Optimization principles for convective heat transfer

Optimization for convective heat transfer plays a significant role in energy saving and high-efficiency utilizing. We compared two optimization principles for convective heat transfer, the minimum entropy generation principle and the entransy dissipation extremum principle, and analyzed their physical implications and applicability. We derived the optimization equation for each optimization principle. The theoretical analysis indicates that both principles can be used to optimize convective heat-transfer process, subject to different objectives of optimization. The minimum entropy generation principle, originally derived from the heat engine cycle process, optimizes the convective heat-transfer process with minimum usable energy dissipation focusing on the heat–work conversion. The entransy dissipation extremum principle however, originally for pure heat conduction process, optimizes the heat-transfer process with minimum heat-transfer ability dissipation, and therefore is more suitable for optimization of the processes not involving heat–work conversion. To validate the theoretical results, we simulated the convective heat-transfer process in a two-dimensional foursquare cavity with a uniform heat source and different temperature boundaries. Under the same constraints, the results indicate that the minimum entropy production principle leads to the highest heat–work conversion while the entransy dissipation extremum principle yields the maximum convective heat-transfer efficiency.     

Thermodynamic optimization of a coiled tube heat exchanger under constant wall heat flux condition

In this paper the second law analysis of thermodynamic irreversibilities in a coiled tube heat exchanger has been carried out for both laminar and turbulent flow conditions. The expression for the scaled non-dimensional entropy generation rate for such a system is derived in terms of four dimensionless parameters: Prandtl number, heat exchanger duty parameter, Dean number and coil to tube diameter ratio. It has been observed that for a particular value of Prandtl number, Dean number and duty parameter, there exists an optimum diameter ratio where the entropy generation rate is minimum. It is also found that with increase in Dean number or Reynolds number, the optimum value of the diameter ratio decreases for a particular value of Prandtl number and heat exchanger duty parameter.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimum wall thickness ratio based on the minimization of entropy generation in a viscous flow between parallel plates

The influence of the geometrical and physical parameters on entropy generation for a viscous flow between infinite parallel walls of finite thickness is studied by solving the momentum and energy conservation equations. The conjugate heat transfer problem in the fluid and solid walls is solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid–wall interfaces. Analytic solutions for the velocity and temperature fields in the fluid and walls are used to calculate the local and global entropy generation rate. Conditions under which this quantity is minimized are determined for certain suitable combination of geometrical and physical parameters of the system. Special attention has been given to the effect of the wall thickness on the entropy generation rate. It is found that the global entropy generation reaches a minimum for specific values of the wall thickness ratio, when the other parameters are fixed.     

Predicting the capacity of a heat exchanger by a thermal network method

In this paper a thermal network method using the effective specific heat model of a refrigerant with phase change is proposed for predicting the capacity of a plate‐fin and tube‐type heat exchanger. The effective specific heat model can attain an accurate result of a condenser's heat exchanging capacity when it has a small number of elements. By comparing calculated results with those of an experiment, it is found that the error in the condenser's calculated capacity is less than 1% when the range of subcool temperature is from 15 to 22 K at the outlet of refrigerant flow. © 2002 Scripta Technica, Heat Trans Asian Res, 31(2): 128–140, 2002; DOI 10.1002/htj.10021     

The application of field synergy number in shell-and-tube heat exchanger optimization design

In the present work the field synergy principle is applied to the optimization design of the shell-and-tube heat exchanger with segmental baffles. The field synergy number which is defined as the indicator of the synergy between the velocity field and the heat flow is taken as the objective function. The genetic algorithm is employed to solve the heat exchanger optimization problems with multiple design variables. The field synergy number maximization approach for heat exchanger optimization design is thus formulated. In comparison with the initial design, the optimal design leads to a significant cost cut on the one hand and an improvement of the heat exchanger performance on the other hand. The comparison with the traditional heat exchanger optimization design approach with the total cost as the objective function shows that the field synergy number maximization approach is more advantageous.     

A numerical model for thermoelectric generator with the parallel-plate heat exchanger

This paper presents a numerical model to predict the performance of thermoelectric generator with the parallel-plate heat exchanger. The model is based on an elemental approach and exhibits its feature in analyzing the temperature change in a thermoelectric generator and concomitantly its performance under operation conditions. The numerical simulated examples are demonstrated for the thermoelectric generator of parallel flow type and counter flow type in this paper. Simulation results show that the variations in temperature of the fluids in the thermoelectric generator are linear. The numerical model developed in this paper may be also applied to further optimization study for thermoelectric generator.     

Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

Effect of fluid thermal properties on the heat transfer characteristics in a double-pipe helical heat exchanger

Heat transfer characteristics of a double-pipe helical heat exchanger were numerically studied to determine the effect of fluid thermal properties on the heat transfer. Two studies were performed; the first with three different Prandtl numbers (7.0, 12.8, and 70.3) and the second with thermally dependent thermal conductivities. Thermal conductivities of the fluid were based on a linear relationship with the fluid temperature. Six different fluid dependencies were modeled. Both parallel flow and counterflow configurations were used for the second study.Results from the first study showed that the inner Nusselt number was dependent on the Prandtl number, with a greater dependency at lower Dean numbers; this was attributed to changing hydrodynamic and thermal entry lengths. Nusselt number correlations based on the Prandtl number and a modified Dean number are presented for the heat transfer in the annulus. Results from the second part of the study showed that the Nusselt number correlated better using a modified Dean number. The counterflow configuration had higher heat transfer rates than the parallel flow, but the ratio of these differences was not different when comparing thermally dependent properties and thermally independent properties.     

Discharge of a thermal storage tank using an immersed heat exchanger with an annular baffle

A number of solar domestic hot water systems and many combined space and water heating systems have heat exchangers placed directly in the storage fluid to charge and/or discharge the tank. Operation of the heat exchanger produces a buoyancy-driven flow within the storage fluid. With a view toward controlling the flow field to increase heat transfer, a cylindrical baffle is inserted in a 350 l cylindrical storage tank. The baffle creates a 40 mm annular gap adjacent to the tank wall. A 10 m-long, 0.3 m² copper coil heat exchanger is placed in the gap. The effects of the baffle on the transient heat transfer, delivered water temperature, heat exchanger effectiveness, and temperature distribution within the storage fluid are presented during discharge of initially thermally stratified and fully mixed storage tanks. The baffle increases the storage side convective heat transfer to the heat exchanger by 20%. This increase is attributed to higher storage fluid velocities across the heat exchanger.     

Application of intensified heat transfer for the retrofit of heat exchanger network

A number of design methods have been proposed for the retrofit of heat exchanger networks (HEN) during the last three decades. Although considerable potential for energy savings can be identified from conventional retrofit approaches, the proposed solutions have rarely been adopted in practice, due to significant topology modifications required and resulting engineering complexities during implementation. The intensification of heat transfer for conventional shell-and-tube heat exchangers can eliminate the difficulties of implementing retrofit in HEN which are commonly restricted by topology, safety and maintenance constraints, and includes high capital costs for replacing equipment and pipelines. This paper presents a novel design approach to solve HEN retrofit problems based on heat transfer enhancement. A mathematical model has been developed to evaluate shell-and-tube heat exchanger performances, with which heat-transfer coefficients and pressure drops for both fluids in tube and shell sides are obtained. The developed models have been compared with the Bell-Delaware, simplified Tinker and Wills-Johnston methods and tested with the HTRI® and HEXTRAN® software packages. This demonstrates that the new model is much simpler but can give reliable results in most cases. For the debottlenecking of HEN, four heuristic rules are proposed to identify the most appropriate heat exchangers requiring heat transfer enhancements in the HEN. The application of this new design approach allows a significant improvement in energy recovery without fundamental structural modifications to the network.     

Fully developed thermal behaviors for parallel flow microchannel heat exchanger

The hydrodynamics and thermal behaviors of the flow in micro-heat exchanger parallel-plate are investigated numerically. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. Effects of different parameters, such as, Knudsen number (Kn), heat capacity ratio (Cr), the effectiveness (e) and number of transfer units (NTU) are investigated. It is found that both the velocity slip and the temperature jump at the walls increase with increasing Kn. On the other hand, at low values of Kn, the NTU increases with increasing Cr, but at high values of Kn the NTU decreases with increasing Cr. With regard to the effect of Cr on e, it is found that increasing Cr leads to a reduction in e and for all Kn.     

Exergy transfer effectiveness on heat exchanger for finite pressure drop

In this paper, exergy transfer effectiveness is defined to describe the performance of heat exchangers operating above/below the surrounding temperature with/without finite pressure drop. It is discussed systemically that the effects of heat transfer units number, the ratio of the heat capacity of cold fluids to that of hot fluids and flow patterns on exergy transfer effectiveness of heat exchangers. Furthermore, the results of exergy transfer effectiveness with a finite pressure drop are compared with those without pressure drop when different objective media, such as ideal gas and incompressible liquid, etc. are applied. The detailed comparisons of the exergy transfer effectiveness with heat transfer effectiveness are also performed for the parallel flow, counter flow and cross flow heat exchangers operating above/below the surrounding temperature.     

A novel design of a heat exchanger for a metal-hydrogen reactor

A metal-hydride reactor equipped by a spiral heat exchanger is experimentally studied. The inserted exchanger provides significant insights into the problem of minimizing the total storage time by manipulating the operating parameters. Performance studies are carried out by varying the supply pressure, volume of the tank, absorption temperature, and overall heat transfer coefficient.     

The thermal modeling of a matrix heat exchanger using a porous medium and the thermal non-equilibrium model

Heat transfer and fluid flow characteristics through a porous medium were investigated using numerical simulations and experiment. For the numerical simulations two models were created: a two-dimensional numerical model and a Fluent™ computational fluid dynamics (CFD) porous media model. The experimental investigation consisted of a flow channel with a porous medium section that was heated from below by a heat source. The results of the numerical models were compared to the experimental data in order to determine the accuracy of the models. The numerical model was then modified to better simulate a matrix heat exchanger. This numerical model then generated temperature profiles that were used to calculate the heat transfer coefficient of the matrix heat exchanger and develop a correlation between the Nusselt number and the Reynolds number.     

Hydrogen storage system based on hydride materials incorporating a helical-coil heat exchanger

Metal hydrides offer the potential to store hydrogen at modest pressures and temperatures with high volumetric efficiencies. The process of charging hydrogen into a metal powder to form the hydride is exothermic. The heat released by the reaction must be removed quickly in order to maintain a rapid charging rate. An effective method for heat removal is to embed a heat exchanger within the metal hydride bed. Here, we investigate the effectiveness of a helical coil heat exchanger tube to remove the heat generated during the absorption process. This paper presents a three-dimensional mathematical model formulated in Ansys Fluent 12.1 to evaluate the transient heat and mass transfer in a cylindrical metal hydride tank embedded with a helical-coil cooling tube. We present results from a parametric study of hydrogen storage efficiency as a function of helical coil pitch and convective heat transfer coefficient (h) within the cooling tube. We also explore the effect of adding aluminum foam to enhance the thermal conductivity of the metal hydride. The parametric study reveals that the mass of stored hydrogen is less sensitive to the coil pitch when aluminum foam is added. It is also found that the absorption rate increases with h as expected, although the rate of improvement diminishes at high values of h. Results were examined at filling times of 3 and 6 min to draw conclusions about the overall effectiveness of this hydrogen storage system. At 3 min, it is found that the addition of 5% Al foam is optimal, and h = 1000 W/m²-K is sufficient to bring the metal hydride to saturation; under these conditions a non-dimensional pitch of 0.5 maximizes the hydrogen absorption. Adding Al foam beyond 5% does not improve volumetric efficiency as the Al foam begins to displace the active hydrogen-absorbing material.     

Analysis and thermal response test for vertical ground heat exchanger with two U‐loop configuration

An in situ thermal response test (TRT) is applied to evaluate the thermal performance of the vertical ground heat exchanger (GHX) with two U‐loop configuration. A line source method is used to derive the thermal conductivity and borehole thermal resistance from the measured data. Analyses are made to improve the interpretation of TRT data and to investigate the active area of interest in the borehole. Load tests of the GHX are performed to examine the daily variations of ground and mean fluid temperatures associated with daily intermittent operation of ground source heat pump system. Results show that while the ground thermal conductivity of two U‐loop GHX is moderately increased, the borehole thermal resistance is significantly reduced, compared with the single U‐loop GHX. Of the borehole thermal resistance components evaluated, the grout thermal resistance is the most governing one in the borehole heat transfer (77% of the total borehole thermal resistance), whereas the convective thermal resistance in the tube is almost negligible (less than 2%). Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of heat exchanger on the performance of a shallow solar pond water heater

In this communication, a mathematical model has been developed to predict the performance of a shallow solar pond water heater with a heat exchanger. Explicit heat balance equations are written for the plate temperature and water tank temperature, as well as for the heat extracting fluid temperature, by properly taking into account the absorption of solar radiation in the body of pond water. It is seen that efficiencies may be achieved as high as 60% at water flow rates of 0.1 – 0.2 kg/s m². Thereafter, the efficiency becomes almost constant at higher flow rates.     

Experimental performance evaluation of a novel heat exchanger for a solar hot water storage system

The performance of a novel heat exchanger unit (‘Solasyphon’) developed for a solar hot water storage system was experimentally investigated. The ‘Solasyphon’ is a simple ‘bolt-on’ heat exchange unit that can be integrated externally to a traditional single-coil hot water cylinder (HWC) avoiding the costly replacement of an existing HWC with a twin-coil HWC. The installation cost of a ‘Solasyphon’ is lower compared to a traditional HWC thus offers greater cost effectiveness. A data acquisition system was designed to compare the thermal performance of an integrated ‘Solasyphon’ HWC with a traditional twin-coil HWC under controlled simulated conditions. The analysis was based on experimental data collected under various operating conditions including different primary supply temperatures (solar simulated); primary supply patterns and draw off patterns. The results indicated that the ‘Solasyphon’ delivered solar heated water directly to the top of the HWC producing a stratified supply at a useable temperature. Under variable solar conditions the ‘Solasyphon’ would transfer the heat gained by a solar collector to a HWC more efficiently and quickly than a traditional HWC. The ‘Solasyphon’ system can reduce installation costs by 10–40% and has a lower embodied energy content due to less material replacement.     

Second law analysis and heat transfer in a cross-flow heat exchanger with a new winglet-type vortex generator

In this paper a second law analysis of a cross-flow heat exchanger (HX) is studied in the presence of a balance between the entropy generation due to heat transfer and fluid friction. The entropy generation in a cross-flow HX with a new winglet-type convergent–divergent longitudinal vortex generator (CDLVG) is investigated. Optimization of HX channel geometry and effect of design parameters regarding the overall system performance are presented. For the HX flow lengths and CDLVGs the optimization model was developed on the basis of the entropy generation minimization (EGM). It was found that increasing the cross-flow fluid velocity enhances the heat transfer rate and reduces the heat transfer irreversibility. The test results demonstrate that the CDLVGs are potential candidate procedure to improve the disorderly mixing in channel flows of the cross-flow type HX for large values of the Reynolds number.