Nonlinear Heat Transfer Model Research Articles

Explicit Exact Solutions of Nonlinear Transient Thermal Models of a Porous Moving Fin using Laplace transform - Exp-function method

The present paper develops explicit and non-power series exact solutions to the nonlinear heat transfer models of conductive-radiative-convective moving-porous fin using Laplace transform - Exp-function method, is presented. The developed solutions are employed for investigation of the included parameters on the transient and steady states studies of the moving-porous fin. The results submitted that the fin temperature is augmented with time increase due to increase heat transfer rate as time progresses. However, thermal parameter of the fin reduces from the its base to its tip. As the porosity, moving, convective-conductive-radiative parameters are increased, the fin temperature are decreased due to increased heat transfer rate. The opposite trend is displayed for the conductive-radiative number. It can be stated that present work will be useful in the analysis of the device.

Stochastic procedures to solve the nonlinear mass and heat transfer model of Williamson nanofluid past over a stretching sheet

The stochastic procedures ANNs-LMB are provided with three categories of sample statistics, testing, training and verification. The nonlinear mass and heat transfer of Williamson nanofluid (MHTWF) on a stretched surface is divided into three profiles, dimensionless stream, concentration and temperature. The statistics, 10 %, 15 % and 75 % for testing, validation and training are provided to solve the nonlinear MHTWF past over a stretched surface. The solutions of the MHTWF are provided using the artificial neural networks (ANNs) together with the novel geographies of Levenberg-Marquardt backpropagation (LMB), i.e., ANNs-LMB. A reference data set is designed for the comparison of the obtained and proposed solutions for the fluid system. The absolute error is used to check the accuracy and precision of the nonlinear MHTWF past over a stretched surface, which have been provided around 10−05-10−08, 10−05-10−07 and 10−05-10−06 for each case of the model. The obtained numerical solutions of the nonlinear fluid dynamics system have been considered for the reduction of mean square error (MSE). The capability and dependability of the stochastic procedure are authenticated using the relative arrangements of MSE, error histograms (EHs), state transitions (STs), correlation and regression.

A Quantitative Study of Non-Linear Convective Heat Transfer Model by Novel Hybrid Heuristic Driven Neural Soft Computing

Heat transfer has a vital role in material selection, machinery efficacy, and energy consumption. The notion of heat transfer is essential in understanding many phenomena related to several engineering fields. Particularly, Mechanical, civil and chemical engineering. The presentation of the heat transfer model in this manuscript is a dedication to the heat transfer characteristics such as conduction, convection, and radiation. The heat energy consumption mainly depends on these characteristics. A better conductive and convective paradigm is required for miniaturization of heat loss or transfer. The phenomenon is mathematically assumed with the required parameters. A new mathematical strategy is also designed and implemented in the manuscript to evaluate the dynamics of heat transfer model. The mathematical approach is the hybrid structure of the Sine-Cosine algorithm and Interior point algorithm. The validation of new technique is evaluated by mean absolute deviation, root mean square errors, and error in Nash–Sutcliffe efficiency. For better illustration, an extensive data set executed by the proposed mathematical strategy is also drawn graphically with convergence plots.

Нeat and mass transfer models at boundary lubrication to determine the transition temperatures

At present, kinetic and thermodynamic methods for assessing the lubricating effect of oils are being increasingly developed. At the limit friction, the reduction of friction and wear of surfaces is due to the ability of the lubricant to form layers of adsorption or chemical origin on the surface. Analytical models of transition temperatures and wear in the limit lubrication mode must be used to mathematically describe the processes in the subsystems and the transition between them. The Fourier equation of thermal conductivity is accepted as the basic calculated dependence. It is assumed that the process of heat propagation under the conditions of formation of lubricating films is not Markovian, i.e. the magnitude of the heat flux is determined by the entire "history" of heat transfer in a certain elementary volume. The equation of motion of a lubricating film over the surface of a body that is being lubricated is obtained from the equation of motion for a Newtonian continuous medium. As a result, nonlinear heat and mass transfer models are obtained to determine the transition temperatures in the formation of boundary lubricating films in the concept of structural-thermodynamic approaches to describe the processes of boundary lubrication of surfaces

Semi-Analytical Solution of a Nonlinear Heat Transfer Model for a Tubular Cocurrent Moving-Bed Reactor With a First-Order Chemical Reaction in the Solid Phase

Abstract The development of mathematical models plays a fundamental role in the design, optimization, and control of processes. Regarding heat transfer in moving bed reactors, the chemical reaction implies the inclusion of a nonhomogeneous and nonlinear term in model equations, making the analytical integration a very difficult task. Up to date, there is not an analytic and/or a semi-analytic solution to a heat transfer model of a moving bed reactor (MBR) with isothermal walls to the distributed parameters in the solid phase. Therefore, starting from analytical solutions of the associated homogeneous (linear) problems and through the spectral expansion of the nonhomogeneous vector, this work presents strategies for determining semi-analytical solutions of nonhomogeneous and nonlinear problems. An MBR with a first-order chemical reaction in the solid phase—kaolinite dehydroxylation in the kaolinite flash calcination process—is selected as the case study; however, the strategies can easily be applied to other nonlinear models. Results for conversion, and fluid and particle temperatures, are given for different parameter values. The solutions perform stable, fast, and accurate. When compared with a hybrid finite difference and finite analytic (FD&FA) numerical method, the solution showed a very good agreement.

Optimization of thermal model and prediction of crystallinity during the laser-assisted tape winding process

Laser-assisted tape placement and tape winding represent the most advanced automated manufacturing technologies for thermoplastic composites. It is important to accurately predict the complete thermal history of the manufacturing process, on which many properties of the product are strongly dependent, such as interlaminar bonding strength and crystallization. In this article, a nonlinear two-dimensional transient heat transfer model was established in ANSYS APDL, and a new temperature closed-loop controlled near-infrared laser heat source was described. Most importantly, the thermal contact pairs were introduced following the activation of elements, and the value of interlaminar thermal contact resistance was obtained by fitting an independent experiment and finite element analysis, which greatly optimized the heat transfer process in the direction of thickness. The thermal model was verified by infrared cameras and an online temperature measuring system based on thermocouples. The results of thermal history are in good agreement with the experiment, which were input into the crystallization kinetics model to predict the evolution and distribution of crystallinity in the laser-assisted tape winding process. The calculated results are coincident with the differential scanning calorimeter test very well, and the crystallinity was about 17% higher than that before manufacturing.

Nonlinear Finite Element Analysis-Based Flow Distribution and Heat Transfer Model

A new strategy for fast, approximate analyses of fluid flow and heat transfer is presented. It is based on Finite Element Analysis (FEA) and is intended for large yet structurally fairly simple heat transfer equipment commonly used in process and power industries (e.g., cross-flow tube bundle heat exchangers), which can be described using sets of interconnected 1-D meshes. The underlying steady-state model couples an FEA-based (linear) predictor step with a nonlinear corrector step, which results in the ability to handle both laminar and turbulent flows. There are no limitations in terms of the allowed temperature range other than those potentially stemming from the usage of fluid physical property computer libraries. Since the fluid flow submodel has already been discussed in the referenced conference paper, the present article focuses on the prediction of the tube side and the shell side temperature fields. A simple cross-flow tube bundle heat exchanger from the literature and a heat recovery hot water boiler in an existing combined heat and power plant, for which stream data are available from its operator, are evaluated to assess the performance of the model. To gain further insight, the results obtained using the model for the heat recovery hot water boiler are also compared to the values yielded by an industry-standard heat transfer equipment design software package. Although the presented strategy is still a “work in progress” and requires thorough validation, the results obtained thus far suggest it may be a promising research direction.

Calorimetry under non-ideal conditions using system identification

We report a model-based method for quantifying heat flow and storage in thermal systems using data from multiple thermal sensors. This approach avoids stringent requirements on the system geometry and sensor positions and enables calorimetry to be performed under a broader range of circumstances than is accessible with existing calorimeters, such as when non-linear heat transfer occurs, when spatially separated heat sources are active, or when multiple thermal masses participate. Using experimental data from a model thermal system, this paper provides a tutorial on the construction of non-linear lumped element heat transfer models and the use of system identification to estimate the parameters of these models from calibration data. The calibrated models are then used to estimate unknown energy inputs to the thermal system from sensor data. Our best model enabled the measurement of the total input energy with 0.02% accuracy; the instantaneous input power could be measured with a root-mean-square error of 10% of the average input power.

Inhomogeneous steady-state problem of complex heat transfer

An inhomogeneous steady-state problem of radiative-conductive heat transfer in a three-dimensional domain is studied in the framework of the P1 approximation of the nonlinear complex heat transfer model. The unique solvability of the problem is proved. The Lyapunov stability of solutions is shown.

Modeling of thermal response and ablation in laminated glass fiber reinforced polymer matrix composites due to lightning strike

Abstract Thermal response and ablation of laminated glass fiber reinforced polymer matrix composites subjected to lightning strike are studied. The associated nonlinear time-dependent heat transfer model includes specific features of lightning arcs observed in physical measurements such as lightning channel radius expansion, non-uniform lightning current density, and associated heat flux. Moving spatially and temporally non-uniform lightning-current-induced heat flux boundary and moving boundary due to material phase transition caused by rapid surface ablation are also included. To predict moving phase boundary in the laminated anisotropic composites, an element deletion method is developed and embedded into finite element analysis (FEA), which is performed using ABAQUS. The Umeshmotion + ALE method based on the user subroutine Umeshmotion and arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique is also used, when applicable (i.e., moving phase boundary is confined within a top layer of the composite laminate). Heat transfer analysis is performed for a non-conductive laminated glass fiber reinforced polymer matrix composite panel representing the SNL 100-00 wind turbine tip. Thermal response of the panel subjected to pulsed and continuing lightning currents at three different lightning protection levels, LPL I, LPL II, and LPL III, is studied. Temperature-dependent anisotropic thermal properties of the composite panel are included in the analysis. The FEA results include temperature distributions and ablation zone profiles. The results show the Umeshmotion + ALE method is sufficient for the pulsed lightning current at all three LPL levels since the moving phase boundary, i.e. the ablation front, is found to be confined within the top layer of the laminate. For the continuing lightning currents at all three LPL levels, the Umeshmotion + ALE method is not applicable since the moving phase boundary comes to rest at depths exceeding the thickness of the top layer of the composite laminate.

High-temperature high-pressure calorimeter for studying gram-scale heterogeneous chemical reactions.

We present an instrument for measuring pressure changes and heat flows of physical and chemical processes occurring in gram-scale solid samples under high pressures of reactive gases. Operation is demonstrated at 1232 °C under 33 bars of pure hydrogen. Calorimetric heat flow is inferred using a grey-box non-linear lumped-element heat transfer model of the instrument. Using an electrical calibration heater to deliver 900 J/1 W pulses at the sample position, we demonstrate a dynamic calorimetric power resolution of 50 mW when an 80-s moving average is applied to the signal. Integration of the power signal showed that the 900 J pulse energy could be measured with an average accuracy of 6.35% or better over the temperature range 150-1100 °C. This instrument is appropriate for the study of high-temperature metal hydride materials for thermochemical energy storage.

Analyzing wellbore stability in chemically-active anisotropic formations under thermal, hydraulic, mechanical and chemical loadings

Several factors influence the stress state in subsurface rocks. In addition to pore pressure and far-field in-situ stresses, thermal and chemical gradients have substantial bearings on the in-situ stress state during and after drilling operations. Drilling inclined boreholes through laminated formations such as shaley sands presents several challenges. Due to their laminated nature, shales demonstrate high degree of elastic anisotropy, and are often chemically-reactive to drilling fluid. The majority of models utilized in the industry assume a homogeneous isotropic elastic static model that fails to give an accurate depiction of the observed borehole failure. In this work, governing equations for anisotropic porochemothermoelasticity are developed to simulate the drilling of an inclined borehole problem in a transversely isotropic rock. Using the developed constitutive and transport equations, a finite element method based numerical model is constructed to estimate the pore pressure, temperature, solute concentration and stress distribution. Nonlinear conductive-convective heat transfer and diffusive-advective solute transfer models are considered in this work to address both high and low permeability formations. Finally, the model is used to assess time-dependent wellbore stability during and after drilling. The novel pseudo-3D analysis developed in this work is advantageous for real-time operations due to its computational speed and stability.

Textile porosity determination based on a nonlinear heat and moisture transfer model

The inverse problems of textile materials design on heat and moisture transfer properties are important and indispensable in applications in the body-clothing-environment system. We present an inverse problem of textile porosity determination (IPTPD) based on a nonlinear heat and moisture transfer model. Adopting the idea of the least-squares, the mathematical formulation of IPTPD is deduced to a regularized optimization problem with collocation method applied. The continuity of the regularized minimization problem is proved. By means of genetic algorithm (GA), the approximate solution of the IPTPD is numerically obtained. To reduce the computational cost, an improved algorithm based on BP neural network with GA is proposed in the numerical simulation. Compared with the direct GA searching, the computational cost is greatly reduced, which presents a similar result.

Nondegeneracy of optimality conditions in control problems for a radiative–conductive heat transfer model

A boundary control problem for a nonlinear steady-state heat transfer model accounting for heat radiation effects is considered. The problem consists in the minimization of a cost functional by controlling the reflection properties of the boundary. The solvability of the control problem is proven, an optimality system is derived, and the nondegeneracy of optimality conditions is established. The results of numerical simulations are presented.

Calibration of aero-structural reduced order models using full-field experimental measurements

The structural response of hypersonic aircraft panels is a multi-disciplinary problem, where the nonlinear structural dynamics, aerodynamics, and heat transfer models are coupled. A clear understanding of the impact of high-speed flow effects on the structural response, and the potential influence of the structure on the local environment, is needed in order to prevent the design of overly-conservative structures, a common problem in past hypersonic programs. The current work investigates these challenges from a structures perspective. To this end, the first part of this investigation looks at the modeling of the response of a rectangular panel to an external heating source (thermo-structural coupling) where the temperature effect on the structure is obtained from forward looking infrared (FLIR) measurements and the displacement via 3D-digital image correlation (DIC). The second part of the study uses data from a previous series of wind-tunnel experiments, performed to investigate the response of a compliant panel to the effects of high-speed flow, to train a pressure surrogate model. In this case, the panel aero-loading is obtained from fast-response pressure sensitive paint (PSP) measurements, both directly and from the pressure surrogate model. The result of this investigation is the use of full-field experimental measurements to update the structural model and train a computational efficient model of the loading environment. The use of reduced order models, informed by these full-field physical measurements, is a significant step toward the development of accurate simulation models of complex structures that are computationally tractable.

Optimal boundary control of a steady-state heat transfer model accounting for radiative effects

A boundary control problem for a nonlinear steady-state heat transfer model accounting for heat radiation effects is considered. The aim of control consists in obtaining a prescribed temperature distribution in a part of the model domain by controlling the boundary temperature. The solvability of this control problem is proven, and optimality conditions are derived. Numerical simulations are presented.

Boundary Design of Reflection Properties of a Steady-State Complex Heat Transfer Model

A boundary multiplicative control problem for a nonlinear steady-state heat transfer model accounting for heat radiation effects is considered. The aim of control consists in obtaining a prescribed temperature or radiative intensity distributions in a part of the model domain by controlling the boundary reflectivity. The solvability of this control problem is proved, and optimality conditions are derived.

Influence of self-protective atmosphere in fiber laser welding of austenitic stainless steel

The thermo-chemical reactions between working atmosphere and molten weld pool in fusion welding process severely affect the weld joint quality and weld metal properties. Hence, the welding atmosphere plays a significant role to decide the weld joint quality. Fiber laser source is popularly being used in recent past over Nd:YAG, CO2, and diode lasers due to characteristic advantages of compact size, high stability and reliability, and deeper penetration. In present work, the characteristic difference between a self-protective atmosphere of argon and open atmosphere have been investigated during fiber laser welding of austenitic stainless steel. A mixed mode beam power of a 2-kW ytterbium fiber laser has been used to conduct the experiments. The characteristic variation in terms of weld pool size and shape, weld bead quality, and top surface profile at various process parameters are analyzed. The experiments are conducted at 800 and 1000-W laser power and 13.33 to 18.33-mm/s laser scanning speed. The study indicates that aspect ratio as well as weld depth of penetration in a self-protective atmosphere of argon is more as compared to open atmospheric condition. The appearance of top surface profile in case of self-protective atmosphere is far better than open atmospheric conditions. Furthermore, a three-dimensional non-linear transient heat transfer model is developed to compute the weld pool dimensions using a Gaussian-distributed volumetric heat source. The result demonstrates that the numerically computed weld pool shape and size are in a fair agreement with experimentally measured macrographs.

Quantifying MLI Thermal Conduction in Cryogenic Applications from Experimental Data

Multilayer Insulation (MLI) uses stacks of low-emittance metalized sheets combined with low-conduction spacer features to greatly reduce the heat transfer to cryogenic applications from higher temperature surrounds. However, as the hot-side temperature decreases from room temperature to cryogenic temperatures, the level of radiant heat transfer drops as the fourth power of the temperature, while the heat transfer by conduction only falls off linearly. This results in cryogenic MLI being dominated by conduction, a quantity that is extremely sensitive to MLI blanket construction and very poorly quantified in the literature. To develop useful quantitative data on cryogenic blanket conduction, multilayer nonlinear heat transfer models are used to analyze extensive heat transfer data measured by Lockheed Palo Alto on their cryogenic dewar MLI and measured by JPL on their spacecraft MLI. The data-fitting aspect of the modeling allows the radiative and conductive thermal properties of the tested blankets to be explicitly quantified. Results are presented showing that MLI conductance varies by a factor of 600 between spacecraft MLI and Lockheed's best cryogenic MLI.

On the inverse problem of thermal conductivity determination in nonlinear heat and moisture transfer model within textiles

This paper focuses on an inverse problem of textile thermal conductivity determination (IPTCD) based on the nonlinear heat and moisture transfer model under low temperature. The conditional well-posedness of the analytical solution and the stability for numerical solution to the inverse problem of determining the left boundary value (IPLB) are derived respectively. The mathematical formulation of IPTCD is presented and deduced to an optimization problem with least squares. By means of Parametrized Fibonacci (PF) search method and Genetic Algorithm (GA), the approximate solution to the IPTCD is numerically obtained.