Energy conversion efficiency of thermoelectric power generators with cylindrical legs

Thermoelectric power generators (TEGs) have been attracted increasing attention recently due to their capability of converting waste heat into useful electric energy without hazardous emissions. This paper develops a theoretical model to analyze the thermoelectric performance of TEGs with cylindrical legs. The influence of heat convection loss between lateral surfaces of thermoelectric legs and ambient environment on the energy conversion efficiency is investigated. For the idealized model, closed-form solutions of optimal electric current, maximum power output and maximum energy conversion efficiency are obtained, a new dimensionless impact factor H is introduced to capture the heat convection effect. The impact factor H depends on the ratio of heat conductivity to heat convection coefficient and geometry size of thermoelectric legs, as well as the temperature ratio of heat sink to hot source. The performance can be evaluated by the figure of merit, impact factor H and temperature gradient across the hot source and heat sink for a well-designed TEG with cylindrical legs. For the case of considering contact resistance, it is found that there exists an optimal leg's height for maximum energy conversion efficiency due to the heat convection on lateral surfaces of thermoelectric leg. The proposed theoretical model in this paper will be very helpful in the designing of actual TEG devices.

Data-Driven Modeling of Geometry-Adaptive Steady Heat Convection Based on Convolutional Neural Networks

Heat convection is one of the main mechanisms of heat transfer, and it involves both heat conduction and heat transportation by fluid flow; as a result, it usually requires numerical simulation for solving heat convection problems. Although the derivation of governing equations is not difficult, the solution process can be complicated and usually requires numerical discretization and iteration of differential equations. In this paper, based on neural networks, we developed a data-driven model for an extremely fast prediction of steady-state heat convection of a hot object with an arbitrary complex geometry in a two-dimensional space. According to the governing equations, the steady-state heat convection is dominated by convection and thermal diffusion terms; thus the distribution of the physical fields would exhibit stronger correlations between adjacent points. Therefore, the proposed neural network model uses convolutional neural network (CNN) layers as the encoder and deconvolutional neural network (DCNN) layers as the decoder. Compared with a fully connected (FC) network model, the CNN-based model is good for capturing and reconstructing the spatial relationships of low-rank feature spaces, such as edge intersections, parallelism, and symmetry. Furthermore, we applied the signed distance function (SDF) as the network input for representing the problem geometry, which contains more information compared with a binary image. For displaying the strong learning and generalization ability of the proposed network model, the training dataset only contains hot objects with simple geometries: triangles, quadrilaterals, pentagons, hexagons, and dodecagons, while the testing cases use arbitrary and complex geometries. According to the study, the trained network model can accurately predict the velocity and temperature field of the problems with complex geometries, which has never been seen by the network model during the model training; and the prediction speed is two orders faster than the CFD. The ability of accurate and extremely fast prediction of the network model suggests the potential of applying reduced-order network models to the applications of real-time control and fast optimization in the future.

Analysis of transient mixed convection in a horizontal channel partially heated from below

The heat convection phenomenon has been investigated numerically (mathematically) for a channel located horizontally and partially heated at a uniform heat flux with forced and free heat convection. The investigated horizontal channel with a fluid inlet and the enclosure was exposed to the heat source from the bottom while the channel upper side was kept with a constant temperature equal to fluid outlet temperature. Transient, laminar, incompressible and mixed convective flow is assumed within the channel. Therefore, the flow field is estimated using Navier Stokes equations, which involves the Boussinesq approximation. While the temperature field is calculated using the standard energy model, where, Re, Pr, Ri are Reynolds number, Prandtl number, and Richardson number, respectively. Reynolds number (Re) was changed during the test from 1 to 50 (1, 10, 25, and 50) for each case study, Richardson (Ri) number was changed during the test from 1 to 25 (1, 5, 10, 15, 20, and, 25). The average Nusselt number (Nuav) increases exponentially with the Reynold number for each Richardson number and the local Nusselt number (NuI) rises in the heating point. Then gradually stabilized until reaching the endpoint of the channel while the local Nusselt number increases with a decrease in the Reynolds number over there. In addition, the streamlines and isotherms patterns in case of the very low value of the Reynolds number indicate very low convective heat transfer with all values of Richardson number. Furthermore, near the heat source, the fluid flow rate rise increases the convection heat transfer that clarified the Nusselt number behavior with Reynolds number indicating that maximum Nu No. are 6, 12, 27 and 31 for Re No. 1, 10, 25 and 50, respectively

Simulation of coupled transient heat and water vapor transfer in porous fiber membrane with different fiber orientations and porosity

The transfer process of heat and water vapor in a porous fiber membrane was investigated through the simulation of a 3D model for optimizing the configuration design. 3D models with different fiber orientations and porosity were constructed by the parameter input method, and the accuracy of the model was validated by the coefficient of determination (R2) between the apparent velocity of the model and the air permeability of the membrane. The permeability of 3D model was used to reflect the discrepancy in fiber orientation of the model. The influences of fiber orientation and porosity on heat and water vapor transfer were surveyed by the coupled physics of heat transfer and dilute substance transfer. Since there was no temperature difference in the entire domain, heat conduction (10−9 W/m2) and moisture convection (10−14 mol·m−2·s−1) were faint in the model. With the diffusion of water vapor in the moisture, the heat convection flux and water vapor diffusion flux gradually decreased and reached equilibrium. When the permeability was increased by adjusting the fiber orientation (from 1.002 to 1.200 m2), the heat convection flux and water vapor diffusion flux followed a similar growth pattern due to the coupling effect of heat transfer and water vapor transfer. The R2 for the heat convection flux and water vapor transmission rate of the simulations and experiments with different porosity (44.87, 47.64 and 50.15%) were 0.999 and 0.923, respectively, which demonstrated the validation of the simulation in heat and water vapor transfer.

Comparative Study on Thermos-Hydraulic Performance of Different Cross Section Shapes of Microchannels with Supercritical CO2 Fluid

The influence of the cross section shape of microchannels on the thermos-hydraulic performance of the supercritical CO2 fluid is an important issue in the design of industrial compact heat exchangers, but few studies have been conducted about this issue. In this paper, comparative studies of the flow and heat transfer performance of SCO2 fluid in horizontal microchannels with circular, semicircular, rectangle, and trapezoidal cross sections were conducted numerically. The comparison is based on the same hydraulic diameter and length for all channel types and is carried out under the same mass flux, outlet pressure, and wall heat flux. The fluid bulk temperature in this analysis ranges from 285 K to 375 K, which covers the pseudocritical point of SCO2. The results show that the circular channel has the highest average heat convection coefficient, while the trapezoidal channel has the worst convective heat transfer performance under the same hydraulic diameter and boundary conditions. The results also indicate that the effect of cross section shape on the heat convection coefficient is significantly greater than that on the channel pressure drop, and the existence of the corner region in the cross section, especially the acute angle, will weaken the heat transfer performance.