Heat exchanger: Optimal separation for vertical rectangular fins protruding from a vertical rectangular base

An experimental investigation of the steady-state rates of heat transfer from an array of vertical rectangular 3 mm thick fins, extending 60 mm perpendicularly out of a 250 mm high vertical rectangular base, is reported. For base temperatures between room temperature (～ 15°C) and 100°C, the optimal separation of the parallel fins, corresponding to the maximum rate of heat loss, is 10 ± 1 mm.     

Heat exchanger design: Optimal uniform separation between rectangular fins protruding from a vertical rectangular base

Steady-state rates of heat loss, from an array of 3 mm thick, 250 mm long, horizontal rectangular duralumin fins extending 60 mm perpendicularly out of a 250 mm × 190 mm vertical rectangular duralumin base, have been measured. With the base, at a uniform temperature of between 40°C and 80°C, in a 20°C ambient environment, two separations of the parallel fins, corresponding to maxima in the rate of heat loss versus fin separation curves ensued, respectively at 12 ± 1 mm and 38 ± 1 mm. The use of the latter maxima (i.e. the optimal separation) leads to the higher rate of heat loss. The heat transfer performances of vertical and horizontal rectangular fin arrays on a vertical rectangular base are compared: using the same geometrical configuration and identical base temperatures in both cases, the vertical fin orientation has the more rapid, steady-state heat loss.     

Heat exchanger design: Thermal performances of rectangular fins protruding from vertical or horizontal rectangular bases

An experimental investigation of the steady-state rates of heat transfer from an array of vertical rectangular fins of 3 mm thickness and 250 mm length, protruding 60 mm perpendicularly upwards from a 250 mm × 190 mm horizontal rectangular base, is reported. For constant (to ±0·1°C) base temperatures between 40°C and 80°C, in an ambient environment of 20±0·2°C, the optimal separation of the parallel fins, corresponding to the maximum rate of heat loss, is 10·5±1·0 mm.The effects of the extent of the fin protrusions on the thermal performances of such vertical fins, on the same base, which was arranged to be either vertical or horizontal, have been studied. The experiments were performed with three different fin protrusions, namely 32 mm, 60 mm and 90 mm, for a base temperature of 40°C above that of the ambient environment. The steady-state rate of heat dissipation from the fin array increased slightly less than linearly with the fin protrusion for both orientations, but the relationship became closer to linear as the fin spacing was increased.A comparison of the abilities to dissipate heat to the room air from the same geometrical configuration having a rectangular fin array but positioned with vertical fins on a vertical base, vertical fins protruding upwards from a horizontal base, or horizontal fins on a vertical base, has been made. The orientation with vertical fins protruding upwards from the horizontal base, is the preferred option because of the relatively high rates of heat transfer that can then be achieved.     

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.     

Enhancing heat transfer rates from closed-sided,open-topped heat exchangers,each having vertical rectangular fins extending upwards from a horizontal base

The almost two-dimensional steady-state rates of heat loss from arrays of uniformly-spaced vertical rectangular fins, extending upwards—in otherwise stagnant air—from horizontal heated bases, have been measured. (The vertical air gaps between the fins were closed at their sides, by insulated vertical end-barriers.) The effects of various combinations of height, thickness and spacing of the fins, for different base temperatures (in the range 40 to 100°C), have been studied.For the configuration considered, in a normal ambient environment (～ 20°C), there is an optimal fin spacing (? 16 mm) corresponding to the greatest steady-state rate of free convective/conductive heat loss through the air from the finned system, and this is almost independent of the temperature of the heat exchanger base (in the range 40–100°C). At this optimal spacing for base temperatures not greater than 50°C, the convective/conductive heat transfer rate from the array increases with the fin height up to about 60 mm, so that it would be uneconomic to employ taller fins if convection/conduction is dominant compared with radiation.If the radiation contribution is also considered, then the optimal spacing corresponding to the maximum total steady-state rate of heat loss through the air is somewhat less than the optimal spacing for which, under the same temperature conditions, the maximum steady-state rate of convective/conductive heat leak occurs. The greater the emissivity of the heat exchanger surfaces, the narrower the optimal uniform gaps between the fins.A two-dimensional finite-difference computer program has been composed to predict the temperature distribution throughout the heat exchanger for a stipulated ambient environmental temperature and experimentally-determined distribution of the heat transfer coefficient over the surfaces of the exchanger. This enables, for instance, any hot spots to be located prior to a proposed design being built.     

Heat transfer of a horizontal spiral heat exchanger under groundwater advection

Groundwater flows at approximately 1–3 m under the ground surface in a given region. If groundwater flow is present, the performance of a horizontal ground heat exchanger (HGHE), buried in a shallow trench, is enhanced. Nevertheless, owing to the general depth at which groundwater is present, research regarding the heat transfer of a ground heat exchanger (GHE) under conditions with groundwater flow has mainly focused on vertical GHE systems. To the authors’ knowledge, no such studies have addressed HGHEs. From a system design perspective, a prediction tool is needed to consider the groundwater flow, optimize the size of the horizontal heat exchanger, minimize the initial cost and maximize the operational efficiency. Therefore, in this study, a moving ring source model was established and solved analytically to describe the temperature response of a spiral heat exchanger with groundwater flow. In addition, experiments were carried out to study the soil temperature variation during the operation of a spiral heater with different water velocities. The validity of the proposed model was proven by the good agreement between the experimental and calculated results. The average virtual tube surface temperature variations of single ring sources in two different configurations are discussed. Furthermore, the average virtual tube surface temperatures of multiple ring sources extending from single arrangements were computed and approximation algorithms were introduced to reduce the calculation time. The approximation approach has been proven to run thousands of times faster than the initial method, and the calculation results are in 97% agreement with those of the initial method. In summary, this study provides a useful tool for the design of spiral heat exchangers.     

Natural convection and radiation from vertically-based arrays of vertical, rectangular fins: a numerical model

A two-dimensional numerical model has been developed for the prediction of natural convection and radiation losses from the surfaces of a vertical rectangular fin array protruding perpendicularly outwards from a vertical rectangular base. The individual contributions of the natural convection and radiation were first estimated separately and then summed to give the overall steady-state rate of heat dissipation through the heat exchanger to the ambient air. The theoretical predictions obtained using this model have been compared with experimental observations from previous investigations.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

Experimental study of natural frost formation over a horizontal tube with annular compact fins under natural convection

This paper presents experimental measurements of natural convection heat transfer and frost deposition over a horizontal fin‐tube. Measurements are made for a fin‐tube of diameter 25.4 mm, fin thickness 0.4 mm, fin center diameter 56 mm, and fin spacing 2 mm. For measurements the ambient air temperature and relative humidity are changed from 18 to 25°C and from 35% to 55%, respectively. The tube surface temperature is changed from –5 to –9 °C, and super cooling degrees of 7.5 to 24.5 °C. Results include a visualization of frost deposition growth, frost accumulation rate, and heat transfer rate with respect to time for each experiment. The results show that cold air starts from the upper point and moves downward and frost deposition starts on the fin tips, and grows with time both radially and angularly. Frost growth thickness changes significantly from top to bottom, where the boundary layers of both thermal and concentration increase at the bottom of the fin‐tube section without considerable separation. Frost growth only takes place on the fin's tip and it blocks the heat and mass transfer from the fin surfaces and the tube base which reduces convection and frost growth considerably. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20397     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

Heat transfer enhancement by using a rectangular wing vortex generator on the triangular shaped fins of a plate‐fin heat exchanger

The present numerical analysis pertains to the heat transfer enhancement in a plate‐fin heat exchanger employing triangular shaped fins with a rectangular wing vortex generator on its slant surfaces. The study has been carried out for three different angles of attack of the wing, i.e., 15°, 20° and 26°. The aspect ratio of the wing is not varied with its angle of attack. The flow considered herein is laminar, incompressible, and viscous with the Reynolds number not exceeding 200. The pressure and the velocity components are obtained by solving the continuity and the Navier– Stokes equations by the Marker and Cell method. The present analysis reveals that the use of a rectangular wing vortex generator at an attack angle of 26° results in about a 35% increase in the combined spanwise average Nusselt number as compared to the plate‐triangular fin heat exchanger without any vortex generator. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20285     

Numerical analysis of natural convection heat transfer from rectangular shrouded fin arrays on a horizontal surface

The main aim of this investigation is to discover the effects of clearance parameters on the steady-state heat transfer. In order to solve the three-dimensional elliptic governing equations, a finite volume based CFD code was used. The clearance gap between fin tips and shroud, the base and fin temperatures and the size and configuration of the finned surfaces were varied during the parametric study. The numerical results have been compared to existing experimental values from the literature and the comparison shows a good agreement. It is found that the heat transfer coefficient increases with the increase in the clearance parameter and it approaches to the value of heat transfer coefficient obtained for unshrouded fin arrays.     

Heat transfer in a rectangular chamber with differentially heated horizontal walls: Effects of a vibrating sidewall

Heat transfer in a gas-filled closed enclosure with differentially heated horizontal walls is investigated numerically. One of the sidewalls vibrates with specified frequency and amplitude to induce forced convective flows in the enclosure. The vibrating and the stationary sidewalls are considered to be thermally insulated while the two horizontal walls are differentially heated. To simulate the flow field, the full compressible form of the Navier–Stokes equations is considered and solved by a highly accurate flux-corrected transport algorithm. In the numerical model, temperature dependant heat conductivity and viscosity are taken into account. The presence of acoustic streaming is found to have significant effect on the heat transfer. Also the presence of temperature gradients in the enclosure is found to affect the formation of acoustically induced streaming flows.     

Numerical investigation of laminar natural convective heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure

A numerical simulation was conducted to investigate the steady laminar natural convective heat transfer for air within the horizontal annulus between a heated triangular cylinder and its circular cylindrical enclosure. The Boussinesq approximation was applied to model the buoyancy-driven effect and the governing equations were solved using the finite volume method. Four different Rayleigh numbers and four different radius ratios were considered, and four different inclination angles for the inner triangular cylinder were investigated as well. The computed flow and temperature fields were demonstrated in the form of streamlines and isotherms. Variations of the maximum stream function and the local and average Nusselt numbers were displayed as functions of the above-mentioned parameters. Correlations of the average Nusselt number were proposed based on curve fitting. At constant radius ratio, inclination angles of the inner triangular cylinder are found to have negligible effects on the average Nusselt number.     

Effect of heat generation/absorption on natural convective boundary-layer flow from a vertical cone embedded in a porous medium filled with a non-Newtonian nanofluid

This work is focused on the study of the natural convection boundary-layer flow over a downward-pointing vertical cone in a porous medium saturated with a non-Newtonian nanofluid in the presence of heat generation or absorption. The transformed boundary layer governing equations are solved numerically. The influences of pertinent parameters such as the heat generation or absorption, the solid volume fraction of nanoparticles and the type of nanofluid on the flow and heat transfer rate in terms of Nusselt number are discussed. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. The generalized governing equations derived in this work can be applied to different cases of non-Newtonian fluids with different values of the power-law viscosity index. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.     

Heat transfer by a piezoelectric fan on a flat surface subject to the influence of horizontal/vertical arrangement

This study presents an experimental work concerning the thermal performance of piezoelectric fans. A total of six piezoelectric fans with various blade geometries are made and tested. The influence of geometric parameters, including the horizontal/vertical arrangement, and location of the piezofan, on the performance of piezofans is examined. It is found that the heat transfer augmentation of the piezofan comes from the entrained airflow during each oscillation cycle and the jet-like air stream at the fan tip, yet these two modes are of the same order of magnitude. The heat transfer performance for vertical arrangement shows a symmetrical distribution and peaks at the center region whereas the horizontal arrangement possesses an asymmetrical distribution and shows an early peak at x/L = 0.25. It is also found that the heat transfer performance for horizontal arrangement is not necessarily lower than that of vertical one. Based on the dimensionless analysis to the test results for the all six fans, a correlation applicable for x/L = 0 is proposed. The mean deviation is 4.8% that can well describe the influence of geometrical parameters.     

Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

Numerical techniques are used to study the receptivity to small-amplitude thermal disturbances of the boundary layer flow of air which is induced by a heated vertical flat plate. The fully elliptic nonlinear, time-dependent Navier–Stokes and energy equations are first solved to determine the steady state boundary-layer flow, while a linearised version of the same code is used to determine the stability characteristics. In particular we investigate (i) the ultimate fate of a localised thermal disturbance placed in the region near the leading edge and (ii) the effect of small-scale surface temperature oscillations as means of understanding the stability characteristics of the boundary layer. We show that there is a favoured frequency of excitation for the time-periodic disturbance which maximises the local response in terms of the local rate of heat transfer. However the magnitude of the favoured frequency depends on precisely how far from the leading edge the local response is measured. We also find that the instability is advective in nature and that the response of the boundary layer consists of a starting transient which eventually leaves the computational domain, leaving behind the large-time time-periodic asymptotic state. Our detailed numerical results are compared with those obtained using parallel flow theory.     

Optimal synthesis and design of Heat Recovery Steam Generation (HRSG) via mathematical programming

Thermal efficiency of Combined Cycle Power Plants (CCPPs) depends strongly on the Heat Recovery Steam Generation (HRSG) design which links the gas cycle with the steam cycle. Therefore, the HRSG must be carefully designed in order to maximize the heat exchanged and to improve the overall performance of the plant.In this paper, a mixed integer non-linear programming (MINLP) model to simultaneously optimize the equipment arrangement, geometric design and operating conditions of CCPPs is proposed. General Algebraic Modelling System (GAMS) is used to implement and to solve the mathematical model. The HRSG model involves discrete decisions connected with the geometric design and the selection of tube diameters as well as the length and width of each solid fin. Continuous variables are used to model the operating conditions of the HRSG and steam turbines (ST). The solution strategy for the resulting model comprises two phases: the first one focuses the process optimization but considering only global energy and mass balances and this phase provides initial-bounds values for the second phase where the complete and rigorous model involving discrete decisions is solved. Different case studies with increasing complexity have been successfully solved. Model validation and results obtained from the MINLP model by considering different objective functions are discussed.     

Heat transfer using a correlation by neural network for natural convection from vertical helical coil in oil and glycerol/water solution

A physical-empirical model is designed to describe heat transfer of helical coil in oil and glycerol/water solution. It includes an artificial neural network (ANN) model working with equations of continuity, momentum and energy in each flow. The discretized equations are coupled using an implicit step by step method. The natural convection heat transfer correlation based on ANN is developed and evaluated. This ANN considers Prandtl number, Rayleigh number, helical diameter and coils turns number as input parameters; and Nusselt number as output parameter. The best ANN model was obtained with four neurons in the hidden layer with good agreement (R > 0.98). Helical coil uses hot water for the inlet flow; heat transfer by conduction in the internal tube wall is also considered. The simulated outlet temperature is carried out and compared with the experimental database in steady-state. The numerical results for the simulations of the heat flux, for these 91 tests in steady-state, have a R ≥ 0.98 with regard to experimental results. One important outcome is that this ANN correlation is proposed to predict natural convection heat transfer coefficient from helical coil for both fluids: oil and glycerol/water solution, thus saving time and improving general system performance.     

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

This 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