Nonlinear Temperature Variation Research Articles

EFG meshless-ANN approach for free vibration analysis of functionally graded material plates on elastic foundation in thermal environments

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Enhanced numerical modeling of natural heat convective phase change for generalized non-Newtonian fluids at high Rayleigh number

Numerical modeling of convective heat transfer employing non-Newtonian fluids is a key issue and represent an interesting challenge in many engineering applications. For this reason, this work develops an enhanced numerical model to predict fast and accurately the convective phase change for generalized non-Newtonian fluids. The strongly thermally coupled model is solved by an improved pressure-correction algorithm (SIMPLERnP) and the Finite Volume Method with accuracy of the third order for the transient terms and second order for the convective boundary conditions and the velocity gradients that allows to calculate the apparent viscosity. The study examines the natural heat convective solidification of the ternary Al-27 %Cu-5.25 %Si alloy with the Herschel-Bulkley rheology at a high Rayleigh number (>107). In addressing the main problem, four crucial aspects are discussed: the validation of the numerical scheme with numerical and experimental results; the modeling of the non-linear temperature variation of the liquid phase change fraction; the non-Newtonian effects of the power index (0.1 ≤ n ≤ 1.9) and yield stress (0≤τ0≤5 Pa) on the heat transfer mechanisms; and finally, the time of computation with the high-order numerical scheme and the enhanced pressure-correction algorithm. The main finding is that FVM/SIMPLERnP provides a significant reduction in the time of computation compared to reliable pressure-correction schemes (SIMPLER and IDEAL), being a robust, accurate and efficient scheme to solve complex natural heat convective phase change problems involve generalized non-Newtonian fluids at high-Rayleigh numbers.

Investigation on the temperature distribution characteristics of steel slag asphalt mixture under different microwave heating and cooling methods

The utilization of steel slag aggregate (SSA) can enhance the microwave absorption efficiency of asphalt mixture, thus increasing its temperature and self-healing capability. In this study, the temperature distribution of basalt porous asphalt concrete (PAC-B), ordinary steel slag porous asphalt concrete (PAC-US), and modified steel slag porous asphalt concrete (PAC-MS) under the influence of different microwave heating and cooling methods were investigated through laboratory tests and numerical simulations. The heating methods including continuous heating, and two intermittent heating methods were used. Using the Monte Carlo method, three-dimensional mesoscopic numerical models were developed to simulate the microwave heating and cooling processes. The temperature of both the aggregates and asphalt mortar were analyzed, considering the influence of particle size on the aggregate temperature. The results revealed that the average inner heating rate of the three specimens is higher than the average surface heating rate. The average surface and inner heating rates of PAC-MS were higher than those of PAC-US and PAC-B. The average surface temperature and inner temperature during the heating process changed linearly, while nonlinear temperature variations were observed during the subsequent cooling phase. Increasing the number of cooling intervals during heating resulted in a more uniform temperature distribution within steel slag aggregate specimens. The results of numerical simulation indicated that the maximum temperature of aggregate was greater than that of asphalt mortar. During the cooling process, the highest temperature of the aggregate continuously decreased, whereas the lowest temperature initially increased before decreasing. The highest average volume temperature for various particle sizes was observed within the range of 4.75–9.5 mm. The laboratory test results were effectively validated by the numerical simulations.

Nonlinear Approximation for Natural Convection Flow Past A Vertical Moving Plate With Nonlinear Thermal Radiation Effect

This piece of work contains significant insight associated with the analysis of fluid transport in the vicinity of a constantly moving vertical plate with nonlinear thermal radiation. The heat transport at the wall surface is assumed to be influenced by convective boundary conditions. Furthermore, thermal transport is considered to be enhanced by nonlinear temperature variation with temperature (NDT). The boundary layer approximation equations are simplified through suitable alteration known as the similarity transformation. The resulting ODEs are translated into the IVP via shooting techniques and then integrated using the RKF45 algorithm in Maple. The impact of the dimensionless parameters dictating the fluid behaviour is demonstrated via graphs and tables. In the cause of the analysis, it is observed that the heat transfer enhances when the fluid flow in the direction +ve x-axis whereas the plate moves in the direction of the -ve x-axis but decreases when the plate and fluid move in the same direction. The skin friction coefficient decreases when the fluid flow is directed toward the +ve x-axis whereas the plate moves toward the -ve x-axis but is enhanced when the plate and the fluid move in the same orientation. The temperature and velocity profiles appreciate with the nonlinear thermal radiation when the motion of the plate and the fluid are on the same axis. The temperature gradient near the wall depreciated gradually due to nonlinear thermal radiation growth but appreciate in the free stream.

Thermal pattern at kueishantao (KST) volcano of Taiwan from satellite-observed temperatures and its implication

Abstract Kueishantao (KST) is an active volcanic island off the northeastern coast of Taiwan. Tectonically, it lies in the south of the Okinawa Trough and opposite to the Ilan plain, in which is the southwestern end of the trough. KST provides a convenient observation site for the subsurface geological and geothermal activity and mechanism at its proximity. Land surface temperature (LST) of volcanoes detected from satellite sensors reflects the thermal status of heat sources in the subsurface. LST thus is a key parameter to the understanding of the volcanic process and geothermal resources. This research utilizes the satellite-observed multi-temporal land surface temperature imagery in 1999–2022 on the Kueishantao volcano of Taiwan to explore its geothermal state. The U.S. NASA Earth-observing satellites onboard three thermal sensors (i.e., Landsat ETM+, Terra ASTER, and Aqua/Terra MODIS) derived time series of land surface temperature from 1999 are employed to define the past and current pattern of geothermal activity plus the future trend of the KST. The spatiotemporal LST distribution of KST volcano is explored and analyzed. The spatial LST distribution of the KST volcano indicates that LST anomaly areas are mainly located on the southeast island, which is well correlated with the possible magma reservoir location from previous geophysical and geological surveys. An increasing trend of two-decade LST time series is revealed from all three thermal sensors. The retrieved surface thermal pattern shows non-linear temperature variations that imply the non-steady-state nature of the subsurface thermal sources at this volcano. In summary, satellite LST observations facilitate the understanding on the subsurface magmatic processes of active volcanoes for further management of geothermal resources.

Entropy generation and thermal analyses of a Cross fluid flow through an inclined microchannel with non‐linear mixed convection

AbstractThe temperature difference of the various applications such as microchannel heat exchangers, microelectronics, solar collectors, automotive systems, micro fuel cells, and microelectromechanical systems (MEMS) is relatively large. The buoyancy force (mixed convection) modeled by the conventional Boussinesq approximation is inadequate since the density of the operating fluids fluctuates non‐linearly with the temperature difference. Therefore, the mixed non‐linear convective transport of the flow of Cross fluid through three different geometric aspects (horizontal, vertical, and inclined) of the microchannel under the non‐linear Boussinesq (NBA) approximation is investigated. Mechanisms of internal heat source, Rosseland radiative heat flux, and frictional heating are incorporated into the thermal analysis. The mathematical construction is proposed using the Cross fluid model for a steady‐state, and subsequent non‐linear differential equations are deciphered by the spectral quasi‐linearization method (SQLM). Graphical sketches were constructed and displayed that explore the stimulus of various key parameters on Bejan number, velocity, temperature, and entropy generation. It is found that the Bejan number and entropy production improved due to the non‐linear density temperature variation. The convective heating boundary conditions augment the entropy production. The pressure gradient accelerates the transport of fluid in a microchannel. Furthermore, among three different geometries, the velocity, entropy production, and temperature are the highest for the vertical microchannel.

Analytical Study on Intricacies of Axial Conduction in Microchannel Heat Sinks

Abstract Microchannel heat sinks are potential devices that remove heat flux from high power density miniaturized electronic components. While the large surface-area-to-volume ratio and high heat transfer coefficient are the key features rendering benefits, the small flow rate and short channel lengths alongside high solid cross section to fluid free flow area make them susceptible to intense axial conduction loss. The conventional models for macrodevices based on the one-dimensional energy equation are often inappropriate in the microdomain. A novel multidimensional analytical model (capable of capturing axial heat transfer in microchannel heat sinks) has been used to study the thermal performance over a varied range of geometric and flow parameters. The effect of axial conduction has been seen in the solid–fluid temperature profiles, interfacial flux distribution and the average amount of heat transferred axially. The results indicate a skewed flux distribution at the fluid–solid interface leading to nonlinear temperature variation when axial conduction is dominant. Moreover, it has been shown that nonlinearity in the fluid temperature introduces significant errors in experimental data reduction, leading to apparently very low Nusselt number estimation. Moreover, this erroneous data interpretation is also linked to the prediction of a strong Reynolds number dependency of the average Nusselt number in the laminar flow regime.

Fully developed free convective flow of a Bingham fluid in a circular pipe with permeable wall

The present work focuses on the convection flow of a Bingham liquid in a circular pipe with permeable wall using nonlinear density temperature variation (NDT) relationship. The novelty of this communication is to study the impression of yield stress, NDT parameter on convective flow of Bingham liquid in a circular pipe with heat source. The governing flow equations are nonlinearly coupled and therefore complex to solve. Hence, perturbation method is applied to transform into linear ordinary differential equation to obtain the velocity and temperature fields. The expressions for velocity, plug flow velocity, temperature, plug flow temperature and heat transfer rate are derived. The outcomes of heat source parameter, permeable parameter, slip parameter and yield stress parameter on the fluid momentum and dimensionless temperature are obtained. The velocity field decreases with increase in yield stress and for negative values of NDT parameter. The increase in the NDT parameter increases the rate of heat transfer. When the yield stress and permeability parameter , our results concur with [Bhargava, R., and R. S. Agarwal. 1979. “Fully Developed Free Convection Flow in a Circular Pipe.” Indian Journal of Pure and Applied Mathematics 10 (3): 357–365]. The results obtained for the flow characteristics reveal many interesting behaviours that warrant further investigation on the non-Newtonian fluid phenomena and NDT variation.

Vibration and Uncertainty Analysis of Functionally Graded Sandwich Plate Using Layerwise Theory

In the present study, free vibration analyses of porous functionally graded material (FGM) sandwich plates are carried out in thermal environment. Two types of sandwich plates such as sandwich with FGM face sheets and homogeneous core and sandwich with homogeneous face sheets and FGM core are considered for free vibration analysis with nonlinear temperature variation over the thickness direction. The metal and ceramic components are assumed to be temperature dependent. The higher-order layerwise theory is adopted with an eight-noded rectangular element to build a finite element model for free vibration analysis. A radial basis function network (RBFN) based surrogate model is developed to investigate the stochastic frequency response due to the uncertain material properties. The accuracy and the efficiency of the RBFN model are established by comparing the results with that of Monte Carlo simulation. Further, the developed surrogate model is implemented to perform various parametric studies and sensitivity analyses. The influence of the volume fraction index, types of porosity, and thermal gradient on the stochastic frequency response are analyzed. Though the influence of different stochastic input parameters is strongly dependent on the volume fraction index, the mass density of metal is found to be the most sensitive parameter for the sandwich plate with FGM face sheets and homogeneous core.

Thermal conductivity of random polycrystalline BC3 nanosheets: A step towards realistic simulation of 2D structures

Boron carbide nanosheets (BC3NSs) are semiconductors possessing non-zero bandgap. Nevertheless, there is no estimation of their thermal conductivity for practical circumstances, mainly because of difficulties in simulation of random polycrystalline structures. In the real physics world, BC3NS with perfect monocrystalline is rare, for the nature produces structures with disordered grain regions. Therefore, it is of crucial importance to capture a more realistic picture of thermal conductivity of these nanosheets. Polycrystalline BC3NS (PCBC3NSs are herein simulated by Molecular Dynamics simulation to take their thermal conductivity fingerprint applying ΔT of 40 K. A series of PCBC3NSs were evaluated for thermal conductivity varying the number of grains (3, 5, and 10). The effect of grain rotation was also modeled in terms of Kapitza thermal resistance per grain, varying the rotation angle (θ/2 = 14.5, 16, 19, and 25°). Overall, a non-linear temperature variation was observed for PCBC3NS, particularly by increasing grain number, possibly because of more phonon scattering (shorter phonon relaxation time) arising from more structural defects. By contrast, the heat current passing across the slab decreased. The thermal conductivity of nanosheet dwindled from 149 W m−1 K−1 for monocrystalline BC3NS to the values of 129.67, 121.32, 115.04, and 102.78 W m−1 K−1 for PCBC3NSs having 2, 3, 5, and 10 grains, respectively. The increase of the grain̛s rotation angle (randomness) from 14.5° to 16°, 19° and 25° led to a rise in Kapitza thermal resistance from 2⨯10−10 m2 K·W−1 to the values of 2.3⨯ 10−10, 2.9⨯10−10, and 4.7⨯ 10−10 m2 K·W−1, respectively. Thus, natural 2D structure would facilitate phonon scattering rate at the grain boundaries, which limits heat transfer across polycrystalline nanosheets.

Prediction of Electropulse-Induced Nonlinear Temperature Variation of Mg Alloy Based on Machine Learning

Electropulse-induced heating has attracted attention due to its high energy efficiency. However, the process gives rise to a nonlinear temperature variation, which is difficult to predict using a traditional physics model. As an alternative, this study employed machine-learning technology to predict such temperature variation for the first time. Mg alloy was exposed to a single electropulse with a variety of pulse magnitudes and durations for this purpose. Nine machine-learning models were established from algorithms from artificial neural network (ANN), deep neural network (DNN), and extreme gradient boosting (XGBoost). The ANN models showed an insufficient predicting capability with respect to the region of peak temperature, where temperature varied most significantly. The DNN models were built by increasing model complexity, enhancing architectures, and tuning hyperparameters. They exhibited a remarkable improvement in predicting capability at the heating-cooling boundary as well as overall estimation. As a result, the DNN-2 model in this group showed the best prediction of nonlinear temperature variation among the machinelearning models built in this study. The XGBoost model exhibited poor predicting performance when default hyperparameters were applied. However, hyperparameter tuning of learning rates and maximum depths resulted in a decent predicting capability with this algorithm. Furthermore, XGBoost models exhibited an extreme reduction in learning time compared with the ANN and DNN models. This advantage is expected to be useful for predicting more complicated cases including various materials, multi-step electropulses, and electrically-assisted forming.

Thermal Buckling of Functionally Graded Sandwich Beams

Thermal buckling of new model of functionally graded (FG) sandwich beams is presented in this study. Material properties and thermal expansion coefficient of FG sheets are assumed to vary continuously along the thickness according to either power-law (P-FGM) or sigmoid function (S-FGM) in terms of the volume fractions of the constituents. Equations of stability are derived based on the generalized higher-order shear deformation beam theory. Thermal loads are supposed to be constant, linear or nonlinear distribution along the thickness direction. An accurate form solution for nonlinear temperature variation through the thickness of S-FGM and P-FGM sandwich beams is presented. Numerical examples are presented to examine the influence of thickness ratio, the inhomogeneity parameter and the thermal loading kinds on the thermal buckling response of various types of FG sandwich beams.

Size-dependent instability of organic solar cell resting on Winkler–Pasternak elastic foundation based on the modified strain gradient theory

The present study employs the modified strain gradient theory (MSGT) in conjunction with the refined shear deformation plate theory to explore the buckling behaviour of simply supported and clamped OSC. The Winkler-Pasternak elastic foundation is implemented to idealise the foundation. The size-dependent effect of the OSC is captured by the three length scale parameters within the MSGT. The Hamilton principle is used to derive the equations of motion and the boundary conditions, and the Galerkin procedure is subsequently implemented to obtain the critical buckling load. Subsequently, the framework is extended to the thermally induced buckling behaviour, and three types of temperature rise patterns, namely uniform, linear and nonlinear temperature variations, along the thickness of the OSC are considered. Several verification studies are conducted to illustrate the accuracy of the present method. Besides, size-dependent material properties are taken into consideration during the numerical experiments. Thorough studies are conducted to demonstrate the difference between critical buckling loads obtained from the MSGT, the modified couple stress theory (MCST), and the classical plate theory (CPT) models. Furthermore, the effects of length scale parameter (h/l), the aspect ratio (a/b), the length-to-thickness ratio (a/h) and the Winkler-Pasternak elastic foundation parameters on the buckling behaviour of the OSC are also revealed by the numerical results.

Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule

In the present paper, free axisymmetric vibrations of functionally graded circular plates subjected to a non-linear temperature distribution along the thickness direction have been studied on the basis of classical plate theory. The top and bottom surfaces of the plate are under uniform thermal environment. The mechanical properties of the plate material are assumed to be temperature-dependent and the plate is graded in thickness direction. The equations for thermo-elastic equilibrium as well as axisymmetric motion for such a plate model have been derived using Hamilton’s principle. Employing generalized differential quadrature rule, the numerical values of thermal displacements from thermo-elastic equilibrium equation and frequencies from the equation of motion for the lowest three modes of vibration have been computed for clamped, simply supported and free plates. The effects of the temperature difference at the surfaces together with material graded index and thickness of the plate on the frequencies have been investigated. The benchmark results for uniform and linear temperature distributions have been computed. For the validity of present considerations and the technique, frequency parameter has been compared for some special cases with published results obtained from other approximate methods.

Buckling analysis of porous FGM sandwich nanoplates due to heat conduction via nonlocal strain gradient theory

This article deals with the analysis of buckling behavior of simply supported porous functionally graded (FG) sandwich nanoplates resting on a Kerr foundation. The material properties of the FG sandwich nanoplate considered to be dependent on temperature and graded continuously along the thickness direction. The analytical equations are obtained using Hamilton’s variational principle, by considering the strain energies due to the thermal loads, and higher order nonlocal strain gradient plate theory which captures the shear deformation influences needless of any shear correction factor. Power-law model is adopted to describe continuous variation of material properties of FG sandwich nanoplate. An accurate solution for nonlinear temperature variation across the sandwich nanoplate thickness of is employed taking into account the thermal conductivity, the inhomogeneity parameter and the sandwich schemes. The numerical results computed indicate the influence of volume fraction index, nonlocal parameter, length scale parameter, porosity coefficient, Kerr foundation and temperature difference on the buckling response.

Influence of Non-Linear Boussinesq Approximation and Convective Thermal Boundary Condition on MHD Natural Convection Flow of a Couple Stress-Nanofluid in a Porous Medium

Nonlinear density and temperature variation’s role (NDT) on the magnetohydrodynamic (MHD) natural convective flow of couple stress fluid with nanoparticles through a vertical porous channel modeled as Darcy-Forchheimer flow is the purpose of our work. The nanoparticles volume fraction is taken into consideration (Buongiorno model). The nonlinear partial differential equations governing this flow were transformed into ordinary differential equations via the similarity technique and simulated numerically using Matlab, following boundary value problem (BVP4c) code. Graphical illustrations, including non-dimensional velocity, temperature, concentration, nanoparticle’s concentration and numerical results containing Nusselt and Sherwood numbers were presented for different values of the non-linear part of the Boussinesq approximation; couple stress parameter, and the Biot number on the walls.

Effect of Hall Currents and Non-Linear Density Temperature Variation on Convective Heat and Mass Transfer Flow of a Viscous Fluid past a Stretching Sheet with Thermo-Diffusion, Chemical Reaction and Heat Source

Effect of Hall Currents and Non-Linear Density Temperature Variation on Convective Heat and Mass Transfer Flow of a Viscous Fluid past a Stretching Sheet with Thermo-Diffusion, Chemical Reaction and Heat Source

Oil exponent thermal modelling for traction transformer under multiple overloads

To quantify the non-linear variation of top-oil temperature with load current, and further investigate the key parameters in the thermal model, a model for calculating the oil exponent is proposed in this study. First, a global oil momentum model was established based on the fluid resistance characteristic. Then, based on the heat transfer coupling relationship between the winding, the oil flow, and the radiator (outside air), a set of control equations describing the oil temperature and the oil flow rate was established by using energy conservation. Simultaneously, the top-oil temperature was recorded from a field traction transformer to verify the physical part of the proposed model. The regression model parameters were identified with the ordinary least-square estimation so the oil exponent can be calculated naturally. The calculated oil exponent of the traction transformer at a wide range of load was 0.7308, so the accuracy was improved by 9.47% compared with the IEEE/IEC recommended value. Newly updated oil exponent was also verified through a dynamic overload heat run test. It is expected that the proposed oil exponent model can help in estimating top-oil temperature with more convenience and accuracy, especially in frequent overload conditions.

Effects of temperature and electromagnetic induction on action potential of Hodgkin–Huxley model

Based on an improved the Hodgkin–Huxley (HH) neuron model which is driven by the electromagnetic induction, the effects of temperature and electromagnetic induction on the action potential of neuron are investigated by numerical computations. It is very interesting that, under the fixed condition of electromagnetic induction, there is a region for the electrical activity of neuron in the external current and temperature parameters plane, the region of electrical firing is similar to the Arnold’ tongue-like structure, and the Arnold’ tongue originates from the nonlinear variation of temperature with the increasing of threshold external current. The effects of temperature and electromagnetic induction on neuronic electrical activity are respectively discussed by using numerical simulations. Our results provide new insights into the roles of temperature in the improved HH neuron model, the existence of Arnold’ tongue-like structure might give some insights for the treatment of neurological diseases such as the epilepsia.

Performance studies on Macro fiber composite (MFC) under thermal condition using Kirchhoff and Mindlin plate theories

Macro fiber composite (MFC) has seen a surge in the applications of energy harvesting, vibration control and health monitoring due it its high flexibility, improved strength and high blocking force. For studying the actuation performance of MFC under electrical and thermal loading, a 2D FE model based on Kirchhoff and Mindlin plate theory is developed and validated using experimental observations. Effect of non-linear variation of temperature across the thickness of the whole structure is studied. The present model is also extended to study the effect of linear variation of the electric field across the thickness of d31 type MFC. Detailed stress analysis is carried out to find the high stress area on the plate. A parametric study is carried out to find the influence of plate thickness and piezoelectric fiber angle on actuation performance.