbulent structure and behavior. The parameters include the five Reynolds number (Re = 5000–25000), three fin heights (H = 35, 40, 45 mm), and five fin width designs (Type-1–Type-5). The objective of this study is to examine the effects of the fin shape of the heat sink on the thermal performance. The results show that the Nusselt number increases with the Reynolds number. The increment of the Nusselt number decreases gradually with the increasing Reynolds number. Furthermore, the effects of fin dimensions on the Nusselt number at high Reynolds numbers are more significant than that at low Reynolds numbers. It is also found that there is potential for optimizing the un-uniform fin width design.     

Numerical investigation of thermal performance of extended surfaces for a novel heat exchanger

The present paper provides a thorough numerical study of variation in geometrical parameters that affect the performance of the novel finned‐tube type heat exchanger design. The finite volume method was employed to discretize and solve the governing partial differential equations of heat conduction. A wide range of constant convective heat transfer coefficient (5 < h < 200 W/m² K) is chosen to reduce the computational time and power, which covers thermal applications of latent thermal energy storage, refrigeration & air‐conditioning, etc. The effects of the ratio of fin spacing of fins to the outer diameter of the tube (0.1 ≤ δ* ≤ 8), the material of fins (copper and stainless steel) and the ratio of fin thickness to the outer diameter of the tube (0.0333 ≤ t* ≤ 0.4) on the performance parameters namely efficiency (η) and effectiveness (ε) of the fins were studied. Temperature contours for a wide range of geometries were depicted. The maximum effectiveness of copper fins is 304.62, whereas that for steel fin is 219.33 with the optimum dimensionless fin thickness reported to be t* = 0.1666. Furthermore, the maximum overall efficiencies of fins were 99.98% and 99.62% for copper and steel fins, respectively.