Generalized constructal optimization of strip laminar cooling process based on entransy theory

A strip laminar cooling process is investigated in this paper. Entransy theory and generalized constructal optimization are introduced into the optimization. Total water flow amount(WFA) in the laminar cooling zone(LCZ) and complex function are taken as the constraint and optimization objective, respectively. The entransy dissipation(ED) and maximum temperature different(MTD) of the strip are simultaneously considered in the complex function. WFA distributions of the headers in the LCZ are optimized. The effects of the total WFA, strip thickness and cooling water temperature on the optimal results are analyzed.The optimal cooling scheme is the eleventh cooling mode for the considered total 257 cooling schemes, and the complex function,ED and MTD of the strip are decreased by 11.59%, 5.59% and 17.58% compared with the initial cooling scheme, respectively.The total WFA and strip thickness have the obvious influences on the optimal cooing scheme, but the cooling water temperature has no influence in the parameter analysis range of this paper. The “generalized optimal construct” derived by minimum complex function shows a compromise between the energy retention and quality of the strip.     

A multi-objective study on the constructal design of non-uniform heat generating disc cooled by radial- and dendritic-pattern cooling channels

A three-dimensional disc model with non-uniform heat generating is built. A series of cooling channels are inserted to cool this disc which is strewn in a hierarchical pattern. To reveal thermal and flow characteristics, a composite objective function comprised of the maximum temperature difference(MTD) and pumping power is constructed. The deployment pattern of cooling channels contains two cases, i.e., the radial-pattern and dendritic-pattern. By capitalizing on constructal design method together with finite element method, the diameter of radial-pattern cooling channels is optimized in the first place. Next, the diameter, angle coefficient and length coefficient of dendritic-pattern cooling channels are three degrees-of-freedom to be stepwise optimized at different heat generating conditions. Furthermore, NSGA-II algorithm is introduced into the multiobjective problem. Upon obtaining its Pareto optimal solution set, Topsis method is invoked to yield the optimal solutions under given weighted coefficients. The heat generation over the entire body and the volume ratio of cooling channels operate as the primary constraints. Based on these premises, constructal design will be stepwise performed by varying three degrees-offreedom. The obtained results state that more heating components or devices should be installed as close to the cooling water inlet as possible. This can further reduce MTD at the same cost of pumping power, thereby improve thermal and flow performance and prolong the lifespan of devices. As optimized with two degrees-of-freedom, the MTD is reduced by 18.6%compared with the counterpart obtained from single degree-of-freedom optimization, while the pumping power is increased by 59.8%. As optimized with three degrees-of-freedom, the MTD is decreased by 6.2% compared with the counterpart from two degrees-of-freedom optimization, while the pumping power is increased by 3.0%. It is manifest that when two sub-objectives form a composite objective, the performance improvement of one sub-objective will inevitably elicit the vitiation of the alternative.     

Constructal design for a steam generator based on entransy dissipation extremum principle

Steam generator is optimized by applying entransy dissipation extremum principle and constructal theory and adopting analyti-cal method.The obtained results show that the optimal spacing between adjacent tubes,the mass flow rate of gas and the maximum entransy dissipation rate all depend on the dimensionless diameter of one tube,the dimensionless pressure difference number and the dimensionless length of flow channel of gas.Besides the three dimensionless groups,the optimal numbers of riser tubes and downco...     

Performance optimization of a class of combined thermoelectric heating devices

Science China Technological Sciences - A detailed model of thermally-driven combined thermoelectric (TE) heating device is established. The device consists of two-stage TE heat pump (TTEH) and...     

Influences of external heat transfer and Thomson effect on the performance of TEG-TEC combined thermoelectric device

A thermodynamic model of a thermoelectric generator (TEG)-driven thermoelectric cooler (TEC) device considering Thomson effect and external heat transfer (HT) is established based on the combination of non-equilibrium and finite time thermodynamic theories. The expressions of cooling capacity and coefficient of performance (COP) are obtained. Performances are compared with and without considering Thomson effect using numerical optimization method. The influences of Thomson effect on the optimal performances, optimum allocations of thermoelectric (TE) element number and HT surface area are discussed. The results indicate that Thomson effect decreases the maximum cooling capacity and COP. More TE elements should be allocated to TEG, and more HT area should be allocated to the heat exchanger (HEX) of TEG, the hot-side HEX of TEG and the cold-side HEX of TEC in the design of the device considering Thomson effect. The results obtained can be used to help design TEG-TEC devices.     

Constructal entransy dissipation rate minimization of a rectangular body with nonuniform heat generation

Based on construtal theory, a nonuniform heat generation problem in a rectangular body is investigated in this paper. Entransy dissipation rate (EDR) is taken as the optimization objective. The optimal body shapes with constant and variable widths of the high conductivity channel (HCC) are derived. For the rectangular first order assembly (RFOA) with constant cross-section HCC, the shape of the RFOA and width ratio of the HCCs are optimized, and the double minimum EDR is obtained. The heat transfer performance of the RFOA becomes worse when the nonuniform coefficient increases. For the RFOA with variable cross-section HCC, the EDR of the RFOA can be minimized for four times. Compared the optimal construct based on minimum EDR of the RFOA with that based on minimum maximum temperature difference, the shape of the former optimal construct is tubbier, and the average temperature difference is lower. In the practical design of electronic devices, when the thermal safety is ensured, the constructal design scheme of the former optimal construct can be adopted to improve the global heat transfer performance of an electronic device.     

Thermodynamic analyses and optimization for thermoelectric devices: The state of the arts

Thermoelectric effect is the most efficient way to convert electric energy directly from the temperature gradient. Thermoelectric effect-based power generation, cooling and heating devices are solid-stated, environmentally friendly, reliable, long-lived, easily maintainable, and easy to achieve miniaturization and integration. So they have unparalleled advantages in the aerospace, vehicle industry, waste heat recovery, electronic cooling, etc. This paper reviews the progress in thermodynamic analyses and optimizations for single- and multiple-element, single- and multiple-stage, and combined thermoelectric generators, thermoelectric refrigerators and thermoelectric heat pumps, especially in the aspects of non-equilibrium thermodynamics and finite time thermodynamics. It also discusses the developing trends of thermoelectric devices, such as the heat sources of thermoelectric generators, multi-stage thermoelectric devices, combined thermoelectric devices, and heat transfer enhancement of thermoelectric devices.     

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 ∝(△(T~n))~m T. 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 ∝(△T)~m T 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 ∝△(T~(-1)) is that the temperature ratio keeps constant. For special cases with Dulong-Petit law q ∝(△T)~(1.25) and an imaginary complex law q ∝(△(T~4))~(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.     

Constructal multidisciplinary optimization of electromagnet based on entransy dissipation minimization

Based on entransy dissipation, the mean temperature difference of solenoid (electromagnet) with high thermal conductivity material inserted is deduced, which can be taken as the fundament for heat transfer optimization using the extremum principle of entransy dissipation. Then, the electromagnet working at steady state (constant magnetic field, constant heat generating rate per unit volume) is optimized for entransy dissipation minimization (i.e. mean temperature difference minimization) with and without vo...     

“Volume-Point” heat conduction constructal optimization with entransy dissipation minimization objective based on rectangular 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 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 elemental area and the first order construct assembly, when the thermal current density in the high conductive link is linear with the length, the optimized shapes of assemble based on the minimization of entransy dissipation are the same as those based on minimization of maximum temperature difference, and the mean temperature difference is 2/3 of the maximum temperature difference. For the second and higher order construct assemblies, the thermal current densities in the high conductive link are not linear with the length, and the optimized shapes of assemble based on the minimization of entransy dissipation are different from those based on minimization of maximum temperature difference. 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 the order, the mean temperature difference does not always decrease, and there exist some fluctuations. Because the idea of entransy describes the heat transfer ability more suitably, all of the heat conduction constructal problems may be re-optimized based on it. Supported by the Program for New Century Excellent Talents in University of China and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)