Entransy Dissipation Minimization Research Articles

Topology optimization and bionic analysis of heat sink fin configuration based on additive manufacturing technology

Fins are extensively employed in heat sinks for high heat flux components. In this study, three distinct objective functions, namely temperature gradient minimization (TO-I type fin), average temperature minimization (TO-II type fin), and entransy dissipation minimization (TO-III type fin), are established for topology optimization design of the heat sink fin structure to effectively minimize the temperature of the heat source. By conducting a comparative analysis of the configuration features and thermal performance of optimized fins with different objective functions, it is evident that the TO-I type fin exhibits superior thermal performance. When the fin volume fraction φ is 0.3, the heat source center temperature of TO-I type fin is 2.67 K and 4.55 K lower than that of TO-II type fin and TO-III type fin, respectively. Meanwhile, the bionic analysis of the optimized fins under different objective functions using fractal theory reveals that the fractal dimension of the TO-I type fin is 1.4038, which is the closest to the average fractal dimension of many kinds of leaf veins in nature (D¯f= 1.3762), which indicates that the optimized fins have the bionic characteristics most similar to those of the leaf blade. Finally, the three topology optimization fins were fabricated using boundary-filtering optimization 3D printing technology. Comparative tests verified the advantage of minimizing the temperature gradient as the objective function of topology optimization and demonstrated its potential for thermal performance and lightweighting applications, especially under high heat source operating conditions.

Optimization of the volume-to-point heat conduction problem with automatic differentiation based approach

Heat conduction optimization problems, such as the volume-to-point problem, have always been core issues in industry and electronics cooling. Existing approaches either limit the solution space by using priori structures, or use manual operation rules to adjust the solutions gradually. And there does not exist a general way to deal with arbitrary objectives. The present study develops a novel method by using automatic differentiation technique. The heat conduction process is converted into a recurrent convolutional neural network equivalently, and the automatic differentiation technique is utilized to calculate the gradient of the final objective with respect to the thermal conductivity field directly. Based on these techniques, the thermal conductivity field is optimized directly to minimize the hot spot temperature. Cases with different heat sinks are introduced to test the proposed optimization method, respectively. Results demonstrate that the average temperature and hot spot temperature are both reduced remarkably after using the proposed method. Furthermore, compared with the previous iteration methods based on entropy generation minimization or entransy dissipation minimization, the proposed method produces similar results when minimizing the average temperature, and reduces the hot spot temperature rising by 17% ∼ 33% when minimizing the hot spot temperature. The optimization method based on automatic differentiation technique exhibits the potential capability of handling with various types of objectives.

Comparative studies on constructal optimizations of discrete heat generation components based on entransy dissipation minimization and maximum temperature minimization

A three-dimensional (3D) turbulent heat dissipation model of cylindrical discrete heat generation components is established on a conductive basis. The whole solid section is set in a square channel with adiabatic walls, and the components, cooled by clean air flowing through the channel, are arranged in a line with equal spacings. The influences of the heat conductivities of the components, intensities of heat sources and velocity of fluid flow on the maximum temperature (MT) of components, the equivalent thermal resistance (ETR) based on entransy dissipation of the heat dissipation system, and the averaged Nu number are investigated with the constructal theory considering variable properties, compressibility and viscous dissipation of air. The total heat generation rate and the total heat conductivity of heat sources are fixed as the constraint conditions. The circumstances in which heat generation rates and heat conductivities of heat sources are unequal are considered. The results show that for the fixed total heat generation rate of heat sources, despite MT or ETR that is taken as the performance index for thermal design, there exists an optimal intensity distribution of heat sources for the best thermal performance of the system. In fact, for different objectives, the optimal intensity distributions of heat sources are corresponding to the best match between the distributions of heat sources and the distributions of temperature gradient. There are different optimal distributions for different velocities of the fluid flow and different optimization objectives. Besides, the averaged Nu number increases with the increase of intensity difference in heat sources, which means that the convective heat transfer is enhanced, but this phenomenon is relatively weak when the velocity of fluid flow is low. For the fixed total heat generation rate of heat sources, when the intensities of heat sources are equal and the thermal conductivities of heat sources are lower than that of the conductive basis, increasing heat conductivities of the heat sources can evidently improve thermal performance of the system; the MT can be lowest when the conductivities of heat sources increase along the fluid flow; and the ETR is lowest when the conductivities of heat sources are equal. Both the MT and the ETR decrease with the increasing velocity of fluid flow. The results can provide some theoretical guidelines for the practical thermal design of the electronic components with different materials and different heat generation rates.

Entransy dissipation minimization for generalized heat exchange processes

This paper investigates the MED (Minimum Entransy Dissipation) optimization of heat transfer processes with the generalized heat transfer law q ∝ (Δ(Tn))m. For the fixed amount of heat transfer, the optimal temperature paths for the MED are obtained. The results show that the strategy of the MED with generalized convective law q ∝ (ΔT)m is that the temperature difference keeps constant, which is in accordance with the famous temperature-difference-field uniformity principle, while the strategy of the MED with linear phenomenological law q ∝ Δ(T−1) is that the temperature ratio keeps constant. For special cases with Dulong-Petit law q ∝ (ΔT)1.25 and an imaginary complex law q ∝ (Δ(T4))1.25, numerical examples are provided and further compared with the strategies of the MEG (Minimum Entropy Generation), CHF (Constant Heat Flux) and CRT (Constant Reservoir Temperature) operations. Besides, influences of the change of the heat transfer amount on the optimization results with various heat resistance models are discussed in detail.

Optimization for a Thermochemical Energy Storage-reactor based on Entransy Dissipation Minimization

Abstract In this paper, a thermochemical energy storage-reactor (TESR) is optimized based on entransy theory to reduce the irreversibility of heat transfer and reaction. Two types of optimization problems including fixed chemical energy conversion and fixed total heat flux are discussed detail. Firstly, the formula of entransy dissipation for the process of TTES is derived based on the entransy balance equation, then a casing TTES with methane-water reforming is optimized for entransy dissipation minimization (EDM). The optimized results based on EDM are also compared with that based on entropy production minimization (EPM). The results show that: there are some similarities and differences between EDM and EPM for optimizing the TESR. The similarity is that the heating temperature along the reaction flow should be non-linear, to decrease the total irreversibility. The difference is that the EDM is focused on decreasing the irreversibility of heat transfer, and the EPM is focused on decreasing the irreversibility of reaction. The total heat consumption based on EDM is lower than that based on EPM when the chemical energy conversion is certain, and the chemical energy conversion based on EDM is higher than that based on EPM when the total heat flux is certain.

The application of exergy destruction minimization in convective heat transfer optimization

An approach of heat transfer enhancement by reducing the irreversibility of process is discussed theoretically. The irreversibility of heat transfer process has been analysed with exergy. The irreversibility of heat transfer process can be expressed with exergy destruction. Other than entropy generation minimization and entransy dissipation minimization, a new approach called exergy destruction minimization is proposed to optimize heat transfer process based on the analysis. By setting exergy destruction rate as an optimization objective and fluid power consumption as a constraint condition, a momentum equation with an additional volume force is constructed through functional variation to numerically simulate convective heat transfer in coupling with energy equation. The approach of exergy destruction minimization is applied in the optimization of convective heat transfer and numerical calculation is carried out to validate this approach in circular tubes. The optimum velocity field with 380% increase in Nu number and 5% increase in flow resistance f is found by the numerical calculation on optimization equations. The results disclose that longitudinal swirl flow with multi-vortexes appears in the flow field, which leads to heat transfer enhancement. The more the vortexes are, the higher Nu number can be gotten. It is found that longitudinal swirl flow with multi-vortexes is a flow pattern with good heat transfer performance in circular tubes. The results of numerical calculation can be used to guide the design for tube inserts.

Optimization of Horizontal Plate Fin Heat Sink in Natural Convection for Electronics Cooling by Simulated Annealing Algorithm

In this study, the simulated annealing (SA) algorithm was adopted to optimize the geometry of horizontal plate fin heat sink by the extreme entransy dissipation principle. The alculation of the entransy dissipation rate was presented in detail. Using the entransy dissipation rate as the objective condition, the geometry optimization of the fin heat sink was conducted. To verify the results, the heat source temperature and the entropy generation rate were also calculated in the procedure. It is found that the entrasy dissipation rate, entropy generation and heat source temperature have the similar trend. The extreme entransy dissipation principle and minimization of entropy generation play similar roles in the geometry optimization of plate fin heat sink.

“Entransy,” and Its Lack of Content in Physics

Here, I show that “entransy” has no meaning in physics, because, at bottom, it rests on the false claim that in order to transfer heat to a solid body of thermodynamic temperature T, the heat transfer must be proportional to T. Entransy “dissipation” is a number proportional to well known measures of irreversibility such as entropy generation and lost exergy (destroyed available work). Furthermore, the “principle of entransy dissipation minimization” adds nothing to existing work based on minimum entropy generation, minimum thermal resistance, and constructal law. The broader trend illustrated by the entransy hoax is that it is becoming easy to take an existing idea, change the keywords, and publish it as new.

Influence of heat leakage on entransy dissipation minimization of heat exchanger

Model of a heat transfer process in heat exchanger with heat leakage is established in this paper. Both the heat flux between the hot and cold fluids and the heat leakage between the cold fluid and outside environment are assumed to obey Newtonian heat transfer law. On condition that the net amount of heat transferred by the cold fluid is given, the optimal temperature configurations of the hot and cold fluids for the minimum entransy dissipation of the heat transfer process are derived by using the optimal control theory. Optimal paths are also compared with the conventional strategies of heat transfer under constant hot fluid temperature and constant heat flux rate operation. The results obtained in this paper could provide some theoretical guidelines for the optimal design and operation of real heat exchangers.

Entransy Dissipation Minimization for Isothermal Crystallization Processes with Diffusive Mass Transfer Law

A class of isothermal crystallization process with the given total mass of crystals is investigated. The mass transfer process is assumed to obey the diffusive mass transfer law [ g∝Δ(c)], and the optimal concentration configuration for the minimum entransy dissipation of the crystallization process is obtained by applying optimal control theory. Numerical examples are provided, and the obtained results are also compared to those of the minimum entropy generation, constant concentration and constant mass flux operations. The results show that 2/3 power of the net mass of crystals for the minimum entransy dissipation of the process change with the time linearly, and the entransy dissipation rate of the process keeps constant, which coincides with the principle of equipartition of entransy dissipation and is significant different from that obtained for the minimum entropy generation of the process; the entransy dissipation for the mass transfer strategy of constant concentration is smaller than that for the mass transfer strategy of constant mass flux; both the entransy dissipation and the entropy generation for the two mass transfer strategies of the minimum entransy dissipation and the minimum entropy generation are smaller than those for the other two mass transfer strategies. The entropy generation characterizes the irreversibility of energy conversion processes, and the mass entransy dissipation characterizes the irreversibility of mass transfer processes. Since the crystallization process is independent of the energy conversion, so the optimization principle should be entransy dissipation minimization.

Entransy dissipation minimization for one-way isothermal mass transfer processes with a generalized mass transfer law

A class of one-way isothermal mass transfer processes is investigated in this paper. Based on the definition of mass entransy, the entransy dissipation function, which reflects the irreversibility of the mass transfer ability loss, is derived. The optimality condition for the minimum entransy dissipation of the mass transfer process with a generalized mass transfer law is obtained by applying an optimal control theory. Special cases for the linear [g∝Δ(μ)] and the diffusive [g∝Δ(c)] mass transfer laws are obtained based on the general optimization results. The obtained results are also compared with strategies of minimum entropy generation, constant concentration ratio and constant concentration difference operations. The results obtained herein can provide some theoretical guidelines for optimal design and operation of practical mass transfer processes.

Entransy dissipation minimization for optimization of heat exchanger design

In this paper, by taking the water-water balanced counterflow heat exchanger as an example, the entransy dissipation theory is applied to optimizing the design of heat exchangers. Under certain conditions, the optimal duct aspect ratio is determined analytically. When the heat transfer area or the duct volume is fixed, analytical expressions of the optimal mass velocity and the minimal entransy dissipation rate are obtained. These results show that to reduce the irreversible dissipation in heat exchangers, the heat exchange area should be enlarged as much as possible, while the mass velocity should be reduced as low as possible.

Constructal entransy dissipation minimization of round tube heat exchanger cross-section

Cross-section of round tube heat exchanger with porous materials is optimized by taking entransy dissipation rate minimization as optimization objective. The non-dimensional mean temperature differences of the cross-section with and without high conducting fins inserted are derived, respectively. By taking the radius ratio R in/ R out between inner radius and outer radius as a design variable, the entransy dissipation rates are minimized. The heat transfer ability of the heat exchanger without high conducting fins inserted is improved as R in/ R out increases, and the non-dimensional mean temperature difference decreases from 2/(3 π) to 1/(3 π). The heat transfer ability of the heat exchanger with high conducting fins inserted is much better than that without high conducting fins inserted, and the entransy dissipation rate varies a little when R in/ R out apart from 1.

Entransy dissipation minimization for a class of one-way isothermal mass transfer processes

A class of one-way isothermal mass transfer processes with Fick’s diffusive mass transfer law [g ∝ Δ(c)] is investigated in this paper. Based on the definition of the mass entransy, the entransy dissipation function which reflects the irreversibility of mass transfer ability loss is derived. The optimal concentration allocations of the key components corresponding to the highand low-concentration sides for the minimum entransy dissipation of the mass transfer process are obtained by applying optimal control theory and compared with the strategies of the minimum entropy generation, constant mass transfer flux (constant concentration difference), and constant concentration ratio (constant chemical potential difference). The results are as follows. For the optimal mass transfer strategy of the minimum entransy dissipation, the product of the square of the key component concentration difference between the high- and the low-concentration sides and the inert component concentration at the low-concentration side is a constant, while for that of the minimum entropy generation, the ratio of the square of the key component concentration difference between the high- and the low-concentration sides to the key component concentration at the low-concentration side is a constant; when the mass transfer process is not involved in energy conversion process, the optimization principle should be the minimum entransy dissipation; the mass transfer strategy of constant concentration difference is superior to that of constant concentration ratio. The results obtained in this paper can provide some theoretical guidelines for optimal designs and operations of practical mass transfer processes.

The entransy dissipation minimization principle under given heat duty and heat transfer area conditions

Under given heat duty and heat transfer area conditions, the equipartition of the entransy dissipation (EoED) principle, the equipartition of the temperature difference (EoTD) principle, and the equipartition of the heat flux (EoHF) principle are applied to the optimization design of a heat exchanger with a variable heat transfer coefficient. The results show that the difference between the results obtained using the EoED and EoTD principles is very small, far smaller than that between the results obtained using the EoED and EoHF principles. The correct entransy dissipation minimization principle is chosen to optimize the parameters in the hot and cold fluids in a two-fluid heat exchanger, under given heat duty and heat transfer area conditions. The results indicate that the proper choice of the two alternative fluids has an important role in the successful application of the entransy dissipation minimization principle. The fluid that could improve the total heat transfer coefficient should be chosen, or the fluid that makes the temperature profiles of the hot and cold fluids parallel and decreases the temperature difference between the hot and cold fluids after optimization simultaneously, could be the proper one.

Principle of equipartition of entransy dissipation for heat exchanger design

In the present work, a principle of equipartition of entransy dissipation (EoED) for heat exchanger design is established, which says that for a heat exchanger design with given heat duty and heat transfer area, the total entransy dissipation rate reaches the minimum when the local entransy dissipation rate is uniformly distributed along the heat exchanger. When the heat transfer coefficient is unfixed, the total entransy dissipation obtained by the EoED principle is less than that obtained by the principle of equipartition of temperature difference (EoTD). Furthermore, the exchanger effectiveness obtained by the EoED principle is larger than that obtained by the EoTD principle. When the heat transfer coefficient is fixed, the EoED principle is equivalent to the EoTD principle. We show that the equipartition of entropy production (EoEP) and EoED principles give rise to difference in entropy generation and entransy dissipation for a heat exchanger optimization design. The discrepancies are caused by distinct features of entropy production minimization and entransy dissipation minimization principles, the former is to optimize the design of heat exchanger by making the lost available work minimum, while the latter is not involved with heat-work conversion. It is found that the entropy generation number is not suitable for evaluating heat exchanger performance, since it directly depends on the inlet and outlet temperatures of working fluids. On the contrary, the entransy dissipation number is not directly related to the inlet and outlet temperatures of working fluids. Therefore, the entransy dissipation number is more suitable for serving as a criterion to evaluate heat exchanger performance.

Entransy dissipation minimization for liquid-solid phase change processes

The liquid-solid phase change process of a simple one-dimensional slab is studied in this paper. By taking entransy dissipation minimization as optimization objective, the optimal external reservoir temperature profiles are derived by using optimal control theory under the condition of a fixed freezing or melting time. The entransy dissipation corresponding to the optimal heat exchange strategies of minimum entransy dissipation is 8/9 of that corresponding to constant reservoir temperature operations, which is independent of all system parameters. The obtained results for entransy dissipation minimization are also compared with those obtained for the optimal heat exchange strategies of minimum entropy generation and constant reservoir temperature operations by numerical examples. The obtained results can provide some theoretical guidelines for the choice of optimal cooling or heating strategy in practical liquid-solid phase change processes.

Constructal entransy dissipation minimization for “volume-point” heat conduction based on triangular element

By taking equivalent thermal resistance, which reflects the average heat conduction effect and is defined based on entransy dissipation, as optimization objective, the “volume to point” constructal problem based on triangular element of how to discharge the heat generated in a fixed volume to a heat sink on the border through relatively high conductive link is re-analyzed and re-optimized in this paper. The constructal shape of the control volume with the best average heat conduction effect is deduced. For the same parameters, the constructs based on minimization of entransy dissipation and the constructs based on minimization of maximum temperature difference are compared, and the results show that the constructs based on entransy dissipation can decrease the mean temperature difference better than the constructs based on minimization of maximum temperature difference. But with the increase of the number of order, the mean temperature difference does not always decrease, and there exists some fluctuations. Because the idea of entransy describes heat transfer ability more suitably, the optimization results of this paper can be put to engineering application of electronic cooling.

Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective

The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For two cases (body with heat generation and body heated externally) of a solid conducting wall with an open cavity, a dimensionless equivalent thermal resistance based on entransy dissipation definition was taken as the optimization objective to optimize the model constructal geometry. Numerical results validated the necessity and feasibility of the presented method. Comparisons of the numerical results based on minimization of dimensionless maximum thermal resistance and minimization of dimensionless equivalent thermal resistance, respectively, showed that there was no obvious difference between the two results when the volume fraction Φ occupied by cavity was small, but the difference between the two results increased with the increases of Φ and the body aspect ratio H/L for any model. The optimal cavities for bodies heated externally were more slender than those for bodies with heat generation. Heat origin had obvious effect on the global performance of heat transfer. The entransy dissipation of body heated externally increased 2―3 times than that of body with heat generation, indicating that the global performance of heat transfer weakened. The method presented herein provides some guidelines for some relevant thermal design problems.

Constructal optimization on T-shaped cavity based on entransy dissipation minimization

The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For a heat transfer model of a rectangular solid wall with an open T-shaped cavity, a dimensionless equivalent thermal resistance based on entransy dissipation is taken as optimization objective, and constructal optimization for the model is carried out when the system volume, the cavity volume and the volume of rectangle occupied by T-shaped cavity are fixed. Numerical results indicate that the optimal geometry construct of cavity can be schemed out based on entransy dissipation extremum principle. The formulation of dimensionless global (maximum) thermal resistance presented in a literature is modified; some new rules which are different from those reported in the literature are obtained based on the minimization of the modified objective. Comparisons of the numerical results show that the optimal system constructs deduced respectively from the two thermal resistance objectives are very different. The optimization by taking equivalent thermal resistance minimization as objective can more effectively reduce mean temperature difference of heat transfer than the optimization by taking maximum thermal resistance minimization as objective, so that the performance of heat transfer for the total system can be improved. The more freedom the cavity has, the better the total system performance is. The correlations of the equivalent thermal resistance and the maximum thermal resistance of the system and three geometric degrees of freedom are found by using function fitting.