Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.     

金属泡沫平板结构内对流换热的数值研究

基于Brinkman-Darcy模型和两方程模型,本文对流体在金属泡沫平板通道内的强制对流换热进行了自编程数值模拟,采用体积平均法对流体在金属泡沫内的流动和换热进行宏观处理。模拟结果表明：流体主流速度随孔密度增大而减小,随孔隙率增大而增大;流体相和固体相之间的局部对流换热系数随孔隙率和孔密度增加而增加,金属泡沫对流换热性能随孔隙率增大而减小,随孔密度增大而增大。金属泡沫强化换热的效果十分明显,可以应用于需要强化换热的紧凑式换热器和散热器。     

Performance optimization of a solar driven heat engine with finite-rate heat transfer

An optimal performance analysis for an equivalent Carnot-like cycle heat engine of a parabolic-trough direct-steam-generation solar driven Rankine cycle power plant at maximum power and maximum power density conditions is performed. Simultaneous radiation-convection and only radiation heat transfer mechanisms from solar concentrating collector, which is the high temperature thermal reservoir, are considered separately. Heat rejection to the low temperature thermal reservoir is assumed to be convection dominated. Irreversibilities are taken into account through the finite-rate heat transfer between the fixed temperature thermal reservoirs and the internally reversible heat engine. Comparisons proved that the performance of a solar driven Carnot-like heat engine at maximum power density conditions, which receives thermal energy by either radiation-convection or only radiation heat transfer mechanism and rejects its unavailable portion to surroundings by convective heat transfer through heat exchangers, has the characteristics of (1) a solar driven Carnot heat engine at maximum power conditions, having radiation heat transfer at high and convective heat transfer at low temperature heat exchangers respectively, as the allocation parameter takes small values, and of (2) a Carnot heat engine at maximum power density conditions, having convective heat transfer at both heat exchangers, as the allocation parameter takes large values. Comprehensive discussions on the effect of heat transfer mechanisms are provided.     

Performance analysis and comparison of an Atkinson cycle coupled to variable temperature heat reservoirs under maximum power and maximum power density conditions

In this paper, performance analysis and comparison based on the maximum power and maximum power density conditions have been conducted for an Atkinson cycle coupled to variable temperature heat reservoirs. The Atkinson cycle is internally reversible but externally irreversible, since there is external irreversibility of heat transfer during the processes of constant volume heat addition and constant pressure heat rejection. This study is based purely on classical thermodynamic analysis methodology. It should be especially emphasized that all the results and conclusions are based on classical thermodynamics. The power density, defined as the ratio of power output to maximum specific volume in the cycle, is taken as the optimization objective because it considers the effects of engine size as related to investment cost. The results show that an engine design based on maximum power density with constant effectiveness of the hot and cold side heat exchangers or constant inlet temperature ratio of the heat reservoirs will have smaller size but higher efficiency, compression ratio, expansion ratio and maximum temperature than one based on maximum power. From the view points of engine size and thermal efficiency, an engine design based on maximum power density is better than one based on maximum power conditions. However, due to the higher compression ratio and maximum temperature in the cycle, an engine design based on maximum power density conditions requires tougher materials for engine construction than one based on maximum power conditions.     

Predicting and optimizing the heat transfer performance of radiator with functionalized graphene nanofluids

Accurately predicting the heat transfer characteristics of coolants used in thermal management of energy systems like heat exchangers, power electronics, and heating, ventilation, and air conditioning is indispensable in maintaining its operating conditions within safety limits. Apart from safety, factors such as power consumption and operating cost are the most important constraints to be considered in designing an energy-efficient and cost-effective cooling solution. In this study, the experimental data available from previous research on the use of functionalized graphene-based nanofluids in compact heat exchangers such as the automotive radiator is used to optimize the heat transfer performance parameters like Nusselt number of the nanofluid, the friction factor, and effectiveness of the heat exchanger. A supervised machine learning technique like the artificial neural network is used to obtain the objective functions of the response variables in terms of input features such as Reynolds number, Prandtl number, the volume concentration of nanoparticles in the base fluid, number of transfer units, heat capacity, the density of nanofluid, pressure drop and velocity. On the current dataset, it is found that by using the Bayesian regularization training algorithm and tangent sigmoidal activation function in the neural network, the best accuracies in the prediction can be achieved. Well-known nature-inspired optimization algorithms like genetic algorithms and simulated annealing are used in optimizing the above-mentioned response variables. Both algorithms converged to the same values of the objective functions. The optimum values of Nusselt number, effectiveness, and friction factor are 105.65, 0.506, and 0.0038, respectively, for the given composition of the nanofluid and radiator configuration.     

Effect of heat exchanger material and fouling on thermoelectric exhaust heat recovery

Thermoelectric devices are being investigated as a means of improving fuel economy for diesel and gasoline vehicles through the conversion of wasted fuel energy, in the form of heat, to useable electricity. By capturing a small portion of the energy that is available with thermoelectric devices can reduce engine loads thus decreasing pollutant emissions, fuel consumption, and CO₂ to further reduce green house gas emissions. This study is conducted in an effort to better understand and improve the performance of thermoelectric heat recovery systems for automotive use. For this purpose an experimental investigation of thermoelectrics in contact with clean and fouled heat exchangers of different materials is performed. The thermoelectric devices are tested on a bench-scale thermoelectric heat recovery apparatus that simulates automotive exhaust. It is observed that for higher exhaust gas flowrates, thermoelectric power output increases from 2 to 3.8 W while overall system efficiency decreases from 0.95% to 0.6%. Degradation of the effectiveness of the EGR-type heat exchangers over a period of driving is also simulated by exposing the heat exchangers to diesel engine exhaust under thermophoretic conditions to form a deposit layer. For the fouled EGR-type heat exchangers, power output and system efficiency is observed to be 5-10% lower for all conditions tested.     

Evaluation of heat exchanger surface coatings

Compact heat exchangers are very popular due to their effectiveness, small footprint and low cost. In order to protect heat exchangers in dirty applications, coatings can be applied to the heat transfer surfaces to extend effectiveness and minimize fouling. Coating selection is extremely important since the wrong coating can decrease unit effectiveness, cause more fouling, and/or erode the surface.An experimental investigation of coating effectiveness in compact plate heat exchangers is presented. New, cleaned and coated plate heat exchangers are considered in this study. Heat exchangers have been exposed to untreated lake water for various time periods. Transient effectiveness results compare the rate of fouling for coated and uncoated heat exchangers. Additional results compare deposit weight gain at the end of the test period and transient observations of heat transfer surface appearance. All heat exchanger combinations showed some deposit accumulation for the period considered.Results indicate that the thermal performance of the unit decreases with time, resulting in an undersized heat exchanger. For the conditions considered here, uncoated plates accumulate deposits up to 50% faster than coated plates and show a decrease in performance of up to 40%. Surface coating, exposure time, fluid velocity and concentration of particles can affect fouling.     

Finite time thermodynamic analysis of an irreversible regenerative closed cycle brayton heat engine

This communication presents the parametric study of an irreversible regenerative Brayton cycle with nonisentropic compression and expansion processes for finite heat capacitance rates of external reservoirs. The power output of the cycle is maximized with respect to the working fluid temperatures and the expressions for maximum power output and the corresponding thermal efficiency are obtained. The effect of the effectiveness of the various heat exchangers and the efficiencies of the turbine and compressor, the reservoir temperature ratio and the heat capacitance rate of heating and cooling fluids and the cycle working fluid on the power output and the corresponding thermal efficiency has been studied. It is seen the effect of cold side effectiveness is more pronounced for the power output while the effect of regenerative effectiveness is more pronounced for the thermal efficiency. It is found that the effect of turbine efficiency is more than the compressor efficiency on the performance of these cycles. It is also found that the effect of sink-side heat capacitance rate is more pronounced than the heat capacitance rate on the source side and the heat capacitance rate of the working fluid.     

Constructal tree-shaped parallel flow heat exchangers

The paper reports the performance of balanced two-stream parallel flow heat exchangers, in which each stream flows as a tree network through its allotted space. The two trees are in parallel flow, and are arranged like two palms pressed against each other. The relationships between effectiveness and number of heat transfer units are developed for several parallel tree flow configurations: (i) constructal dichotomous trees covering uniformly a rectangular area, (ii) trees on a disk-shaped area, and (iii) trees on a square-shaped area. In configurations (ii) and (iii) each stream flows between the center and the periphery of the area. Configurations (i) and (ii) are trees with minimal resistance to fluid flow. Configuration (iii) is designed by minimizing the length of each duct in the network. The performance of the parallel flow configurations is compared with the performance of counterflow configurations. The future use of dendritic heat exchangers in devices with maximal heat transport density is proposed.     

Comparison of heat pump performance using fin-and-tube and microchannel heat exchangers under frost conditions

Vapor compression heat pumps are drawing more attention in energy saving applications. Microchannel heat exchangers can provide higher performance via less core volume and reduce system refrigerant charge, but little is known about their performance in heat pump systems under frosting conditions. In this study, the system performance of a commercial heat pump using microchannel heat exchangers as evaporator is compared with that using conventional finned-tube heat exchangers numerically and experimentally. The microchannel and finned-tube heat pump system models used for comparison of the microchannel and finned-tube evaporator performance under frosting conditions were developed, considering the effect of maldistribution on both refrigerant and air sides. The quasi-steady-state modeling results are in reasonable agreement with the test data under frost conditions. The refrigerant-side maldistribution is found remarkable impact on the microchannel heat pump system performance under the frost conditions. Parametric study on the fan speed and the fin density under frost conditions are conducted as well to figure out the best trade-off in the design of frost tolerant evaporators.     

Double-pass flow heat transfer in a parallel-plate channel for improved device performance under uniform heat fluxes

A design of inserting in parallel an impermeable sheet to divide an open conduit into two subchannels for conducting double-pass laminar countercurrent operations under uniform heat fluxes, resulting in substantially improved the heat-transfer rate, has been designed and investigated theoretically by using an eigenfunction expansion in terms of power series for the homogeneous part and an asymptotic solution for the non-homogeneous part. The theoretical results of heat-transfer efficiency enhancement in double-pass parallel-plate heat exchangers are represented graphically and compared with those in the single-pass operations without an impermeable sheet inserted. The influence of the impermeable-sheet location on the heat-transfer efficiency enhancement as well as on the power consumption increment in double-pass operations has also been delineated.     

Heat transfer performance and exergy analyses of a corrugated plate heat exchanger using metal oxide nanofluids

Heat exchangers have been widely used for efficient heat transfer from one medium to another. Nanofluids are potential coolants, which can afford excellent thermal performance in heat exchangers. This study examined the effects of water and CuO/water nanofluids (as coolants) on heat transfer coefficient, heat transfer rate, frictional loss, pressure drop, pumping power and exergy destruction in the corrugated plate heat exchanger. The heat transfer coefficient of CuO/water nanofluids increased about 18.50 to 27.20% with the enhancement of nanoparticles volume concentration from 0.50 to 1.50% compared to water. Moreover, improvement in heat transfer rate was observed for nanofluids. On the other hand, exergy loss was reduced by 24% employing nanofluids as a heat transfer medium with comparing to conventional fluid. Besides, 34% higher exergetic heat transfer effectiveness was found for 1.5 vol.% of nanoparticles. It has a small penalty in the pumping power. Hence, the plate heat exchanger performance can be improved by adapting the working fluid with CuO/water nanofluids.     

Effects of fin shapes on heat transfer in microchannel heat sinks

In the present study, compact water cooling of high‐density, high‐speed, very‐large‐scale integrated (VLSI) circuits with the help of microchannel heat exchangers were investigated analytically. This study also presents the result of mathematical analysis based on the modified Bessel function of laminar fluid flow and heat transfer through combined conduction and convection in a microchannel heat sink with triangular extensions. The main purpose of this paper is to find the dimensions of a heat sink that give the least thermal resistance between the fluid and the heat sink, and the results are compared with that of rectangular fins. It is seen that the triangular heat sink requires less substrate material as compared to rectangular fins, and the heat transfer rate per unit volume has been almost doubled by using triangular heat sinks. It is also found that the effectiveness of the triangular fin is higher than that of the rectangular fin. Therefore, the triangular heat sink has the ability to dissipate large amounts of heat with relatively less temperature rise for the same fin volume. Alternatively, triangular heat sinks may thus be more cost effective to use for cooling ultra‐high speed VLSI circuits than rectangular heat sinks.     

Simple method for estimation of effectiveness in one tube pass and one shell pass counter-flow heat exchangers

In one tube pass and one shell pass counter-flow heat exchangers, when both streams change temperature by different amounts, the effectiveness is defined as the temperature change for the stream with lower capacity divided by the maximum possible change and the effectiveness depends on the number of transfer units and the thermal capacity ratio. In this paper, an attempt has been made to formulate a simple-to-use method which is easier than existing approaches, less complicated and with fewer computations for accurate and rapid estimation of effectiveness in one tube pass and one shell pass counter-flow heat exchangers as a function of number of transfer units and the thermal capacity ratio. The proposed method permits estimating the exit temperature for a one tube pass and one shell pass counter-flow heat exchanger without a trial-and-error calculation. The average absolute deviations between the reported data and the proposed correlations are found to be less than 2% demonstrating the excellent performance of proposed correlation. The tool developed in this study can be of immense practical value for engineers and scientists to have a quick check on the effectiveness in one tube pass and one shell pass counter-flow heat exchangers at various conditions without opting for any experimental measurements. In particular, practice engineers would find the predictive tool to be user-friendly with transparent calculations involving no complex expressions.     

A synthesis of fluid and thermal transport models for metal foam heat exchangers

Metal foam heat exchangers have considerable advantages in thermal management and heat recovery over several commercially available heat exchangers. In this work, the effects of micro structural metal foam properties, such as porosity, pore and fiber diameters, tortuosity, pore density, and relative density, on the heat exchanger performance are discussed. The pertinent correlations in the literature for flow and thermal transport in metal foam heat exchangers are categorized and investigated. Three main categories are synthesized. In the first category, the correlations for pressure drop and heat transfer coefficient based on the microstructural properties of the metal foam are given. In the second category, the correlations are specialized for metal foam tube heat exchangers. In the third category, correlations are specialized for metal foam channel heat exchangers. To investigate the performance of the foam filled heat exchangers in comparison with the plain ones, the required pumping power to overcome the pressure drop and heat transfer rate of foam filled and plain heat exchangers are studied and compared. A performance factor is introduced which includes the effects of both heat transfer rate and pressure drop after inclusion of the metal foam. The results indicate that the performance will be improved substantially when a metal foam is inserted in the tube/channel.     

A review of the applications of heat pipe heat exchangers for heat recovery

The waste heat recovery by heat pipes is accepted as an excellent way of saving energy and preventing global warming. This paper is a literature review of the application of heat pipes heat exchangers for the heat recovery that is focused on the energy saving and the enhanced effectiveness of the conventional heat pipe (CHP), two-phase closed thermosyphon (TPCT) and oscillating heat pipe (OHP) heat exchangers. The relevant papers were allocated into three main categories, and the experimental studies were summarized. These research papers were analyzed to support future works. Finally, the parameters of effectiveness of the CHP, TPCT and OHP heat exchangers were described. This review article provides additional information for the design of heat pipe heat exchangers with optimum conditions in the heat recovery system.     

Heat-transfer, pressure-drop and performance relationships for in-line, staggered, and continuous plate heat exchangers

Basic heat-transfer and pressure-drop results for laminar airflow through arrays of in-line or staggered plate segments have been determined from numerical solutions of the fluid flow and energy equations. The results depend on only a single dimensionless parameter which encompasses the relevant geometrical and fluid flow quantities. Application of the results was made to compare the performance of the two types of segmented-plate arrays with each other and with the parallel-plate channel. At constant mass flow rate and constant heat-transfer surface area, the heat-transfer effectiveness . of the segmented arrays is appreciably higher than that of the parallel-plate channel, both in the range of small and intermediate effectiveness values. In addition, for a fixed heat duty corresponding to an intermediate value and for a constant mass flow, the heat-transfer area of the segmented arrays is only about a third of that for the parallel-plate channel. Under constant pumping power and constant surface area conditions, the heat transfer for the segmented arrays exceeds that for the parallel-plate channel when the effectiveness of the latter is less than 0.65–0.75. Under most conditions, the staggered array yields better performance than the in-line array, but situations are identified where the reverse is true.     

Comparison of solar heat exchangers

This paper summarizes and compares the theoretical heat transfer characteristics of solar heat exchangers. Comparisons are made with a number of heat exchanger targets used in solar energy applications. The efficiencies of flat-plate, circular flat-plate, cylindrical, cylindrical annulus, spherical annulus and elliptic cylindrical heat exchangers are presented for comparison. Simplified lumped analysis expressions are derived for these heat exchangers, and the results compare very well with the more complicated distributive analysis results over a range of Nusselt numbers frequently encountered in solar energy applications. The influence of thermal and velocity profiles is also discussed. From this study it appears that the annular geometry yields higher efficiencies especially at large Nusselt numbers. A secondary aim of this paper is to provide a summary of the heat transfer characteristics of heat exchangers with different geometries in sufficient detail that would allow a designer of solar energy equipment to quickly make calculations for a particular application.     

Influence of channel geometry on the performance of a counter flow microchannel heat exchanger

Microchannel heat exchangers (MCHE) can be made with channels of various geometries. Their size and shape may have considerable effect on the thermal and hydraulic performance of a heat exchanger. In this paper numerical simulation is carried out to solve 3D developing flow and 3D conjugate heat transfer of a balanced counter flow microchannel heat exchanger (CFMCHE) to evaluate the effect of size and shape of channels on the performance of CFMCHE for the same volume of heat exchanger. The effect of shape of the channels on its performance is studied for different channel cross-sections such as circular, square, rectangular, iso-triangular and trapezoidal. Results show that for the same volume of a heat exchanger, increasing the number of channels lead to increase in both effectiveness and pressure drop. Moreover circular channels give the best overall performance (thermal and hydraulic) among various channel shapes. New correlations are developed to predict the value of heat exchanger effectiveness and performance index as a function of relative size of channels with overall heat exchanger volume, Reynolds number and thermal conductivity ratio.     

Compact potential of exhaust heat exchangers for engine waste heat recovery using metal foams

To improve the practicability of the waste heat recovery system for internal combustion engines, the compact potential of exhaust heat exchangers using metal foams is investigated. In the present study, the performance of compact exhaust heat exchangers is compared with that of a conventional shell and tube heat exchanger in a real test bench. Both heat transfer and pressure drop performance are considered when assessing the performance of heat exchangers because these two factors normally show a trade‐off relationship when designing exhaust heat exchangers. Compared with the conventional heat exchanger, the compact heat exchanger can achieve a similar pressure drop, and at the same time the heat transfer is increased by 30%, whereas the volume and the weight are each reduced by 2/3. The performance of compact heat exchangers with six types of Ni metal foams is also investigated under different mass flow rates and thicknesses of the porous layer. Results show that the optimum compact heat exchanger enhances the comprehensive performance 1.9 times compared with original one. This study shows that metal foams have great potential in realizing a compact exhaust heat exchanger for engine waste heat recovery.