Nonlinear Thermal Model Research Articles

Melting heat transfer analysis of Sisko fluid over a moving surface with nonlinear thermal radiation via Collocation method

The objective of the present model is to examine the magnetohydrodynamic (MHD) non-Newtonian (Sisko) nanofluid flow over a linear stretching sheet. The thermal management is examined through melting heat transfer. Buongiorno’s model has been used to study the Brownian and thermophoresis effects inside the nanofluid. Furthermore, nonlinear thermal radiation model is also considered. Mathematical model of considered physical problem consists of coupled nonlinear partial differential equations: conservation of mass, momentum, energy, and concentration equation. The numerical solution is obtained by using Collocation Method after being transformed into ordinary differential equations by means of an appropriate similarity transformation. The quantities of interest, that are, nanofluid velocity, temperature, concentration, skin friction, heat and mass transfer rate, are examined against the emerging physical parameters. The obtained results revealed that the rate of heat and mass transfer is an increasing function while skin friction coefficient is decreasing functions of melting parameter. An increase in the thermal radiation effects enhances the heat and mass transfer rates. Increase in power law index decreases velocity, temperature and concentration distribution. On the other hand, skin friction, heat and mass transfer rate is enhanced due to increase in power law index.

A Fast Leakage-Aware Full-Chip Transient Thermal Estimation Method

Accurate and fast thermal estimation is important for the runtime thermal regulation of modern microprocessors due to excessive on-chip temperatures. However, due to the nonlinear relationship between the leakage power and temperature, full-chip thermal estimation methods suffer slow speed and scalability issue when the increasing static leakage power is considered. In this work, we propose a new fast leakage-aware full-chip thermal estimation method. Unlike traditional methods, which use iteration to handle the leakage-temperature nonlinearity dependency issue, the new method applies a dynamic linearization algorithm, which adaptively transforms the original nonlinear thermal model into a number of local linear thermal models. In order to further improve the thermal estimation efficiency, a specially-designed adaptive model order reduction method is integrated into the thermal estimation framework to generate local compact thermal models. Our numerical results show that the new method is able to accurately estimate full-chip transient temperature distribution by fully considering the nonlinear leakage-temperature dependency with fast speed. On different chips with core number ranging from 9 to 36, it achieved 85x to 589x speedup in average against traditional iteration based method, with average thermal estimation error to be around 0.2°C.

On-line estimation of the tool-chip interface temperature field during turning using a sequential inverse method

It is well known that the direct measurement of temperature distribution at the tool-chip interface in a machining process is difficult to accomplish. Thus, this paper provides an on-line inverse technique to estimate the temperature field at the tool-chip interface of a turning tool, using temperatures measured at some sensor-accessible locations. A sequential Tikhonov regularization method (STRM) is proposed to determine the transient heat flux imposed at the tool-chip interface, by solving an inverse heat conduction problem (IHCP). Then, the temperature field at the tool-chip interface is computed by solving the three-dimensional non-linear thermal model, with a method combining Duhamel’s superposition theorem with the finite element method. The procedure proposed shows a superiority in on-line applications due to its high computational efficiency and independence of future measurements. A comparison of the STRM with several other inverse methods in the literature was made through numerical tests. Experimental cutting tests on Ti-6Al-4V titanium alloy were done to validate the thermal model and method. Both numerical and experimental tests show that the proposed method can provide an efficient and easy-to-implement strategy for on-line temperature field monitoring of machine tools.

A Prewelding Pipe-Heating System

The computation of the parameters and operating mode of the induction heater for large-diameter pipes for preventing thermal stresses in welding is considered. Thermal processes at various ambient temperatures and with an arc moving along the welded butt combined are analyzed. Increased accuracy of the computations is provided using the nonlinear thermal task model taking into account phase transitions. The proposed split-face inductor design provides convenient installation and high reliability. The inductor’s selected frequency and power make it possible to solve the problem of matching with the power source without any transformer. The inductor design includes a ferrite-magnet wire, which has made it possible to use double-section loop winding.

Computational Design of Microvascular Radiative Cooling Panels for Nanosatellites

This novel application of microvascular panels as nanosatellite radiator panels involves the key challenge of satisfying design constraints involving the coolant temperatures and pressure drop across the microchannel network. To address this challenge, the radiator panels are represented by dimensionally reduced hydraulic and nonlinear thermal models. The interface-enriched generalized finite element method and the Newton–Raphson scheme are then combined to solve the resulting nonlinear equations. Next, an interface-enriched generalized finite element method-based sensitivity analysis of the nonlinear equations is developed and combined with an existing sequential quadratic programming algorithm to solve an optimization problem specifically formulated to optimize the thermal performance of the radiator. The resulting thermal performance of the optimized designs is not only superior to that of the reference designs but is also in excellent agreement with an analytical model derived based on the assumption of near-monotonic variation in the coolant temperature along the microchannel network. A feasibility study on a reference design and an optimized design shows that only the latter can satisfy all design constraints with appropriately chosen flow rates. Solutions of the thermal and hydraulic models are also verified with ANSYS FLUENT simulations.

Three-stage Nonlinear Thermal Model for Microspeakers in Mobile Phones牋

Since microspeakers are widely used in mobile phones, high power is usually applied to obtain sufficient output sound pressure. However, the electric power is almost converted into heat, leading to the thermal problem in microspeakers. Compared with large loudspeaker, microspeakers are smaller and the under yoke is relatively closed, causing the heat transfer more complex. In this study, a three-stage nonlinear thermal model was proposed for analyzing the thermal behavior in microspeakers. The inside air is a buffer area between the voice coil and magnet, and modeled as a middle stage of the heat transfer. The forced convection is still significant in microspeakers while the eddy current can be ignored. In order to obtain the thermal parameters of the model, a corresponding parameter identification method was put forward. The basic linear parameters and forced convection parameters were all obtained by measuring and fitting the temperature curves of voice coil at different single tones. A series of experiments were conducted to verify the proposed model and parameter identification method, and the results showed good aggrement between the measured and predicted temperature curves for different input signals. The proposed model was valid and accurate, and may be helpful for the design and application of microspeakers.

Analysis of Heat Generation During Friction Stir Processing of Aluminium Similar Joints

In this paper, study of heat generation during friction stir processing of similar joints of AA6061-T6 is carried out. A three dimensional (3D), transient, non-linear thermal model was developed using ANSYS 16.2 software to simulate the heat generation profile during Friction Stir Processing of similar Aluminum plates. The results showed that the observed temperature rise in the model shows that heat generation during the second and third load steps is due to friction between the tool shoulder and work piece, as well as plastic deformation of the work piece material. It was also observed that friction is responsible for generating most of the heat needed, while the contribution of heat due to plastic deformation is less significant. Because the tool-penetration is shallow and the tool pin is ignored, the plastic heat is small compared to frictional heat.

Non-linear thermal simulation at system level: Compact modelling and experimental validation

In this work, a general methodology to extract compact, non-linear transient thermal models of complex thermal systems is presented and validated. The focus of the work is to show a robust method to develop compact and accurate non-linear thermal models in the general case of systems with multiple heat sources. A real example of such a system is manufactured and its thermal behaviour is analyzed by means of Infra-Red thermography measurements. A transient, non-linear Finite-Element-Method based model is therefore built and tuned on the measured thermal responses. From this model, the transient thermal responses of the system are calculated in the locations of interest. From these transient responses, non-linear compact transient thermal models are derived. These models are based on Foster network topology and they can capture the effect of thermal non-linearities present in any real thermal system, accounting for mutual interaction between different power sources. The followed methodology is described, verification of the model against measurements is performed and limitations of the approach are therefore discussed. The developed methodology shows that it is possible to capture strongly non-linear effects in multiple-heat source systems with very good accuracy, enabling fast and accurate thermal simulations in electrical solvers.

Prediction of Temperature distribution in Straight Fin with variable Thermal Conductivity and Internal Heat Generation using Legendre Wavelet Collocation Method

Due to increasing applications of extended surfaces as passive methods of cooling, study of thermal behaviors and development of mathematical solutions to nonlinear thermal models of extended surfaces have been the subjects of research in cooling technology over the years. In the thermal analysis of fin, various methods have been applied to solve the nonlinear thermal models. This paper focuses on the application of Legendre wavelet collocation method to the prediction of temperature distribution in longitudinal rectangular fin with temperature-dependent thermal conductivity and internal heat generation. The numerical approximations by the method are used to carry out parametric studies of the effects of the model parameters on the temperature distribution in the fin. The results show that the thermal performance of the fin is favoured at low values of thermogeometric parameter and internal heat generation decreases the performance of the fin. The results can serve as verification of the solutions of other methods of analysis of the component.

Arthropod Development’s Response to Temperature: a Review and New Software for Modeling

Among environmental factors, temperature has a direct and crucial influence on the key life processes of survival, development, reproduction, and movement of poikilothermic animals and hence their population dynamics. The lower and upper temperature thresholds and optimal temperature have ramifications for all major life processes, where within a specific range, a temperature change results in a proportional rise or fall of the rate of any given process. There are some basic approaches for modeling development response to temperature in arthropods. The oldest and most widely used model is a simple linear description of arthropod development in relation to temperature. The linear model forms the basis of the well-known thermal summation or degree-day (DD) approach to timing prediction. The second approach for predicting arthropod development rate is nonlinear mathematical models. However, given the fundamental role of thermal models in forecasting and integrated pest management programs, the main purpose of this paper was to facilitate the use of thermal models to estimate the developmental response of arthropods to temperature and select the appropriate model with a view to goodness-of-fit and generalizability by designing a user-friendly software. In this paper, the linear and most common nonlinear thermal models and the main criteria for selecting appropriate models are also reviewed.

Underground MV power cable joints: A nonlinear thermal circuit model and its experimental validation

The analysis of the thermal stress of underground MV power cable joints under different environmental conditions, both in normal operation and during faults, is crucial to assess any correlation between the occurrence of overheatings and the anomalous increase of failures (two to three times compared to previous years) which have been observed in the Italian distribution network during summer 2015 (the hottest year ever since 1880). In order to perform this analysis, we have developed a nonlinear circuit model that is able to estimate, both in stationary conditions and in transient ones, temperature profiles inside MV joints, referring to different environmental conditions and with current flowing both in the core conductor and in the metallic shield. The model has been implemented in the Simulink environment and then it has been validated with a set of experimental tests, specifically set up in order to check its performance in steady state and during transients. The numerical results were always in good agreement with the measurements. Subsequently, the circuit model has been employed to perform a predictive analysis of the joint internal temperatures, which may be achieved in operation and during faults by varying the ambient temperature. In all cases, the temperature limits tolerated by insulations have never been exceeded.

Evaluation of Classical Models for Thermal and Moisture Transport in Stone Walls of Historical Buildings

This paper concerns the evaluation and the validation of a heat and moisture transfer models in stone walls using in situ measurements on an instrumented wall. Firstly, a pure thermal (respectively moisture) diffusion problems are considerate, then this problem was combined with convection on the external edge of model. It is found that, despite of an uncoupled approach, the nonlinear thermal diffusive model performs quite well and reproduces perfectly the measured temperatures. It is the same for the convective-diffusive thermal problem, where the temperature on the surface wall is also reproduced quite well. An improvement of this second type problem results could be expected by taking into account the radiation. Otherwise, the both cases of moisture transfer problem (purely diffusive or diffusive-convective problem) are ill-simulated by the Kunzel’s model.

Thermo-mechanical analysis in pulsed laser cladding of WC powder on Inconel 718

An uncoupled thermo-mechanical finite element model is developed to simulate the laser-cladding process of tungsten carbide (WC) on Inconel 718. First, a non-linear three-dimensional transient thermal model is developed, which calculates transient temperature distribution in the local clad area. Thermal load attributed to laser beam is implemented to the workpiece by using a developed subroutine. Thermal and mechanical material properties are introduced temperature dependent. All the major physical phenomena associated to the laser-cladding process, such as heat radiation, thermal conduction, and convection heat losses, are taken into account in the developed model. Subsequently, using the thermal history of the thermal analysis, a mechanical analysis is performed, from which the residual stresses are calculated. Both thermal and mechanical analysis results are verified through experimental works. Results show that the temperature profile and clad dimensions are strong function of the heat source and conductivity of material. It is concluded that the laser power and cladding velocity have significant effect on residual stresses. Also, it is found that the longitudinal stresses are approximately three times the transverse ones. Results of mechanical analysis reveal that by increasing input energy, residual stresses increase and number of cracks decreases in the cladded layer.

Fast Nonlinear Dynamic Compact Thermal Modeling With Multiple Heat Sources in Ultra-Thin Chip Stacking Technology

This paper presents a model-order reduction technique to extract nonlinear dynamic compact thermal models (DCTMs) with multiple (>1) heat sources. The approach leads to nonlinear DCTMs of small state-space dimensions that allow accurately reconstructing the whole temperature and heat flux fields induced by arbitrary power waveforms in complex structures composed of many materials with thermal conductivities showing different values and temperature dependences. The DCTM extraction requires a small fraction of the CPU time needed for the simulation of a power step response using the finite element method (FEM), while ensuring a very high level of precision. Therefore, the adoption of the proposed strategy is a viable alternative to FEM for performing efficient and accurate nonlinear transient analyses: The advantage of using a DCTM is magnified if many power input waveforms have to be considered for the same structure since any further simulation of the extracted DCTM is nearly instantaneous. As a case study, the proposed technique is used to investigate the impact of two cooling solutions on the thermal behavior of a three-die module in ultra-thin chip stacking technology.

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple 17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices.

Non-linear dual-phase-lag model for analyzing heat transfer phenomena in living tissues during thermal ablation

In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method.

Operator-based nonlinear temperature control experiment for microreactor group actuated by Peltier devices

In this paper, operator-based nonlinear water temperature control for a group of three connected microreactors actuated by Peltier devices is proposed. To control the water temperature of tube in the microreactor, the temperature change of aluminum effects is considered. Therefore, the temperature change of aluminum becomes the part of an input of the tube. First, nonlinear thermal models of aluminum plates and tubes that structure the microreactor are obtained. Then, an operator based nonlinear water temperature control system for the microreactor is designed. Finally, the effectiveness of the proposed models and methods is confirmed by simulation and experimental results.

A simplified approach to numerical simulation of LFW process of Ti6Al4V alloy: investigation on friction and temperature

In the present study, the process modeling of linear friction welding of titanium alloy Ti6Al4V is carried out. Two major stages of the process as warm-up and osci-forging are identified and simulated consecutively to generate the temperature field within the model. A transient, two-dimensional, nonlinear thermal model with moving heat source is developed for the purpose using finite element approach. An implicit solution scheme is employed in numerical analysis to solve instationary thermomechanical problem. Good agreement between the numerical results and the experimental measurements available in the literature is found. The presented results can guide the design of welded joints through LFW processes.

Blending Glowworm Swarm Optimization Algorithm with Thermal-Mechanical Coupling Finite Element Model for Optimization Method of Box Structure Welding Technology

Welding sequence is the important influence factor of the temperature field and residual stress and deformation in welding structure, At present, determining the welding sequence is usually based on experience and test method. For complex structure it is very difficult to get the optimum welding sequence. This study is aiming to settle the problem of solving the optimum welding sequence of complex box welding structure. In our study, we take the welding deformation as objective function, and then, associate glowworm swarm optimization algorithm with thermal-mechanical coupling and nonlinear thermal elastoplastic finite element model to optimize numerical simulation, eventually the optimum welding sequence is determined. Optimization results demonstrate that the optimum welding sequence obtained by our method has small welding deformation and little change rate. At the same time, our method is faster, more accurate, more effective than the traditional experience or test method.

A combined optical-thermal model for near-infrared laser heating of thermoplastic composites in an automated tape placement process

A combined optical-thermal model is presented for near-infrared laser heating of carbon fibre reinforced thermoplastic composites in an automated tape placement process. For the first time a three dimensional ray tracing model is presented for a near-infrared laser tape placement process which captures the unique anisotropic scattering behaviour of the composite. Predicted irradiance distributions on the composite are subsequently applied to a 2D non-linear finite element thermal model. It is shown that a shadow is present in the process and causes a significant drop in temperature prior to the consolidation zone. The effect of various source and surface model simplifications was also studied. The modelled temperature profiles agree well with experimental data. Substrate fibre orientation was investigated and found to have only a small influence on the temperature history.