Heat transfer enhancement in annular fins using functionally graded material

This study presents a new approach on the heat transfer enhancement of annular fins with constant thickness using functionally graded materials. The thermal conductivity of the annular fin is assumed to be graded along the fin radius as a power‐law function. The resulting fin equation is solved by an approximate analytical method using the mean value theorem. The variable coefficients of second and third terms in the second‐order differential equation of the fin are replaced with their mean values along the fin radius. Several different graphs regarding the computed temperature profile, fin tip temperature, and fin efficiency are plotted with respect to the radii ratio thermo‐geometric parameter, and inhomogeneity parameter. It is demonstrated that the inhomogeneity parameter plays an important role on the heat transfer enhancement of the annular fin. However, for large radii ratios the effect of the inhomogeneity parameter decreases. Finally, it is stated that application of the functionally graded material in the annular fins, enhances the heat transfer rate between the fin and surrounding fluid resulting from the higher fin efficiency in comparison to the homogeneous annular fin. It is hoped that the results obtained from this study arouse interest among thermal designers and heat exchanger industries. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 603–617, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21053     

Heat transfer from rotating short radial blades

Fluid flow and heat transfer from a rotating short radial blade is analysed, using rotating coordinate system, by Von Karman-Pohlhausen integral method, when the relative fluid motion is laminar. The transport rates for the blade are compared with those for a flat plate and for a rotating disk. Results of heat-transfer experiments, using blades of different included angles, are reported for both laminar and turbulent flow regimes, and are compared with theoretical predictions, as well as with other available data in the literature.     

Heat transfer analysis of mutually irradiating fins

Apparent emittance of a longitudinal rectangular fin system with an opening angle, accounting fin-to-fin radiation interaction and also with surfaces that reflect radiation in both diffuse and specular regimes has been evaluated. The governing equation of the problem is a complicated integro-differential equation. This equation has been solved with the Gauss-Jacobi orthogonal collocation method, which possesses the quality of exceptional accuracy with a few numbers of nodes. Finally, the minimum mass design of the fin has been arrived at.     

Differential transformation method to determine heat transfer in annular fins

Fins are the extended surfaces that are utilized to afford a significant increase in the surface area for heat transference between a heated source and a colder ambient liquid. To enhance the heat transference rate from the exterior surface of a circular conduit, radial, or concentric annular fins are used. Fins are utilized in heat exchanging devices like superheaters, electrical equipment, computer CPU heat sinks, car radiators, refrigeration, and heat exchangers. Motivated by these applications, the current paper explores the thermal attribute of an annular fin with variable thermal conductivity. The framed equations are articulated in terms of nonlinear ordinary differential equations. One of the most effective techniques, the differential transformation method has been implemented to find the analytical solution. The domination of nondimensional parameters on the thermal gradient of the fin has been analyzed graphically. Furthermore, the variation in radial and tangential stress in an annular fin for various dimensionless parameters has been examined with a graphical explanation. Results reveal that the thermal gradient of fin increases for improved values of variable thermal conductivity parameters. The greater values of thermogeometric parameters result in a higher heat transfer.     

Heat transfer in an annular gap

Heat-transfer coefficients were measured for the flow in the annular space between an inner rotating cylinder and an outer stationary one, with superimposed axial flow. The problem was stimulated by the desire for additional information on the design of cooling systems for electric motors of high power density. The speeds of rotation were such as to include Taylor numbers up to about 10⁶, and the range of Reynolds numbers based on the axial velocity components and the gap distance were extended to 7000. Experiments were performed at three different Prandtl numbers 2.5, 4.5 and 6.5.     

Heat transfer enhancement from micro pin fins subjected to an impinging jet

An experimental investigation was carried out to study the single-phase stagnation point jet impingement heat transfer on smooth and micro pin fin structures using water and R134a. The experiments were carried out for a single jet (d_j = 2.0 mm) impinging on a 2 × 2 mm micro-heater over a wide range of Reynolds numbers. Both an unfinned and a micro structured impingement surfaces were investigated. The micro structures consisted of an array of 64 circular micro pin fins fabricated using MEMS microfabrication. The micro pin fins had diameters of 125 μm, heights of 230 μm, and pitches of 250 μm with an area enhancement of A_total/A_base = 2.44. The jet stand-off ratio and area ratio (A_j/A_base) were 0.86 and 0.785, respectively. Nusselt numbers were found to increase with increasing Reynolds numbers. Correlations from the literature for impingement zone Nusselt numbers were found to underpredict the experimental results. Significant enhancement of the heat transfer coefficients were observed as a result of the presence of the micro pin fins on the impingement surface. Enhancement factors as high as 3.03 or about 200% increase in the heat transfer coefficients were demonstrated. Enhancements are attributed to flow mixing, interruption of the boundary layers, and augmentation of turbulent transport.     

Heat transfer from multiple row arrays of low aspect ratio pin fins

Pin fin arrays are used in many applications to enhance heat transfer. In modern gas turbines, for example, airfoils are designed with sophisticated internal and external cooling techniques. One method for cooling is routing air from the compressor through intricate cooling channels embedded in turbine airfoils. Heat transfer from the blade to the coolant air can be increased by installing arrays of cylindrical pedestals often referred to as pin fins. Pin fin arrays increase heat transfer by increasing the flow turbulence and surface area of the airfoil exposed to the coolant.For the current study, experiments were conducted to determine the effects of pin spacing on heat transfer and pressure loss through pin fin arrays for a range of Reynolds numbers between 5000 and 30,000. Results showed that spanwise pin spacing had a larger effect than streamwise spacing on array pressure loss while streamwise spacing had a larger effect than spanwise spacing on array heat transfer.     

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.     

Performance of annular fins with different profiles subject to variable heat transfer coefficient

Performance of annular fins of different profiles subject to locally variable heat transfer coefficient is investigated in this paper. The performance of the fin expressed in terms of fin efficiency as a function of the ambient and fin geometry parameters has been presented in the literature in the form of curves known as the fin-efficiency curves for different types of fins. These curves, that are essential in any heat transfer textbook, have been obtained based on constant convection heat transfer coefficient. However, for cases in which the heat transfer from the fin is dominated by natural convection, the analysis of fin performance based on locally variable heat transfer coefficient would be of primer importance. The local heat transfer coefficient as a function of the local temperature has been obtained using the available correlations of natural convection for plates. Results have been obtained and presented in a series of fin-efficiency curves for annular fins of rectangular, constant heat flow area, triangular, concave parabolic and convex parabolic profiles for a wide range of radius ratios and the dimensionless parameter m based on the locally variable heat transfer coefficient. The deviation between the fin efficiency calculated based on constant heat transfer coefficient, reported in the literature, and that presently calculated based on variable heat transfer coefficient, has been estimated and presented for all fin profiles with different radius ratios.     

Heat transfer correlations for PCM-based heat sinks with plate fins

Characterization of melting process in a Phase Change Material (PCM)-based heat sink with plate fin type thermal conductivity enhancers (TCEs) is numerically studied in this paper. Detailed parametric investigations are performed to find the effect of aspect ratio of enclosure and the applied heat flux on the thermal performance of the heat sinks. Various non-dimensional numbers, such as Nusselt number (Nu), Rayleigh number (Ra), Stefan number (Ste) and Fourier number (Fo) based on a characteristic length scale, are identified as important parameters. The half fin thickness and the fin height are varied to obtain a wide range of aspect ratios of an enclosure. It is found that a single correlation of Nu with Ra is not applicable for all aspect ratios of enclosure with melt convection taken into account. To find appropriate length scales, enclosures with different aspect ratios are divided into three categories, viz. (a) shallow enclosure, (b) rectangular enclosure and (c) tall enclosure. Accordingly, an appropriate characteristic length scale is identified for each type of enclosure and correlation of Nu with Ra based on that characteristic length scale is developed.     

Heat transfer from a rotating disk in a parallel air crossflow

The heat transfer from a rotating disk in an air stream parallel to the plane of rotation is of importance in the assessment of disk brake performance. Numerically determined heat transfer coefficients and correlations are accordingly presented for a large range of rotational and crossflow velocities. These were obtained by means of large-eddy-simulations (LES). The extreme conditions of a stationary disk in an air crossflow and a rotating disk in still air are also considered. It is found that a critical ratio between the rotational and the crossflow Reynolds numbers exists with respect to rotational heat transfer augmentation. Only above this critical value, rotational heat transfer augmentation sets on in case of laminar crossflow Reynolds numbers. This phenomenon is directly linked to a flow instability that leads to a periodic vortex generation, and which can be described by the classical Landau model. For higher angular velocities, the wake becomes fully turbulent, and the transition is very rapid.     

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.     

Heat transfer through rotating roll of contact dryer

This paper covers results of experimental and theoretical researches referring to the technique of contact drying. Research of roll system parameters was made in case of lack of drying material layer and in case of existence of drying material layer on the surface of rotating roll in exploitation conditions. Based on the research results, the criteria equations were given which characterize heat transfer in the dynamic conditions of dryer roll rotation.     

Heat transfer on a radially rotating heated cylinder

Experiments are conducted to investigate the convective heat transfer on a radially rotating heated cylinder. In the experiment, one uses cold air-hot cylinder instead of hot air-cold blade in a real engine. The hollow bakelite test rotating cylinder is pasted with a heater made of 0.03 mm thin film of stainless steel. The maximum air stream velocity is 20 m/s with the corresponding Reynolds number of 1.2 × 10⁵ that is high enough to simulate the real turbine blade of Re ≈ 10⁵. The rotation-induced cross stream flow affect the heat transfer coefficient on the cylinder surface. The effect is more prominent for the cases with higher rotational speeds and lower Reynolds numbers. Due to rotation, the heat transfer enhancement at lower Reynolds number is greater than those at a higher one.     

Heat transfer from a spinning disk during semi-confined axial impingement from a rotating nozzle

Conjugate heat transfer from a uniformly heated spinning solid disk of finite thickness and radius during a semi-confined liquid jet impingement from a rotating nozzle is studied. The model covers the entire fluid region including the impinging jet on a flat circular disk and flow spreading out downstream under the spinning confinement plate and free surface flow after exposure to the ambient gaseous medium. The model examines how the heat transfer is affected by adding a secondary rotational flow under semi-confined jet impingement. The solution is made under steady state and laminar conditions. The study considered various plate materials such as aluminum, copper, silver, constantan and silicon. Ammonia, water, flouroinert FC-77 and MIL-7808 oil were used as working fluids. The range of parameters covered included Reynolds number (220–900), Ekman number (7.08 × 10^?5–∞), nozzle-to-target spacing (β = 0.25–1.0), disk thicknesses to nozzle diameter ratio (b/d_n = 0.25–1.67), Prandtl number (1.29–124.44) and solid to fluid thermal conductivity ratio (36.91–2222). It was found that a higher Reynolds number increased local heat transfer coefficient reducing the interface temperature difference over the entire disk surface. The rotational rate also increased local heat transfer coefficient under most conditions. An engineering correlation relating the Nusselt number with other dimensionless parameters was developed for the prediction of the system performance.     

Convective heat transfer and pressure drop of annular tubes with three different internal longitudinal fins

Pressure drop and heat transfer characteristics of air in three annular tubes with different internal longitudinal fins were investigated experimentally at uniform wall heat flux. The tested tubes have a double‐pipe structure with the inner blocked tube as an insertion. Three different kinds of fins, plain rectangle fin, plain rectangle fin with periodical ridges and wave‐like fin, were located peripherally in the annulus. The friction factor and Nusselt number can be corrected by a power‐law correction in the Reynolds number range tested. It was found that the tube with periodical ridges on the plain fin or with wave‐like fin could augment heat transfer; however, the pressure drop was increased simultaneously. In order to evaluate the comprehensive heat transfer characteristics of the tested tubes, two criteria for evaluating the comprehensive thermal performance of tested tubes were adopted. They are: 1) evaluating the comprehensive heat transfer performance under three conditions: identical mass flow, identical pumping power, and identical pressure drop; 2) the second law of thermodynamics, i.e., the entropy generation. According to the two different evaluating methods, it was found that the tube with wave‐like fins provided the most excellent comprehensive heat transfer performance among the three tubes, especially when it was used under higher Reynolds number conditions. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(1): 29–40, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20186     

Heat transfer performances of vertical rectangular fins protruding from rectangular bases: Effect of fin length

The effects of increasing the fin length from 250 to 375 mm on (i) the steady-state rate of heat loss and (ii) the optimal uniform fin separation of vertical rectangular fins protruding from a horizontal or a vertical rectangular base, have been investigated experimentally. A constant base temperature, 40 (±0·3)°C above that of the ambient environment, was used.     

Heat transfer and flow characteristics of offset fins in the low-Reynolds-number region

The characteristics of heat exchangers with offset-type plate fins for space stations are studied for Reynolds numbers less than 300 based on the hydraulic diameter. A three-dimensional analysis is carried out to study the effects of the following parameters on the heat transfer and the flow characteristics: (a) the thermal boundary layer developing on the bottom plate and on the fins on the plate, (b) the aspect ratio (height/pitch) of the cross section of the flow passage, the fin thickness, the fin length in the direction of the flow, the thermal conductivity of the fluid and the fins, and the Prandtl number of the fluid. The results obtained are as follows. (1) The heat-transfer coefficient on the fin surface is characterized by the thermal-conductivity ratio of fluid to fin material. When the thermal conductivity of the fin material approaches that of the fluid, the heat-transfer coefficient on the fin surface becomes low. (2) The optimum condition of the aspect ratio depends on the value of the thermal-conductivity ratio between the fluid and the fins. (3) When the aspect ratio becomes large or small, the friction factor of offset fins approaches that of fully developed duct flow with the same aspect ratio as the Reynolds number decreases. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(4): 249–261, 1997