Nonlinear Temperature Profile Research Articles

Thermal Vibration Analysis of Functionally Graded Porous Plates Reinforced by Graphene Platelets Supported by Arbitrarily Distributed Kerr Foundations Under a Nonlinear Temperature Profile

Thermal Vibration Analysis of Functionally Graded Porous Plates Reinforced by Graphene Platelets Supported by Arbitrarily Distributed Kerr Foundations Under a Nonlinear Temperature Profile

Output performance improvement for thermoelectric transistor with the consideration of the Thomson effect and geometry optimization

Despite significant attention paid to thermoelectric generators in the energy conversion field, their limited output performance has restricted their large-scale applications. Therefore, there is a pressing need to conceive a novel thermoelectric device concept that can strengthen their competitiveness. In this context, the concept and principle of thermoelectric (TE) transistor with ultrahigh performance is a demand-driven innovation. Built on the foundation of a PNP structure, TE transistor only relies on the Seebeck voltage to operate normally. This work employs P-type Bi0.5Sb1.5Te3 and N-type Bi2Te2.97Se0.03 as the component materials. By considering the conduction heat, Joule heat, Thomson heat, and temperature-dependent material properties, a one-dimensional heat transfer model was used to obtain the nonlinear temperature profile inside TE transistor. Further, the structure and operation conditions of TE transistor with varying geometric dimensions were determined based on the hole concentration distribution and build-in voltage variation. Finally, the optimal concentrations and geometric dimensions of TE transistor were obtained using a compromise method. The calculation results reveal that TE transistor can achieve an optimal output power of 133.7 mW under a temperature difference of 50 K (Th = 353 K, Tc = 303 K) with the corresponding conversion efficiency of 7.73%. This work provides theoretical guidance for future experimental validation of TE transistor.

Exploring the mechanical response of functionally graded hollow disks: insights from rotation, gravity and variable heat generation

PurposeThe purpose of the study is to perform elastic stress and deformation analysis of a functionally graded hollow disk under different conditions (rotation, gravity, internal pressure, temperature with variable heat generation) and their combinations.Design/methodology/approachThe classical method of solution, Navier's equation, is used to solve the governing equation. The analysis considers thermal and mechanical boundary conditions and takes into account the variation of material properties according to a power law function of the radius of the disk and grading parameter.FindingsThe findings of the study reveal distinct trends and behaviors based on different grading parameters. The influence of gravity is found to be negligible, resulting in similar patterns to the pure rotation case. Variable heat generation introduces non-linear temperature profiles and higher displacements, with stress values influenced by grading parameters.Practical implicationsThe study provides valuable insights into the behavior of displacement and stresses in hollow disks, offering a deeper understanding of their mechanical response under varying conditions. These insights can be useful in the design and analysis of functionally graded hollow disks in various engineering applications.Originality/valueThe originality and value of this study lies in the consideration of various loading combinations of rotation, gravity, internal pressure and temperature with variable heat generation. Furthermore, the study of effect of various angular rotations, temperatures and pressures expands the understanding of the mechanical behavior of such structures, contributing to the existing body of knowledge in the field.

Experimental investigation of a novel standing-wave thermoacoustic engine based on PCHE and supercritical CO2

The pursuit of high amplitude and low onset temperature difference is one important topic in thermoacoustic engines. In this paper, a novel standing-wave thermoacoustic engine is constructed working with supercritical CO2, whose core components are integrated as a printed circuit heat exchanger (PCHE). Our experimental results confirm that at any location on the resonator, the pressure obeys a cosine law with time, and the whole pressure field exhibits a seesaw-like spatiotemporal behavior. Under a fixed charging mass, the amplitude of pressure oscillation increases with temperature difference, obeying a power law relation. The maximum amplitude achieved in this work is 0.419 MPa at a temperature difference of 151.0 °C and a mean pressure of 9.621 MPa. Besides, the frequency with an average of 7.6 Hz shows weak variations. The onset temperature difference decreases as the critical pressure is approached, and the minimum value achieved is 14.8 °C. Moreover, the cooling effect of oscillating CO2 to the high-temperature portion of the stack is revealed, causing the strongly nonlinear temperature profile along the stack. This paper manifests that supercritical CO2 and PCHE are highly prospective to be employed in thermoacoustic devices.

Deep Autoencoder Thermography for Defect Detection of Carbon Fiber Composites

Infrared thermography (IRT) is an economical nondestructive testing technique for structural health monitoring of composite materials. However, the nonlinear nature of the thermographic data and the adverse effects of noise and inhomogeneous backgrounds prevent it from achieving satisfactory results. Most of the existing thermographc data analysis methods are supervised and/or linear, which therefore are not favorable for nonlinear feature extraction of unlabeled thermograms. In this work, a deep autoencoder thermography (DAT) method is proposed for detecting subsurface defects in composite materials. The multi-layer network structure of DAT can handle nonlinear temperature profiles, and the output of the intermediate hidden layer is visualized to highlight defects. The layer-by-layer feature visualization reveals how the model extracts defect features. A loss inflection point scheme is utilized to determine a suitable depth of the model. Moreover, a new quantitative index is proposed to compare the defect detectability of different methods.

Thermal vibration analysis of functionally graded graphene platelets-reinforced porous beams using the transfer function method

Functionally graded graphene platelets-reinforced (FG-GPL) porous materials are advanced, designable, lightweight, and high-strength composite materials promising in launch vehicles, space shuttles, and hypersonic vehicles as integrated heat-protection and load-bearing structures. Thermal vibration analysis ensures service safety in environments with dynamic thermal loads. A free vibration analysis model of an FG-GPL porous beam was proposed based on the micromechanical model and Timoshenko beam theory (TBT) under a nonlinear temperature profile. First, three types of functionally graded porosity distributions and graphene-platelet dispersion patterns were assumed along the thickness direction of the beam. Material properties, including elastic modulus, Poisson’s ratio, and density, were calculated using the Gaussian random field scheme and Halpin–Tsai model. Second, a nonlinear temperature profile was established considering the influence of porosity and graphene platelets by solving a one-dimensional–heat-conduction equation. Third, the governing equations of thermal vibration of the beam were obtained using the TBT and Hamilton’s principle. The frequencies of different porosity distributions and graphene-platelet dispersion pattern combinations were calculated by solving the governing equations using the transfer function method. Finally, the results were validated, and the parameter effects of the temperature profiles, weight fraction of graphene platelets, porosity coefficient, and thermal gradient on the fundamental frequencies were analyzed. Compared to a linear temperature profile, the frequency under a nonlinear temperature profile is hardly changed for the combined symmetrically distributed porosity and GPL beams, while it is different for the asymmetric combinations.

Dynamics of magnetohydrodynamic nonlinear radiative flow of diamond‐Co3O4/EG hybrid nanofluid with homogeneous—heterogeneous reactions

AbstractNewtonian fluid flow analysis is quickly becoming one of the most important areas of study. These liquids have an extensive range of engineering and industrial uses, including in cooling systems, food processing, nuclear reactors, paint and adhesives, and drilling rigs. Hybrid nanofluids, on the other hand, are vital to the heat transmission process. This research aims to examine the hybrid nanofluid's three‐dimensional nonlinear radiative magnetohydrodynamic flow over a stretching surface. Ethylene glycol is considered a base fluid, whereas diamond and Cobalt tetroxide (Co3O4) are considered hybrid nanoparticles. The approach also takes into account the catalytic property of homogeneous—heterogeneous processes. The governing fluid equations are computed by Homotopy analysis method and compare the result with shooting technique after employing appropriate transformations. The result of different constraints on temperature profiles and velocity profiles are scrutinized and graphically depicted as well as through the construction of table. A graphical comparison has been made between Nusselt number and skin friction for hybrid nanofluid and nanofluid respectfully. The finding of our study is that the velocity profile decreases for the high value of magnetic parameter. In the presences of nonlinear radiation temperature profile enhances. In transferring heat, the hybrid nanofluid is more effective than nanofluid. This work can be used in various industries to increase their efficiency.

Dynamic Analysis of Sigmoid Bidirectional FG Microbeams under Moving Load and Thermal Load: Analytical Laplace Solution

This paper presents for the first time a closed-form solution of the dynamic response of sigmoid bidirectional functionally graded (SBDFG) microbeams under moving harmonic load and thermal environmental conditions. The formulation is established in the context of the modified couple stress theory to integrate the effects of microstructure. On the basis of the elasticity theory, nonclassical governing equations are derived by using Hamilton’s principle in combination with the parabolic higher-order shear deformation theory considering the physical neutral plane concept. Sigmoid distribution functions are used to describe the temperature-dependent thermomechanical material of bulk continuums of the beam in both the axial and thickness directions, and the gradation of the material length scale parameter is also considered. Linear and nonlinear temperature profiles are considered to present the environmental thermal loads. The Laplace transform is exploited for the first time to evaluate the closed-form solution of the proposed model for a simply supported (SS) boundary condition. The solution is verified by comparing the predicted fundamental frequency and dynamic response with the previously published results. A parametric study is conducted to explore the impacts of gradient indices in both directions, graded material length scale parameters, thermal loads, and moving speed of the acted load on the dynamic response of microbeams. The results can serve as a principle for evaluating the multi-functional and optimal design of microbeams acted upon by a moving load.

Wiener-Neural-Network-Based Modeling and Validation of Generalized Predictive Control on a Laboratory-Scale Batch Reactor.

Batch reactors are large vessels in which chemical reactions take place. They are mostly found to be used in process control industries for processes such as reactant mixing, waste treatment of leather byproducts, and liquid extraction. Modeling and controlling of these systems are complex due to their highly nonlinear nature. The Wiener neural network (WNN) is employed in this work to predict and track the temperature profile of a batch reactor successfully. WNN is different from artificial neural networks in various aspects, mainly its structure. The brief methodology that was deployed to complete this work consisted of two parts. The first part is modeling the WNN-based batch reactor using the provided input–output data set. The input is feed given to the reactor, and the reactor temperature needs to be maintained in line with the optimal profile. The objective in this part is to train the neural network to efficiently track the nonlinear temperature profile that is provided from the data set. The second part is designing a generalized predictive controller (GPC) using the data obtained from modeling the reactor to successfully track any arbitrary temperature profile. Therefore, this work presents the experimental modeling of a batch reactor and validation of a WNN-based GPC for temperature profile tracking.

Observation and modelling of snow and sea ice mass balance and its sensitivity to atmospheric forcing during spring and summer 2007 in the Central

Snow depth and sea ice thickness were observed applying an ice mass balance buoy (IMB) in the drifting ice station Tara during the International Polar Year in 2007. Detailed in situ observations on meteorological variables and surface fluxes were taken during May to August. For this study, the operational analyses and short-term forecasts from two numerical weather prediction (NWP) models (ECMWF and HIRLAM) were extracted for the Tara drift trajectory. We compared the IMB, meteorological and surface flux observations against the NWP products, also applying a one-dimensional thermodynamic sea ice model (HIGHTSI) to calculate the snow and ice mass balance and its sensitivity to atmospheric forcing. The modelled snow depth time series, controlled by NWP-based precipitation, was in line with the observed one. HIGHTSI reproduced well the snowmelt onset, the progress of the melt, and the first date of snow-free conditions. HIGHTSI performed well also in the late August freezing season. Challenges remain to model the “false bottom” observed during the melting season. The evolution of the vertical temperature profiles in snow and ice was better simulated when the model was forced by in situ observations instead of NWP results. During the melting period, the nonlinear ice temperature profile was successfully modelled with both forcing options. During spring and the melting season, total sea ice mass balance was most sensitive to uncertainties in NWP results for the downward longwave radiation, followed by the downward shortwave radiation, air temperature, and wind speed. Citation : Cheng B, Vihma T, Palo T, et al. Observation and modelling of snow and sea ice mass balance and its sensitivity to atmospheric forcing during spring and summer 2007 in the Central Arctic. Adv Polar Sci, 2021, 32(4): 309-323, doi: 10.13679/j.advps.2021.0047

Two-Dimensional Transient Heat Transfer Model for High-Temperature Laser-Scanning Confocal Microscopy

Abstract High-temperature laser-scanning confocal microscopy (HT-LSCM) has proven to be an excellent experimental technique through in situ observations of high temperature phase transformation to study kinetics and morphology using thin disk steel specimens. A 1.0 kW halogen lamp within the elliptical cavity of the HT-LSCM furnace radiates heat and imposes a nonlinear temperature profile across the radius of the steel sample. When exposed at the solid/liquid interface, this local temperature profile determines the kinetics of solidification and phase transformation morphology. A two-dimensional numerical heat transfer model for both isothermal and transient conditions is developed for a concentrically solidifying sample. The model can accommodate solid/liquid interface velocity as an input parameter under concentric solidification with cooling rates up to 100 K/min. The model is validated against a commercial finite element analysis software package, strand7, and optimized with experimental data obtained under near-to equilibrium conditions. The validated model can then be used to define the temperature landscape under transient heat transfer conditions.

Thermal shock response of porous functionally graded sandwich curved beam using a new layerwise theory

This paper, for the first time, presents the thermal shock response of porous functionally graded (FG) sandwich curved beams subjected to thermal shocks. The authors have used a higher-order layerwise beam theory developed for the analysis. This new layerwise theory has a higher-order displacement field for the core and a linear displacement field for top and bottom facesheets maintaining the continuity of displacement at the layer interface. The top and bottom layers of the functionally graded sandwich curved beam are made of pure ceramic and pure metal constituent, respectively, and the core is considered to be made of functionally graded material (FGM) having porosity. The top surface of the beam is subjected to thermal shocks the bottom surface is kept at a reference temperature or is thermally insulated. The solution for the nonlinear temperature profile is obtained using the Crank-Nicolson method. An eight-noded isoparametric element having seven degrees of freedom per node is used to develop the finite element formulation. The governing differential equation is obtained using the Hamilton’s principle, and the resulting transient problem is solved using the Newmark constant acceleration integration method. The effects of curvature, thickness, core to facesheet thickness ratio, intensity of the thermal shock, porosity coefficient, and boundary conditions are investigated on thermally induced vibration response of porous FG sandwich curved beams. The analysis reveals that the proposed finite element formulation is straight forward, accurate, and widely applicable for the analysis of porous functionally graded sandwich curved beams.

Thermal vibration characteristics of pre/post-buckled bi-directional functionally graded tapered microbeams based on modified couple stress Reddy beam theory

This paper investigates the nonlinear vibration characteristics of pre- and post-buckled nonuniform bi-directional functionally graded (BDFG) microbeams subjected to nonlinear thermal loading. The formulations derived herein are based on thermoelastic constitutive relations of the higher-order Reddy beam theory in conjunction with the modified couple stress theory, von Karman nonlinear strains, and physical neutral plane concept, for the first time. Power-law model is employed to describe the continuous variation of temperature-dependent thermomechanical material properties of BDFG in both the thickness and length directions. Variable microstructure length scale parameter and Poisson’s ratio in both directions are considered. The variable coefficient nonlinear governing equations and associated boundary conditions of nonuniform BDFG microbeam in the thermal environment are derived utilizing the Hamilton principle. The obtained equations are discretized using the differential quadrature method accounting for various boundary conditions, and iterative Newton’s method is adopted to solve the resulting nonlinear algebraic equations. The developed model and solution procedure are validated by comparing the predicted results with those in the available literature. To this end, extensive parametric studies are carried out to explore the influence of linear and nonlinear temperature profiles, microstructure length scale parameter ratio, microstructure length scale parameter-to-thickness ratio, gradient indices in thickness and length directions, material-temperature dependency, and taperness parameters on the nonlinear vibration response and higher-order mode frequencies of tapered BDFG microbeams accounting different boundary conditions.

Beyond phonon hydrodynamics: Nonlocal phonon heat transport from spatial fractional-order Boltzmann transport equation

Spatially convoluting formulations have been used to describe nonlocal thermal transport, yet there is no related investigation at the microscopic level such as the Boltzmann transport theory. The spatial fractional-order Boltzmann transport equations (BTEs) are first applied to the description of nonlocal phonon heat transport. Constitutive and continuity equations are derived, and two anomalous behaviors are thereafter observed in one-dimensional steady-state heat conduction: one is the power-law length-dependence of the effective thermal conductivity, κeff∝Lβ with L as the system length, and the other is the nonlinear temperature profile, Tx−Tx=0∼x1+η. A connection between the length-dependence and nonlinearity exponents is established, namely, β=−η. Furthermore, we show that the order of these BTEs should be restricted by the ballistic limit. In minimizing problems, the nonlocal models in this work give rise to different results from the case of Fourier heat conduction, namely that the optimized temperature gradient is not uniform.

New high-resolution gridded dataset of daily mean, minimum, and maximum temperature and relative humidity for Central Europe (HYRAS)

This study presents daily high-resolution (5 km × 5 km) grids of mean, minimum, and maximum temperature and relative humidity for Germany and its catchment areas, from 1951 to 2015. These observational datasets (HYRAS) are based upon measurements gathered for Germany and its neighbouring countries, in total more than 1300 stations, gridded in two steps: first, the generation of a background field, using non-linear vertical temperature profiles, and then an inverse distance weighting scheme to interpolate the residuals, subsequently added onto the background field. The modified Euclidian distances used integrate elevation, distance to the coast, and urban heat island (UHI) effect. A direct station-grid comparison and cross-validation yield low errors for the temperature grids over most of the domain and greater deviations in more complex terrain. The interpolation of relative humidity is more uncertain due to its inherent spatial inhomogeneity and indirect derivation using dew point temperature. Compared with other gridded observational datasets, HYRAS benefits from its high resolution and captures complex topographic effects. HYRAS improves upon its predecessor by providing datasets for additional variables (minimum and maximum temperature), integrating temperature inversions, maritime influence and UHI effect, and representing a larger area. With a long-term observational dataset of multiple meteorological variables also including precipitation, various climatological analyses are possible. We present long-term historical climate trends and relevant indices of climate extremes, pointing towards a significantly warming climate over Germany, with no significant change in total precipitation. We also evaluate extreme events, specifically the summer heat waves of 2003 and 2015.

Effect of nonlinear temperature and concentration profiles on the stability of a layer of fluid with chemical reaction

Investigation of the onset of thermosolutal convection with chemical reaction is carried out for different types of basic temperature and concentration gradients using linear theory and energy method. An unconditional nonlinear stability with exponential decay of finite amplitude perturbations is achieved and the Galerkin technique is utilized to solve the resulting eigenvalue problem obtained from linear and nonlinear analysis. The numerical scheme is validated with existing results and the results are obtained for linear, parabolic, inverted parabolic, piecewise linear, oscillatory, and step-function profiles of temperature and concentration gradients. The linear and nonlinear results show the existence of subcritical instability.

Development of full spectrum correlated k-model for spectral radiation penetration within liquid fuels

In this paper, full spectrum correlated k-distribution (FSCK) models are developed for several liquid fuels including decane, ethanol, ethylene glycol, heptane, and toluene. The models were built using high-resolution absorption spectra, collected from the literature. To validate the novel FSCK models, they were used to solve radiative heat transfer within liquid pools assuming three temperature profiles (i.e. constant temperature, linear and nonlinear temperature profiles) and the calculated transmissivity and radiative heat source of FSCK were compared with those of using high resolution absorption spectra and the gray models implementing Planck mean absorption coefficient. The sensitivity analysis was performed for the accuracy of the FSCK results with number of quadrature points for different fuels. Using seven quadrature points for FSCK model has been found to be sufficient for providing good accuracy of spectral radiative heat transfer within the liquid fuels with a reasonable computational cost. Moreover, we studied the effect of the reference temperature used in FSCK model and found out that for the pool fire scenario, the FSCK provides its best accuracy if an equivalent temperature representing the radiation feedback from the flame is used as the reference temperature. Comparison of computational costs of high-resolution spectral radiation calculations and FSCK method revealed a significant computational gain by use of FSCK model.

Simple Empirical Temperature Gradient Prediction Model for Jointed Plain Concrete Pavements: Development and Validation

The aim of this paper is to propose a simple empirical prediction model for temperature gradients within concrete slabs of jointed plain concrete pavements (JPCPs) based on data collected by the Pavement Conditions Monitoring System at Shanghai Pudong International Airport. Temperature data (7,056 data sets) were obtained at the center and corner of the concrete slab and evaluated via statistical analysis. Equivalent linear temperature gradients were employed to quantify the nonlinear temperature profiles throughout the depth of the concrete slab. The surface temperature was obtained via the regressed quadratic function of the temperature profile. For simplicity and effectiveness, concrete slab thickness, surface temperature, air temperature, and time were selected as the input variables. A simple empirical model for predicting the temperature gradient in the concrete slab was developed using multiple regression analysis and validated by field temperature data. The results show no significant difference between the temperatures measured at the center and corner of the concrete slab. Hence, measurement location appears to have little effect on the monitoring of temperature in JPCPs. The results also show that the calculated surface temperature is valid for establishing the empirical model. Moreover, the statistical analysis results indicate that the empirical model fits the data well and all the coefficients in the model are significant at 5% significance. The final results of the model validation demonstrate that the proposed empirical model is reliable and can be conveniently used to predict the temperature gradients within concrete slabs of JPCPs.

Buoyancy-surface tension driven forces on electro-thermal-convection in a rotating dielectric fluid-saturated porous layer: effect of cubic temperature gradients

This paper analyses the onset of buoyancy-surface tension driven forces on rotating electro-thermal-convection in a dielectric fluid-saturated porous layer under the influence of different basic temperature gradients. The lower surface is rigid-isothermal, and the upper surface is stress-free and flat at which the Robin-type of thermal boundary condition is invoked. The principle of exchange of stability is valid and the stability eigenvalue problem is solved numerically using the Galerkin method. The parameters influencing the stability characteristics of the system are the thermal Rayleigh number (\( R_{t} \)), electric Rayleigh number (\( R_{e} \)), Marangoni number (\( Ma \)), Taylor number (\( Ta \)), Darcy number (\( Da \)), Biot number (\( Bi \)) and the viscosity ratio (\( \varLambda \)). The onset of convection is delayed for a nonlinear temperature profile when compared to the linear temperature profile. It is observed that the strength of surface tension force and an AC electric field is to hasten the onset. The system is found to be more stable with increasing \( Bi \), \( Ta \) and \( \varLambda \) as well as decrease in \( Da \). The surface tension and electric forces complement each other and always observed to be \( Ma_{c} < \text{R}_{ec} \).

Heat current fluctuations and anomalous transport in low-dimensional carbon lattices

Molecular dynamics simulations and nonequilibrium importance sampling are used to study the heat transport of low dimensional carbon lattices. For both carbon nanotubes and graphene sheets heat transport is found to be anomalous, violating Fourier's law of conduction with a system size dependent thermal conductivity and concomitant nonlinear temperature profiles. For carbon nanotubes, the thermal conductivity is found to increase as the square root of the length of the nanotube, while for graphene sheets the thermal conductivity is found to increase as the logarithm of the length of the sheet. The particular length dependence and nonlinear temperature profiles place carbon lattices into a universality class with nonlinear lattice models, and suggest that heat transport through carbon nano-structures is better described by a Levy walk rather than simple diffusion.