Nonlinear Thermal Model Research Articles

Optimization of MTI structure based on material characteristics under extreme aerodynamic heating environment

Thermal insulation structure is a key factor to protect a high-speed aircraft to work safely and complete various tasks. The multilayer thermal insulation (MTI) structure has attracted much attention because of its light weight and good thermal insulation effect. The performance of an MTI structure is not only related to its physical sizes, but also closely related to the material optimization and temperature influences. A transient nonlinear thermal transfer model of the MTI structure is established, and a numerical solution strategy of the nonlinear thermal transfer model is proposed. Considering material selection, introducing the temperature influence of materials, and taking the geometric dimensions and equivalent mechanical properties of the MTI structures as constraints, an optimization frame of the MTI structures is established. Then two intelligent methods are adopted to solve the problem. Using the aerodynamic heating environment of X-43 flight trajectory, the results of a typical high-speed aircraft show that the proposed optimization framework can reduce the structural mass density from 13.95 kg‧m−2 to 9.10 kg‧m−2 by about 34.8 %. The temperature effect analysis shows that the temperature variation has an important influence on the optimization results. If the temperature effect on material properties is not considered, the optimized design scheme may not meet the temperature design constraints (The maximum temperature of the inner surface is 410 K, far exceeding the maximum allowable temperature of 320 K) which further leads to structural failures. Finally, the reliability and rationality of the optimization scheme are verified by a finite element model (FEM). The equivalent modulus of the optimized MTI structure is 146 GPa and the mass area density of the MTI structure is 7.7 kg‧m−2. The optimization design method of an MTI structure proposed in the current paper provides a technical support and lays a foundation for the overall design of a high-speed aircraft.

Thermal Characteristics of Spindle System Based on the Comprehensive Effect of Multiple Nonlinear Time-Varying Factors

The thermal characteristics of the spindle system for CNC machine tools are influenced by multiple factors which are nonlinear and time-varying. In this paper, a nonlinear time-varying thermal characteristics solving model for the spindle system was established based on the numerical solution method. Through theoretical deduction and data fitting, mathematical models of nonlinear time-varying factors including the friction torque generated by lubricants, convective heat transfer coefficient, and coolant and ambient temperature are constructed. The temperature and displacement of the spindle system at each time step are solved by considering the comprehensive effect of multiple nonlinear time-varying factors. And the actual temperature and axial deformation data of the spindle system are obtained through thermal characteristics detection experiments. By comparing solution results affected by multiple nonlinear time-varying factors and by non time-varying factors with experimental data, it can be concluded that the nonlinear time-varying thermal characteristics model has advantages in reflecting the trend of numerical changes and the accuracy of result solving over a method considering non time-varying factors and the solution values of temperature affected by multiple nonlinear time-varying factors are almost consistent with detection values and the relative errors are all within ±3%. The relative error of axial deformation between the value solved by the model and the detection value is close to −1%. This conclusion demonstrates the rationality and accuracy of the thermal characteristics solving model and the construction of nonlinear time-varying factors. This study is of great significance for exploring the thermal characteristics of the spindle system and improving CNC machine tool performance in depth.

Multi-time scale thermal tribological dynamics coupling model of the helicopter intermediate reducer under severe loss of lubrication

There is no lubrication in the contact area, which leads to a significant influence of the thermal characteristics on the friction dynamics and life of the helicopter intermediate reducer because the helicopter experiences severe loss of lubrication. In this study, for evaluating the non-linear friction dynamics and transient thermal network models of the intermediate gearbox, a multi-time scale coupling method was proposed to establish a proportional allocation method between the oil film region and the rough peak contact region of the tooth surface by considering the effect of temperature and to study the adsorption film under the condition of severe lubrication loss. The coupled thermal and kinetic characteristics of the severe lubrication loss condition were obtained by calculating the friction coefficients in the lubricated and dry-friction regions. The results showed that the friction coefficient of the bevel gear tooth surface fluctuated between 0.1 and 0.6, and the degree of the gear axis trajectory shift was more evident owing to the increase in the friction force excitation caused by the increase in the friction coefficient.

Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning

We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.

Risk-Averse scheduling of integrated electricity-heat systems considering multi-energy network operations for resilience enhancement against contingencies

The increasing penetration of renewable energy and the growing frequency and severity of extreme weather events pose a significant challenge to the secure and economic operation of local energy systems. This paper presents a risk-averse scheduling model of the integrated electricity and heat system (IEHS) for resilience enhancement against contingencies. A tri-level formulation is proposed to formulate the worst line outage events and identify the optimal resilience enhancement strategies. The main idea is to find the least-cost scheduling solution that meets the predefined resilience requirements. The model incorporates multi-energy network operations that integrate network reconfiguration in the PDN and mass flow rate control in the DHN. This approach provides more flexibility for load restoration in the face of uncertainties. A nonlinear thermal flow model is adopted to realistically capture thermal dynamics, and a tractable linear approximation is then proposed to balance accuracy and tractability. To solve this tri-level mixed integer program, an efficient solution method based on the nested column-and-constraint-generation algorithm is developed for the proposed IEHS scheduling model. Numerical studies indicate that the proposed model provides optimal solutions that are cost-effective to enhance the resilience of IEHS at minimum expense.

Transient Thermal Cooling of Electronics Systems using Functional Graded Fins: Hybrid Computational Analysis

Passive cooling of electronics systems requires the use of fins and spines. Improved heat transfer enhancements in the systems have been achieved through porosity, magnetic field, functionally graded materials, etc. However, the space and time-dependent analysis of passive device with inherent nonlinearities and explorations of conditions at the tip have not been fully presented. Therefore, this work presents an application of hybrid computation analysis using combined methods of Laplace transformation and Legendre wavelet collocation to the space and time-dependent nonlinear thermal models of a longitudinal conductive-radiative functionally graded extended surface. The spatial-dependent thermal conductivity is considered for three different cases. The present analysis results demonstrated good agreement with numerical results. The significances of the model's pertinent parameters on the fin’s performance are thoroughly considered and scrutinized with the aid of graphical illustrations. The fin tip thermal response decreases with an increase in conductive-convective parameters, but it increases as time progresses. The in-homogeneity index is directly proportional to the FGM fin temperature. However, the convective term is inversely proportional to the fin’s thermal distribution. The fin temperature under quadratic-law heat conductivity of the passive device shows an enhanced performance of lower thermal distribution than the linear- and exponential-law heat conductivity. Ultimately, the study provides a very useful in the design of the fin with FGM.

Channel Temperature Analysis and Nonlinear Thermal Model of AlGaN/GaN HEMTs Including Steady-State and Transient

The thermal analysis of GaN-based high electron-mobility transistors (HEMTs) is carried out from steady-state and transient aspects, respectively. An improved closed-form nonlinear thermal model based on device structure is proposed. In the steady-state case, the plane layer is added on the basis of the original partition, and the effect of thermal boundary resistance on channel temperature is also considered. In addition, the operating temperature of each gate finger is predicted based on the thermal coupling, and the nonlinear thermal model is extended to the transient by combining the thermal time constant. The validity of our presented model is verified by comparing the simulation results with the experimental data. Furthermore, this model is also embedded in the surface-potential-based current model to verify the self-heating effect in the circuits.

Extending Life of Lithium-Ion Battery Systems by Embracing Heterogeneities via an Optimal Control-Based Active Balancing Strategy

This article formulates and solves a multiobjective fast charging-minimum degradation optimal control problem (OCP) for a lithium-ion battery module made of series-connected cells equipped with an active balancing circuitry. The cells in the module are subject to heterogeneity induced by manufacturing defects and nonuniform operating conditions. Each cell is expressed via a coupled nonlinear electrochemical, thermal, and aging model and the direct collocation approach is employed to transcribe the OCP into a nonlinear programming problem (NLP). The proposed OCP is formulated under two different schemes of charging operation: 1) same charging time (OCP-SCT) and 2) different charging time (OCP-DCT). The former assumes simultaneous charging of all cells irrespective of their initial conditions, whereas the latter allows for different charging times of the cells to account for heterogeneous initial conditions. The problem is solved for a module with two series-connected cells with intrinsic heterogeneity among them in terms of state of charge and state of health. Results show that the OCP-DCT scheme provides more flexibility to deal with heterogeneity, boasting of lower temperature increase, charging current amplitudes, and degradation. Finally, a comparison with the common practice of constant current (CC) charging over a long-term cycling operation shows that promising savings, in terms of retained capacity, are attainable under both control (OCP-SCT and OCP-DCT) schemes.

Impact of Cattaneo–Christov double diffusion theory and Arrhenius pre-exponential factor law on flow of radiative Reiner–Rivlin nanofluid over rotating disk

Reiner–Rivlin nanofluid flow due to rotating disk has significance in manufacturing of computer disks, pumping of liquid metals, spin coating, centrifugal machinery, turbo-machinery, crystal growth and rotational viscometer. In light of such real and relevant industrial applications, this study deals with the numerical investigation of unsteady rotationally symmetric flow of Reiner–Rivlin nanofluid over a stretchable rotating disk. The purpose of this investigation is to explore heat transfer characteristics of Reiner–Rivlin nanofluid subject to radial stretched surface implementable in several thermal systems. For facilitation of heat transport in complex thermal systems, mathematical models, such as Cattaneo–Christov, Buongiorno and nonlinear thermal radiation models, are assumed to be introduced. Runge–Kutta–Fehlberg technique along with shooting method is used for numerical computation of the transformed equations. It is captivating that radial and circumferential velocities decelerate with rise in Reiner–Rivlin and stretching strength parameters, respectively. Amplified thermal relaxation and Reiner–Rivlin parameters led to diminution of wall temperature gradient. Nanoparticle concentration profiles exhibit opposite behavior in response to escalation of activation energy and reaction rate parameters.

Thermal analysis and entropy generation of Darcy-Forchheimer ternary nanofluid flow: A comparative study

Ternary nanofluid is a novel class of working fluids with excellent heat transfer properties. A combination of three solid nanoparticles consisting of SWCNTs, TiO2, and MoS2 is investigated for Darcy-Forchheimer water-based ternary nanofluids. The related mathematical models are established by considering linear, quadratic and nonlinear thermal radiations. Numerical results and entropy generation analysis reveal the considerable influence of nonlinear thermal radiation on temperature and the reduced Nusselt number of ternary nanofluids. With the help of multiple quadratic regression, the impact of relevant parameters on the reduced Nusselt number is studied in depth. The results show that the temperature and Nusselt number are always the highest in the nonlinear thermal radiation model compared with the linear and quadratic ones, and they are most sensitive to the changes of Rd and δ. The thermal radiation properties of ternary nanofluids may potentially lead to more efficient solar energy conversion. This comparative study illustrates the advantages of ternary nanofluids in improving solar radiation utilization efficiency with nonlinear thermal radiation.

Unsteady state heat transfer analysis of a convective-radiative rectangular fin using Laplace Transform-Galerkin weighted residual method

The present investigation is concerned with the development of non-power series solutions for the unsteady state nonlinear thermal model of a radiative-convective fin having temperature-variant thermal conductivity using Laplace transform-Galerkin weighted residual method. In the study, it is demonstrated that the symbolic solutions do not involve a large number of terms, complex mathematical analysis, high computational cost, and time as compared to the power series solutions in previous studies. The solutions allow effective predictions of the extended surface thermal performance over a large domain and time. The results of the non-power series solutions are verified numerically, and very good agreements are established. Parametric studies are carried out with the aid of the symbolic non-power solutions. It is found that as the conductive-convective and conductive-radiative increase, temperature distribution decreases since the rate of heat transfer becomes augmented and hence, the fin thermal efficiency is improved. Additionally, when the thermal conductivity of the fin increases, the temperature distribution in the passive device increases. The temperature increases with time at the different positions in the fin. Following the time histories of the solution, it is shown that unsteady state solutions converge to a steady state as time progresses. It could therefore be stated the developed non-power series analytical solutions provide a good platform for comparison of the nonlinear thermal analyses of fins in thermal systems.

Explicit Thermal Resistance Model of Self-Heating Effects of AlGaN/GaN HEMTs with Linear and Non-Linear Thermal Conductivity

We presented an explicit empirical model of the thermal resistance of AlGaN/GaN high-electron-mobility transistors on three distinct substrates, including sapphire, SiC, and Si. This model considered both a linear and non-linear thermal resistance model of AlGaN/GaN HEMT, the thickness of the host substrate layers, and the gate length and width. The non-linear nature of channel temperature-visible at the high-power dissipation stage-along with linear dependency, was constructed within a single equation. Comparisons with the channel temperature measurement procedure (DC) and charge-control-based device modeling were performed to verify the model's validity, and the results were in favorable agreement with the observed model data, with only a 1.5% error rate compared to the measurement data. An agile expression for the channel temperature is also important for designing power devices and monolithic microwave integrated circuits. The suggested approach provides several techniques for investigation that could otherwise be impractical or unattainable when utilizing time-consuming numerical simulations.

An energy-dependent electro-thermal response model of CUORE cryogenic calorimeter

The Cryogenic Underground Observatory for Rare Events (CUORE) is the most sensitive experiment searching for neutrinoless double-beta decay (0νββ) in 130Te. CUORE uses a cryogenic array of 988 TeO2 calorimeters operated at ∼10 mK with a total mass of 741 kg. To further increase the sensitivity, the detector response must be well understood. Here, we present a non-linear thermal model for the CUORE experiment on a detector-by-detector basis. We have examined both equilibrium and dynamic electro-thermal models of detectors by numerically fitting non-linear differential equations to the detector data of a subset of CUORE channels which are well characterized and representative of all channels. We demonstrate that the hot-electron effect and electric-field dependence of resistance in NTD-Ge thermistors alone are inadequate to describe our detectors' energy-dependent pulse shapes. We introduce an empirical second-order correction factor in the exponential temperature dependence of the thermistor, which produces excellent agreement with energy-dependent pulse shape data up to 6 MeV. We also present a noise analysis using the fitted thermal parameters and show that the intrinsic thermal noise is negligible compared to the observed noise for our detectors.

Convection of 3D MHD non‐Newtonian couple stress nanofluid flow via stretching surface

AbstractThis study involvesthe numerical modeling of steady thermal radiation and chemical reaction on non‐Newtonian fluid motion via a bidirectional stretching surface. We have taken convective boundary conditions, and heat sources on the stretching surface. The working fluid of the present study is Casson fluid (“non‐Newtonian”) with couple stress. The self‐similarity forms of the nonlinear thermal radiative flow model are obtained by using similarity variables. Furthermore, the numerical results are computed with the help of fourth‐order Runge–Kutta–Fehlberg method with a shooting algorithm after reducing nonlinear partial differential equations have been translated into strong ordinary differential equations (ODEs). Impacts of the various flow physical parameters especially Biot number, nonlinear thermal radiation, and heat source parameters containing nonlinear ODEs are discussed in detail for distinct numerical values. A comparison of calculated results with the known numerical results made with the previously published literature is mentioned and obtained a good agreement. Finally, we found that the (“coefficient of skin friction”) declines along directions, respectively, with via while the opposite direction follows with respect to and the (“heat transfer rate”), (“mass transfer rate”) increase with via while opposite direction follows with respect to .

Nonlinear transient thermal analysis of a convective–radiative fin: A comparative study of two approximate analytical methods

Developments of analytical solutions to nonlinear equations provide very good physical insights into the nonlinear phenomena. The nonlinear transient thermal responses of extended surfaces have been widely studied analytically with the aid of different methods based on power series solutions. Such solutions come with large numbers of terms that are not convenient for use in practice. In this work, a non-power series solution is presented for the nonlinear transient thermal analysis of the passive device. Also, a comparative study of two analytical methods, Laplace transform-Galerkin weighted residual and differential transformation methods is presented to analyze transient nonlinear thermal model of radiative–convective fin considering varying thermal conductivity. The obtained analytical solutions are verified analytically and numerically, and very good agreements are established. The symbolic results are employed to check the influences of model parameters on passive device’s thermal performance. It is found that as the conductive–convective, and conductive–radiative parameters increase, temperature distribution decreases since heat transfer becomes augmented and hence, the fin thermal efficiency is improved. The temperature distribution increases through the fin as thermal conductivity increases. At the different positions in the fin, the temperature increases with an increase in time. The time histories of the solution shows that transient solutions converge to a steady state and the fin tip temperature increases as time progresses. The developed approximate analytical solutions provide very good platforms for the nonlinear thermal analyses of fins and proper design of the extended surfaces in thermal systems.

Quantitative analysis of the inhibition effect of rising temperature and pulse charging on Lithium dendrite growth

• The effects of temperature on Li dendrites and "dead lithium" are simulated using the phase field model. • The dendrite suppression mechanism of pulse charging strategy is clarified. • The number Da is proposed to analyze quantitatively suppressing of Li dendrites. Lithium (Li) metal is considered a promising negative electrode material for high theoretical energy batteries. However, the growth of Li dendrite increases polarization, reduces battery capacity, and connects the positive and negative electrodes, which will probably lead to explosions. Therefore, inhibiting Li dendrites is critical for Li metal battery application and safety. In this paper, the effect of temperature on Li dendrite is analyzed quantitatively by coupling the nonlinear phase-field and thermal models. The effect of temperature on “dead Li” is also studied. The suitable frequency for Li dendrite inhibition can be obtained by changing the frequency of the pulse charging. On the basis of the simulation results, the mechanisms of inhibiting Li dendrites by rising temperature and pulse charging are also analyzed. The investigation of the average growth rate of dendrites under different overpotential values and diffusion coefficients indicates that the gap between the reaction and diffusion rates must be narrowed to inhibit Li dendrites. This work provides a deep understanding of and direction toward inhibiting Li dendrites.

Analysis of the residual stress in additive manufacturing of Ti-6Al-4V

Minimizing the residual stress build-up in metal-based additive manufacturing plays a pivotal role in selecting a particular material and technique for making an industrial part. However, there are still some limitations for this application, especially the unfavourable final shape and undesired macroscopic properties of metallic parts built in additive manufacturing systems. The distortion or crack due to the residual stress of these parts leads usually to severe problems for some kinds of metal additive manufacturing technology. Therefore, it is necessary to study the distribution of residual stress in the process, which can provide an important reference for the process control of laser cladding. Taking Ti-6Al-4V (TC4) alloy as the research object, a nonlinear sequential thermal mechanical coupling model is established by combining the finite element numerical simulation and experimental deformation measurement. A least squared cost function between the Finite Element Cladding model and the experimental deformation measurement is proposed, and the finite element model updating method is constructed to retrieve the heat source parameters of TC4 Alloy in laser cladding. By comparing the numerical results with the experiment, the rationality of the inversion results of heat source parameters is verified. After that, the stress near the cladding layer is analyzed, and the influence of temperature field on the mechanical field distribution is further studied through the affects of stress distribution.

Energy Efficient Thermal Comfort Control for Residential Building Based on Nonlinear EMPC

For purpose of achieving the desired thermal comfort level and reducing the economic cost of maintaining the thermal comfort of green residential building, an energy efficient thermal comfort control strategy based on economic model predictive control (EMPC) for green residential buildings which adopts household heat metering is presented. Firstly, the nonlinear thermal comfort model of heating room is analyzed and obtained. A practical nonlinear thermal comfort prediction model is obtained by using an approximation method. Then, the economic cost function and optimization problem of energy-saving under the necessary thermal comfort requirements are constructed to realize the optimal economic performance of the dynamic process. The energy efficient thermal comfort MPC (EETCMPC) is designed. Finally, the comparison and analysis between EETCMPC and Double-layer Model Predictive Control (DMPC) is simulated. The simulation results reveal that when the clothing insulation is typical, the energy efficiency of EETCMPC is 8.9% and 11.6%, respectively, in the two simulation scenarios. When the clothing insulation varies with temperature, the energy efficiency of EETCMPC is 7.29% and 9.15%, respectively, and the total energy consumption is reduced by about 1.65% and 14.6%, respectively, compared with the typical clothing insulation. The economic performance is improved in the thermal comfort dynamic process of heating room.

Model validation of mechanical face seals in two-phase flow conditions

A steady-state one-dimensional axisymmetric numerical model of a mechanical seal in two-phase flow is presented. In this work a non-linear thermal model is implemented using a coupled (monolithic) approach, linking the fluid film and sealing rings. It is solved for the temperature fields of the fluid and solids, heat fluxes between fluids and solids, enthalpy of the fluid, and the vapor mass fraction, using Newtons method. The novelty of this approach lies in 1) the thermal coupling between fluid and solids, and 2) the implementation of saturation curves to couple temperature, enthalpy, and vapor mass fraction. The temperature across the seal gap is described by an analytical parabolic temperature profile by assuming a plane Couette flow in the radial direction. From this assumption, an equation for the wall heat fluxes is derived, which couples the temperature fields of the fluid and solids. The IAPWS-IF97 standard for the thermodynamic properties of water is used to obtain non-linear equations that couples the fluid temperature, enthalpy and the vapor mass fraction. The model and its implementation is described in detail. Several cases of seal behavior and two-phase flow are studied and show good agreement with other results from literature, validating the coupled approach for modelling phase-change in mechanical seals.

Influence of the size and the material of the magnetic core on thermal properties of the inductor

The paper analyses the influence of the size, the shape and the ferromagnetic material which is used to make a ferromagnetic core on thermal parameters of an inductor. The investigations were carried out for: inductors containing toroidal cores made of the ferrite F867 materials with the different outer diameter, for toroidal cores made of different materials, such as the ferrite SM −100 and the powdered iron (−26), (−52) with the same outer diameter, and for cores made of F867 materials with the same value of effective volume, but different shapes, such as: a U-core and a cup core. The method of measurements and the results of investigations for selected ferromagnetic cores are presented. The obtained results show that various factors mentioned earlier have a significant influence on thermal parameters of an inductor and it is reasonable to formulate a nonlinear compact thermal model of an inductor using the measurement results presented in this paper.