Multiobjective optimization and analytical comparison of single‐ and 2‐stage (series/parallel) thermoelectric heat pumps

The thermodynamic modeling of various thermoelectric devices does not consider the influence of nonlinear Thomson effect. It leads to incomplete solutions of the heat transfer equations and serious analytical errors. On the other hand, appropriate balance among various performance parameters of thermoelectric devices is also required to improve its operating characteristics. In this context, the thermodynamic modeling on the basis of first/second laws for multielement single‐ and 2‐stage (series/parallel) thermoelectric heat pumps, including the influence of Thomson effect in combination with Fourier heat conduction and Joule effects, is done. The optimization of the heat pumps has been carried out to obtain the optimal values of 4 input parameters by using the second version of nondominated sorting genetic algorithm in matrix laboratory. The optimal values from Pareto frontier of dual/triple objectives are obtained through 3 decision makings viz. Shannon's entropy, Fuzzy Bellman‐Zadeh, and TOPSIS. It is observed that triple‐objective optimization gives much lower difference between ideal and obtained solution, termed as deviation index, as compared with the single/dual one. Additionally, sensitivity analysis has been carried out to study the influence of Thomson effect on heating capacity and coefficient of performance of the pumps. To validate the evolutionary algorithm, the optimal values are compared with analytical ones from previous literature.     

The influence of the Thomson effect on the performance of a thermoelectric cooler

The temperature distribution of a thermoelectric cooler under the influence of the Thomson effect, the Joule heating, the Fourier’s heat conduction, and the radiation and convection heat transfer is derived. The influence of the Thomson effect on the temperature profiles, on the fraction of the Joule’s heat that flows back to the low-temperature side, and consequently on the maximum attainable temperature difference and the maximum allowable heat load are emphasized and explored. The results suggest that the cooling efficiency of a thermoelectric cooler can be improved not only by increasing the figure-of-merit of the thermoelectric materials but also by taking advantage of the Thomson effect. A possible development direction for the thermoelectric materials is thus given.     

New technique for short term storage sizing

In the present work, a thermal evaluation and optimisation for the components of a solar water heating system was studied. An implicit graphical method was developed to estimate the optimum A_c and V on the basis of the load requirements as well as maximum system efficiency. This method depends on the temperature of hot water extracted for the load, as well as the annual solar factor. The developed method was applied to estimate the optimum dimensions when a daily quantity of hot water (175 l) at 60°C was extracted. The final results showed that with the given load requirements and a solar factor 70%, the optimum A_c and V were 16 m² and 700 l, respectively.     

Cooling potential of an evaporative cooling tower: Parametric studies

Dependence of the cooling potential of an evaporative cooling tower on the tower parameters (height h, cross-sectional area A_t, evaporative pad area A_p, packing factor of evaporating pads F_p and flow resistance f) has been investigated. The performance of the tower is studied for two different climates, namely hot-dry and composite, typified by Jodhpur and Delhi.     

Segmented thermoelectric generator: exponential area variation in leg

The innovative design of segmented thermoelectric generator with exponential area variation is introduced. Thermal efficiency and power output are assessed for various values of the design parameter (a = (L/x) ln[A_a/A(x)], where A_a is constant, and a is the dimensionless geometric parameter, L is the pin length, and A(x) is the pin cross‐sectional area), external load parameter (R_L/R₀, ratio of external electrical resistance to reference electrical resistance), and temperature parameter (θ = T_low/T_high, ratio of cold junction temperature to high junction temperature). The device efficiency obtained is validated through the previous experimental data for various hot and cold junction temperature differences. The findings reveal that thermal efficiency resulted from the current study agrees well with the experimental data. The innovative design of the segmented thermoelectric generator with exponentially decaying pin configuration enhances the thermal efficiency and output power as compared with the device having a single material pin configuration. Increasing temperature ratio results in the reduction in the thermal efficiency and the output power of thermoelectric generator. In addition, lowering the external load parameter improves the thermal efficiency and the output power of the thermoelectric device. The design parameter that maximizes the thermal efficiency of the thermoelectric generator does not maximize the device output power.     

Numerical simulation of nanostructured thermoelectric generator considering surface to surrounding convection

Thermoelectric systems (TE) can directly convert heat to electricity and vice-versa by using semiconductor materials. Therefore, coupling between heat transfer and electric field potential is important to predict the performance of thermoelectric generator (TEG) systems. This paper develops a general two-dimensional numerical model of a TEG system using nanostructured thermoelectric semiconductor materials. A TEG with p-type nanostructured material of Bismuth Antimony Telluride (BiSbTe) and n-type Bismuth Telluride (Bi₂Te₃) with 0.1 vol.% Silicon Carbide (SiC) nanoparticles is considered for performance evaluations. Coupled TE equations with temperature dependant transport properties are used after incorporating Fourier heat conduction, Joule heating, Seebeck effect, Peltier effect, and Thomson effect. The effects of temperature difference between the hot and cold junctions and surface to surrounding convective on different output parameters (e.g., thermal and electric fields, power generation, thermal efficiency, and current) are studied. Selected results obtained from current numerical analysis are compared with the results obtained from analytical model available in the literature. There is a good agreement between the numerical and analytical results. The numerical results show that as temperature difference increases output power and amount of current generated increase. Moreover, it is quite apparent that convective boundary condition deteriorates the performance of TEG.     

Experimental and theoretical investigation of a solar heating system with heat pump

In this study, the performance of a solar heating system with a heat pump was investigated both experimentally and theoretically. The experimental results were obtained from November to April during the heating season. The experimentally obtained results are used to calculate the heat pump coefficient of performance (COP), seasonal heating performance, the fraction of annual load met by free energy, storage and collector efficiencies and total energy consumption of the systems during the heating season. The average seasonal heating performance values are 4.0 and 3.0 for series and parallel heat pump systems, respectively. A mathematical model was also developed for the analysis of the solar heating system. The model consists of dynamic and heat transfer relations concerning the fundamental components in the system such as solar collector, latent heat thermal energy storage tank, compressor, condenser, evaporator and meteorological data. Some model parameters of the system such as COP, theoretical collector numbers (N_c), collector efficiency, heating capacity, compressor power, and temperatures (T₁, T₂, T₃, T_T) in the storage tank were calculated by using the experimental results. It is concluded that the theoretical model agreed well with the experimental results.     

Double‐diffusive natural convection in a partially heated enclosure using a nanofluid

This paper analyzes numerically the effect of double‐diffusive natural convection of a water–Al₂O₃ nanofluid in a partially heated enclosure with Soret and Dufour coefficients. The top horizontal wall has constant temperature T_c, while the bottom wall is partially heated T_h, with T_h > T_c . The concentration in the top wall is maintained higher than the bottom wall C_c < C_h. The remaining bottom wall and the two vertical walls are considered adiabatic. Water is considered as the base fluid. The governing equations are solved by the Penalty Finite Element Method using Galerkin's weighted residual scheme. The effect of the parameters, namely, Rayleigh number and solid volume fraction of the nanoparticles on the flow pattern and heat and mass transfer has been depicted. Comprehensive average Nusselt and Sherwood numbers, average temperature and concentration, and mid‐height horizontal and vertical velocities at the middle of the cavity are presented as functions of the governing parameters mentioned above. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21010     

Heat-pump-assisted dryer part 2: Experimental study

The performance of an experimental heat-pump-assisted dryer under operating conditions of some practical interest was studied. The system was operated using R11 and R12. The approach velocity of air to the evaporator and the superheat of the working fluid at the exit of the evaporator were identified as the critical parameters for optimization. The system was evaluated with respect to coefficient of performance (COP) and specific energy consumption (SEC). The (COP)_A, and (SEC) values obtained using R11 were 3.5 and 3500 kJ/kg, respectively, and the corresponding values for R12 were 2.5 and 1800 kJ/kg. In spite of the lower (COP)_A, for R12, the corresponding (SEC) values were better because the system could be operated without any additional electrical heating with R12.     

Analysis on the cooling performance of the thermoelectric micro-cooler

Numerical analysis has been carried out to figure out the performance of the thermoelectric micro-cooler with the three-dimensional model. A small-size and column-type thermoelectric cooler is considered and Bi₂Te₃ and Sb₂Te₃ are selected as the n- and p-type thermoelectric materials, respectively. The thickness of a thermoelectric element considered is 5–20 μm. The effect of parameters such as the temperature difference, the current, the thickness of a thermoelectric element, and the number of thermoelectric pairs on the performance of the cooler has been investigated. The predicted results show that the performance can be improved for the thick element with the large number of thermoelectric pairs or the small cross-sectional area of the element.     

An exact heat transfer analysis of spherical products subjected to forced-air cooling

The thermal analysis of forced-air cooling processes being of primary concern, an experimental and analytical study program was undertaken to investigate the heat transfer during the cooling of figs as spherical food products. The process conditions were analysed according to a mathematical model to gain a better understanding of the product's behaviour. The heat transfer between the product and air was influenced by conduction inside the product, convection outside the product, radiation, respiratory heat rate (internal heat generation), and moisture evaporation at the surface of the product. These situations were considered as three cases, such as h = h_c, h = h_c + h_c, and h = h_c, + h_r + h_e. The four various air velocities of 1.1, 1.5, 1.75, and 2.5 m/s were applied in the experimental study. The results obtained by the mathematical model in the estimation of the heat transfer rates from the products were compared with the experimental data, and the best agreement was found for the third case (h = h_c + h_r + h_e). The fastest cooling was accomplished with the highest airflow velocity.     

Parametric study on the thermoelectric conversion performance of a concentrated solar‐driven thermionic‐thermoelectric hybrid generator

A concentrated solar‐driven thermionic‐thermoelectric hybrid generator composed of solar heat collector, thermionic generator (TIG), thermoelectric generator (TEG), and radiator is introduced in this paper. A theoretical model of thermoelectric conversion performance for the hybrid generator is built up based on the heat source of the concentrated solar radiation rather than isothermal heat source. Based on the model, the impacts of related parameters on the internal temperature distributions, output power, and efficiency have been discussed. Moreover, the optimal operating conditions of the TIG‐TEG hybrid device at its maximum output power and efficiency have been determined. Results show that when cascading the TEG with the TIG, there is very little change of the TIG cathode temperature in most conditions, namely, T_C ≈ T_C′. Meanwhile, the anode temperature becomes higher, and the TEG cold end temperature T₂ is close to the anode temperature T_A′ for the single TIG system, ie, T_A > T_A′ ≈ T₂. In theory, the optimal concentrated solar radiation I₀ for the maximum output power P_max and the maximum efficiency η_max differs, which are I_0,P = 2.5 × 10⁶ W/m² and I_0,η = 2 × 10⁶ W/m², respectively, whereas the output power and efficiency of the TIG‐TEG hybrid system simultaneously reach their maximum values when the optimal TIG anode temperature T_A,opt = 1025 K, the optimal TIG output voltage V_opt = 2 V, and the optimal ratio of load resistance to internal resistance (R₂/R)_opt = 2. However, in practice, the parameter values of I₀, Φ_A, and T_A should be strictly controlled under 1.8 × 10⁶ W/m², 1.4 eV, and 660 K, respectively. Generally, the maximum output power and efficiency of the hybrid TIG‐TEG system are, respectively, 35% and 4% higher than that of the single TIG.     

A Finite Volume Analysis of Thermoelectric Generators

ABSTRACT

The electric power produced by a thermoelectric generator (TEG) is strongly influenced by the applied heat sink. While a TEG is aimed at harvesting waste heat, the optimization of the efficiency of the heat sink is a key task for the design of waste heat recovery systems implementing TEG. A TEG model is proposed and implemented in an open source toolbox for field operation and manipulation (OpenFOAM) for the purpose of performing optimizations of the heat sink, using a commercially available TEG as basis. This model includes the multi-physics thermoelectric coupled effects. Conservation principles of energy and current are considered simultaneously. This includes the thermal and electric conduction, Seebeck effect, Peltier effect, Thomson effect, and Joule heating. Particular attention is given to a proper modeling of the boundary conditions. The thermoelectric model is implemented in such a way that it can readily be combined with other physical models in OpenFOAM. The model is validated by comparing the predictions to analytical results, measurements as well as the simulation data of other authors.     

MODELING AND OPTIMIZATION OF SINGLE-ELEMENT BULK SiGe THIN-FILM COOLERS

Abstract

Modeling and optimization of bulk SiGe thin-film coolers are described. Thin-film coolers can provide large cooling power densities compared to commercial thermoelectrics. Thin-film SiGe coolers have been demonstrated with maximum cooling of 4°C at room temperature and with cooling power density exceeding 500 W/cm². Important parameters in the design of such coolers are investigated theoretically and are compared with experimental data. Thermoelectric cooling, joule heating, and heat conduction are included in the model as well as non-ideal effects such as contact resistance, geometrical effects, and three-dimensional thermal and electrical spreading resistance of the substrate. Simulations exhibit good agreement with experimental results for bulk Si and SiGe thin-film coolers. It turned out that in many spot cooling applications using two n- and p-elements electrically in series and thermally in parallel does not give significant improvement over single leg elements. This is in contrast to conventional thermoelectric modules and is due to the aspect ratio and special geometry of thin film coolers. With optimization of SiGe thin-film cooler, simulations predict it can provide over 16°C with cooling power density of over 2000 W/cm².     

Constructal design associated with genetic algorithm to minimize the maximum deflection of thin stiffened steel plates

This paper deals with the application of stochastic technique allied to the constructal design (CD) method and computational modeling for the optimization of composed plates reinforced by stiffeners. More specifically, it seeks to determine the optimal geometric configuration of the stiffened plate that minimizes its maximum deflection. For this purpose, a simply supported rectangular plate (with no stiffeners) was adopted as a reference. Then, a set of geometric configurations was proposed, through the application of CD method, by transforming a volume fraction (ϕ) of the reference plate into longitudinal and transverse stiffeners, maintaining the total volume, in-plane dimensions, boundary conditions, and loading. Regarding the optimization procedure, the genetic algorithm (GA) was chosen as the optimization method, and the geometric parameters considered as degrees of freedom were as follows: the number of longitudinal (N_ls) and transverse (N_ts) stiffeners; the thickness of the longitudinal (t_ls) and transverse (t_ts) stiffeners; and longitudinal and transverse stiffeners' heights ratio (h_ts/h_ls). Moreover, several values of ϕ were considered. Results indicated a great influence of the geometry on the mechanical behavior of the stiffened plates, as the optimal geometric configuration obtained here led to a reduction of over 98% in the maximum deflection in comparison with the reference plate.     

Testing of box-type solar cooker: Second figure of merit F2 and its variation with load and number of pots

The performance of a box-type solar cooker can be represented in terms of two figures of merit, F₁ and F₂. The second figure F₂ is a controlling factor in the sensible heating of a load. The present work validates F₂ by computing this figure from experimental data by two different procedures and comparing the results. An attempt has also been made to provide some guidelines for selecting a suitable temperature interval for determination of F₂. The results of some experiments to study the effect of number of pots and the load on F₂ have also been presented. It is recommended that for standardization tests should be conducted at full load.     

Optimization of the irreversible Stirling heat engine

The effects of inefficiencies in the compression, expansion and regeneration processes on engine performance have been evaluated theoretically for a Stirling heat engine operating in a closed regenerative thermodynamic cycle. The irreversible cycle has been optimized by using the maximum power density technique. Maximized power and maximized power density are obtained for different n_ex, τ, α_c, α_h, η_c, η_ex and η_reg values. The maximum efficiencies have been found very close to the values corresponding to the maximum power density conditions but far from the values at maximum power. It has been found that the engines designed by considering the maximum power density have high efficiencies and small sizes under the same prescribed conditions. Copyright © 1999 John Wiley & Sons, Ltd.     

Thermodynamic modelling of a solid state thermoelectric cooling device: Temperature–entropy analysis

This article presents the temperature–entropy analysis, where the Thomson effect bridges the Joule heat and the Fourier heat across the thermoelectric elements of a thermoelectric cooling cycle to describe the principal energy flows and performance bottlenecks or dissipations. Starting from the principles of thermodynamics of thermoelectricity, differential governing equations describing the energy and entropy flows of the thermoelectric element are discussed. The temperature–entropy (T–S) profile in a single Peltier element is pictured for temperature dependent Seebeck coefficient and illustrated with data from commercial available thermoelectric cooler.     

Experimental investigation and numerical analysis for one-stage thermoelectric cooler considering Thomson effect

This study conducts experimental investigation and numerical analysis for one-stage thermoelectric cooler (TEC) considering Thomson effect. Three Seebeck coefficient models are applied to numerically and experimentally study the Thomson effect on TEC. Results show that higher current, higher hot side temperature, or lower heat load can increase the temperature difference between the cold and hot sides. Opposite trends are found for COP. Specific current should be chosen as the upper threshold in thermoelectric cooler design. The cooling performance can improve when the Thomson heat maintains positive.