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.     

The Use of Porous Fins for Heat Transfer Augmentation in Parallel-Plate Channels

In this study, a steady, fully developed laminar forced convection heat augmentation via porous fins in isothermal parallel-plate duct is numerically investigated. High-thermal conductivity porous fins are attached to the inner walls of two parallel-plate channels to enhance the heat transfer characteristics of the flow under consideration. The Darcy–Brinkman–Forchheimer model is used to model the flow inside the porous fins. This study reports the effect of several operating parameters on the flow hydrodynamics and thermal characteristics. This study demonstrates, mainly, the effects of porous fin thickness, Darcy number, thermal conductivity ratio, Reynolds number, and microscopic inertial coefficient on the thermal performance of the present flow. It is found that the highest Nusselt number is achieved at fully filled porous duct which requires the highest pumping pressure. The results show that using porous fins requires less pumping pressure with comparable high heat augmentation weight against fully filled porous duct. It is found that higher Nusselt numbers are achieved by increasing the microscopic inertial coefficient (A), the Reynolds number (Re), and the thermal conductivity of the porous substrate k ₂. The results show that heat transfer can be enhanced (1) with the use of high thermal conductivity fins, (2) by decreasing the Darcy number, and (3) by increasing microscopic inertial coefficient.     

Constructal multi-scale structure of PCM-based heat sinks

This paper inquires the effectiveness of a PCM-based heat sink as a reliable solution to portable electronic devices. This sink is composed of a PCM with low thermal conductivity and fins to boost its conductivity. The optimization is subjected to fixed heat sink volume filled with PCM between vertical equidistant fins. New fins are installed in the unheated space existing in each enclosure which is not involved in thermal distribution from vertical fins to the PCM. Based on the same principle, new fins generations are augmented stepwise to the multi-scale structure. The steps of adding fins will continue up to the point that the objective function reaches its maximal value, i.e., maximizing the longest safe operation time without allowing the electronics to reach the critical temperature. The results indicate that in each length of the enclosure, the optimum volume fraction and the best fins distance values exist in which the heat sink performance becomes maximum, and adding more fins lowers the performance of the heat sink. Increasing the enclosure’s length by \(2^{n}\) does not change them. For an enclosure with constant length, the optimal number of steps for adding fins within the enclosure is a function of the fin thickness. The results indicate that increasing the thickness changes the optimal number of adding fins inside the enclosure (normally a decrease). As the fin thickness is lowered, there will be a higher effect by adding vertical fins in the enclosure. Numerical simulations cover the Rayleigh number range \(2\times 10^{5}\le \hbox {Ra}_{\mathrm{H}} \le 2.7\times 10^{8}\), where H is the heat sink height.     

A study on heat transfer of the optimization in circular fins of parabolic profile with variable thermal parameters

Circular fins are used extensively in heat exchange devices to increase the heat transfer. For economic purposes, the traditional approach to the optimization of fins consists of minimizing the comsumption (investment) of fin material for the excution of a specified heat transfer task. The minimum weight cooling fin has optional profile to be a concave parabola. Therefore, the optimum geometric dimensions of circular fins of parabolic profile with variable thermal parameters are studied. The effect of the two pertinent physical parameters-thermal conductivity variation parameter α and the index of the heat transfer coefficient variationm upon the optimum geometric dimensions is also studied. The results pressented can be used as the design guideline for engineering practice.     

A Taguchi approach for determination of optimum design parameters for a heat exchanger having circular-cross sectional pin fins

The present work submits an investigation about the optimal values of design parameters and performance analysis for a heat exchanger having cylindrical pin fins positioned in a rectangular channel. The experiments covered the following range: Reynolds number 13,500–42,000, the clearance ratio (C/H) 0, 0.33 and 1, the interfin spacing ratio (S _y /D) 1.208, 1.944 and 3.417. In the experimentation, Taguchi method was employed, and Nusselt number and friction factor were considered as performance parameters. While the optimum parameters were determined, due to the goals (above aims) more than one being, the trade-off among goals was considered. First of all, each goal was optimized, separately. Then, all goals were optimized together, considering the priority of goals, and the optimum results were found to be Reynolds number of 42,000, fin height of 50 mm and pitch of 3.417. The performance analysis also was made under a constant pumping power constraint, and the results showed that the use of cylindrical pin fins may lead to an advantage on the basis of heat transfer enhancement.     

Thermally developing flow in finned double‐pipe heat exchanger

A numerical solution of the convective heat transfer in the thermal entry region of the finned double‐pipe is carried out for the case of hydro‐dynamically fully developed flow when subjected to uniform wall temperature boundary condition. Adaptive axial grid size is used in order to cater for the variation of large solution gradients in the axial direction. It has been observed that the thermal entrance region is highly effective and there is a substantial enhancement in the heat transfer coefficient. A maximum of 76.4877% increase has been observed in the thermal entrance region as compared with the fully developed region for 24 fins and H*=0.6 when R?=0.25, whereas for R?=0.5 the maximum increase is 75.0308% for the same number of fins of same height. It has been observed that no geometry consistently perform better throughout the entrance region. However, the geometries that have optimal performance in the fully developed region perform better in the developing region on average terms. Results show that the Nusselt number and the thermal entrance length are dependent upon various geometrical parameters such as ratio of radii of the inner and the outer pipe, fin height and the number of fins. The limiting case results match well with the literature results. This validates our numerical procedure and computer code. Copyright © 2010 John Wiley & Sons, Ltd.     

Natural convection in inclined rectangular enclosures with perfectly conducting fins attached on the heated wall

The natural convection heat transfer in inclined rectangular enclosures with perfectly conducting fins attached to the heated wall is numerically studied. The parameters governing this problem are the Rayleigh number (10²≤Ra≤2×10⁵), the aspect ratio of the enclosures (2.5≤A=H′/L′≤∞), the dimensionless lengths of the partitions (0≤B=?′/L′≤1), the aspect ratio of micro-cavities (A≤C=h′/L′≤0.33), the inclination angle (0≤φ≤60^°) and the Prandtl number (Pr=0.72). The results indicate that the heat transfer through the cover is considerably affected by the presence of the fins. At low Rayleigh numbers, the heat transfer regime is dominated by conduction. When B≈0.75 and C≈0.33, the heat transfer through the cold wall decreases considerably. This trend is enhanced when the enclosure is inclined. Useful engineering correlations are derived for practical applications.     

Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature

An analysis is presented for fully developed laminar convective heat transfer in a pipe provided with internal longitudinal fins, and with uniform outside wall temperature. The fins are arranged in two groups of different heights. The governing equations have been solved numerically to obtain the velocity and temperature distributions. The results obtained for different pipe-fins geometries show that the fin heights affect greatly flow and heat transfer characteristics. Reducing the height of one fin group decreases the friction coefficient significantly. At the same time Nusselt number decreases inappreciably so that such reduction is justified. Thus, the use of different fin heights in internally finned pipes enables the enhancement of heat transfer at reasonably low friction coefficient.Nomenclature A_f dimensionless flow area of the finned pipe, Eq. (8) - a_f flow area of the finned pipe - C_p specific heat at constant pressure - f coefficient of friction, Eq. (12) - H₁, H₂ dimensionless fin height h₁/r_o h₂/r_o - h₁, h₂ fin heights - average heat transfer coefficient at solid-fluid interface - KR fin conductance parameter, k_s/k_f - k_f thermal conductivity of fluid - k_s thermal conductivity of fin - l pipe length - mass flow rate - N number of fins - Nu Nusselt number, Eqs. (15) and (16) - P pressure - Q total heat transfer rate at solid fluid interface - Q_f1, Q_f2 heat transfer rate at fin surface - q_w average heat flux at pipe-wall, Q/(2 r_ol) - R dimensionless radial coordinate r/r_o - Re Reynolds Number, Eq. (13) - r radial coordinate - r_o radius of pipe - r₁, r₂ radii of fin tips - T temperature - T_b bulk temperature - U dimensionless velocity, Eq. (2) - U_b dimensionless bulk velocity - u_z axial velocity - z axial coordinate - angle between the flanks of two adjacent fins - half the angle subtended by a fin - angle between the center-lines of two adjacent fins - angular coordinate - dynamic viscosity - density - dimensionless temperature, Eq. (6) - _b dimensionless bulk temperature     

Coupling of the methods of successive approximations and undetermined coefficients for the prediction of the thermal behaviour of uniform circumferential fins

This study addresses a distinct, unsophisticated computational procedure for solving approximately, but analytically, the one-dimensional heat equation for circumferential fins of uniform thickness with constant properties. This differential equation with variable coefficients, called the modified Bessel equation of zero order, is subject to a prescribed temperature at the base and zero heat rejection at the tip. Approximate temperature distributions and companion heat transfer rates of excellent quality have been obtained by adequately blending a polynomial curve fit, the method of successive approximations and the method of undetermined coefficients. Detailed error distributions are also presented for real uniform circumferential fins using the exact solution by modified Bessel functions as the baseline case. The calculations of analytic character were carried out with a symbolic algebra software, Maple V, on a personal computer. Received on 23 October 1997     

Experimental study on the heat transfer and pressure drop of a cross-flow heat exchanger with different pin–fin arrays

In this study, convective heat transfer and pressure drop in a cross-flow heat exchanger with hexagonal, square and circular (HSC) pin–fin arrays were studied experimentally. The pin–fins were arranged in an in-line manner. For the applied conditions, the optimal spacing of the pin–fin in the span-wise and stream-wise directions has been determined. The variable parameters are the relative longitudinal pitch (S _L /D = 2, 2.8, 3.5), and the relative transverse pitch was kept constant at S _T /D = 2. The performances of all pin–fins were compared with each other. The experimental results showed that the use of hexagonal pin–fins, compared to the square and circular pin–fins, can lead to an advantage in terms of heat transfer enhancement. The optimal inter-fin pitches are provided based on the largest Nusselt number under the same pumping power, while the optimal inter-fin pitches of hexagonal pin–fins are S _T /D = 2 and S _L /D = 2.8. Empirical equations are derived to correlate the mean Nusselt number and friction coefficient as a function of the Reynolds number, pin–fin frontal surface area, total surface area, and total number. Consequently, the general empirical formula is given in the present form.

Transient conjugated mixed-convective heat transfer in a vertical plate channel with one wall heated discretely

 This study presents a numerical solution of the unsteady conjugated mixed-convection heat transfer in a vertical plate channel with one wall suddenly subjected to either isoflux or isothermal discrete heat sources. The effects of the dimensionless heat source length H ₁, the dimensionless spacing between heat sources H ₂, the dimensionless channel length L, the dimensionless heated-plate thickness B _l, the wall-to-fluid conductivity ratio K and the ratio of Grashof number to Reynolds number Gr/Re on the interface heat flux, Nusselt number and bulk fluid temperature are discussed in detail. Results show that the discrete heating can cause the heat transfer direction conversely from the fluid to the heated plate during the transient period, which is more significant for the cases with larger L and H ₂. For the system with isoflux discrete heat sources, the time required to reach the steady-state is shorter for larger H ₂. While the trend is reverse for system with isothermal discrete heat sources. Additionally, a higher ratio of the input energy is axially conducted through the plate wall from heated sections to unheated regions for a larger H ₂ and B _l or smaller L. Received on 9 November 1998     

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.     

Multi‐objective optimization of a rotating cooling channel with staggered pin‐fins for heat transfer augmentation

A rotating channel with staggered pin‐fins is formulated numerically and optimized for performance (heat transfer/required pumping power) using a Kriging meta‐model and hybrid multi‐objective evolutionary algorithm. Two design variables related to cooling channel height, pin diameter, and spacing between the pins are selected for optimization, and two‐objective functions related to the heat transfer and friction loss are employed. A design of experiment is performed, and 20 designs are generated by Latin hypercube sampling. The objective function values are evaluated using a Reynolds‐averaged Navier–Stokes solver, and a Kriging model is constructed to obtain a Pareto‐optimal front through a multi‐objective evolutionary algorithm. Rotation in a cooling channel with staggered pin‐fins induces Coriolis force that causes a heat transfer discrepancy between the trailing (pressure) and leading (suction) surfaces, with a higher Nusselt number on the trailing surface. The tradeoff between the two competing objective functions is determined, and the distribution of the Pareto‐optimal solutions in the design space is discussed through k‐means clustering. In the optimal designs, with a decrease in spacing between the pins, heat transfer is enhanced whereas friction loss is increased. Copyright © 2011 John Wiley & Sons, Ltd.     

A flow visualization study of the flow in a 2 D array of fins

A study of the flow field in a 2 D arrangement of fins was carried out by means of flow visualization in a vertical water tunnel. A similar arrangement of fins had been tested as a conceptual heat sink, and the heat transfer measurement showed a dependence of the heat transfer qualities on the geometrical parameters of the fin's array. The current study examines the complex flow field structure in order to obtain a better understanding of the convection process. The model is built of several series of fins, generating a multi-cell structure. The investigation included a systematic variation of the fins' chord and inclination angle, as well as the flow velocity. Two main flow structures were observed. In the first one, the flow separates from the leading edge of each fin. Due to the influence of its neighbouring fins, the flow re-attaches to the fin, creating a closed separation zone. A vortex fills this separation zone. The main flow accelerates in the passage that is created between the separation bubble and the neighbouring fin. In the second flow structure, the flow separates from both leading and trailing edges of each fin. The separation is in alternating order and generates a nonsteady pair of vortices. This separation pattern is similar to that of a single plate at high angle of attack, and the effect of the neighbouring fins is only to narrow the wake. The pressure drop across the model was measured and correlated to a single nondimensional variable on a single curve.List of symbols a distance between fins' axis - A current A (Figs. 4 and 5) - B current B (Figs. 4 and 5) - C fin chord - e blockage ratio = (C + T )/(a2-C-T) - E blockage ratio = C sin + T cos /a - Gr Grashof number - L length - P total pressure drop - Re Reynolds number - S nondimensional variable (Fig. 8) - T fin width - V velocity - inclination angle - kinematic viscosity     

Enhancement of heat and mass transfer in metal hydride beds with the addition of Al plates

A numerical study is made of transient heat and mass transfer in metal hydride beds in the hydriding process with the addition of internal aluminum plates. The two-dimensional equations governing the hydration kinetics, hydrogen flow and heat transfer are solved by using the iterative method based on the finite-volume technique. It is found that the heat transfer is enhanced by the installation of aluminum plates, and the ratio of the gap distance between the aluminum plates (H) and the thickness of the bed (L) emerges to be an important parameter. The reaction process is also strongly influenced by H/L. An optimal value of H/L exists to yield the fastest reaction rate, which is also shown to depend on other relevant parameters, such as the thickness of hydride bed and the inlet pressure. Received on 17 July 1998     

Hypersonic tail-fin heat transfer

The flow and heat transfer on the windward surface of tail fins has been experimentally investigated for Mach numbersM =5 and 8 and Re_L=(0.6–1.1)·10⁶ (L is the length of the central chord of the wing on which the fins are mounted). Two lines of flow divergence and, consequently, two zones of enhanced heat transfer on the surface of the fin have been detected. The angle of inclination of the fin to the wing surface, the angle of attack of the wing and the radius of the wing-fin junction were varied.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 18–25, March–April, 1993.The authors wish to thank S. D. Fonov and T. A. Ershova for the digital analysis of the photographs obtained by the thermal indicator coating and laser knife-edge methods.     

Experimental study on the pressure drop and heat transfer characteristics of tubes with internal wave-like longitudinal fins

Experiments were performed to determine the heat transfer and pressure drop characteristics in the entrance and fully developed regions of tubes with internal wave-like longitudinal fins. The test tube has a double-pipe structure, with the inner tube as an insertion. The wave-like fins are in the annulus and span its full width. Experiments were conducted for two cases: one with the inner tube blocked (no air flowing through it) and the other with the inner tube unblocked. The outer tube was electrically heated. Local and average heat transfer coefficients and friction factors were measured. The friction factor and Nusselt number correlations in the fully developed region were obtained in the Reynolds number range of 9×10² to 3.5×10³. It has been found that the wave-like fins enhance heat transfer significantly with the blocked case being superior. In addition, the in-tube heat transfer process is characterized by an earlier transition from laminar to turbulent flow and Reynolds number-dependent thermal entrance length. Received on 12 May 1998     

Heat transfer from rotating finned heat exchangers with different orientation angles

The local and average heat transfer characteristics of spoke like fins that extend outward from a rotating shaft have been determined experimentally. The experiments encompassed a number of geometrical parameters, including the length and chord of the fins, the number of fins deployed around the circumference of the shaft and the orientation angles of the fin. The experiments cover a wider range of rotational speeds, which varies from 25 up to 2,000 rpm. Three wire heat flux sensors have been used in conjunction with a slip ring apparatus to evaluate the local and average heat transfer coefficients. The output results indicated that, the heat transfer transition on rotating fins occurs at Reynolds number lower than encountered on the stationary rectangular fins in crossflow. In general, with non zero incidence angle, the rotating system acts as a fan and creates axial air motion, which enhance the heat transfer rate. However, the effect of orientation angle reduces with increasing the rotational speed. The Nusselt number data are independent of the number of fins in the circumferential array at high rotational speed and are weakly dependent at low Reynolds numbers. To facilitate the use of the results for design, correlations were developed which represent the fin heat transfer coefficient as a continuous function of the investigated independent parameters.     

Numerical analysis of turbulent convection heat transfer from an array of perforated fins

Numerical investigation is made for three-dimensional fluid flow and convective heat transfer from an array of solid and perforated fins that are mounted on a flat plate. Incompressible air as working fluid is modeled using Navier–Stokes equations and RNG based k ? ? turbulent model is used to predict turbulent flow parameters. Temperature field inside the fins is obtained by solving Fourier’s conduction equation. The conjugate differential equations for both solid and gas phase are solved simultaneously by finite volume procedure using SIMPLE algorithm. Perforations such as small channels with square cross section are arranged streamwise along the fin’s length and their numbers varied from 1 to 3. Flow and heat transfer characteristics are presented for Reynolds numbers from 2 × 10⁴ to 4 × 10⁴ based on the fin length and Prandtl number is taken Pr = 0.71. Numerical computations are validated with experimental studies of the previous investigators and good agreements were observed. Results show that fins with longitudinal pores, have remarkable heat transfer enhancement in addition to the considerable reduction in weight by comparison with solid fins.