Thermal Relaxation Time Research Articles

A thermoelastic model with higher order time derivatives for a crack in a rotating solid

This article represents a refined one-temperature thermoelastic model with higher order time derivatives and phase-lags for a Mode-I crack in a rotating fiber-reinforced solid. The crack is subjected to a stipulated temperature and normal stress. The exact expressions of displacement, temperature and stress components are obtained by normal mode analysis. Some generalized thermoelasticity theories are obtained as special cases. The convergency of the present refined model is tabulated and is compared with other theories. The variations of the temperature, displacements and stresses are presented graphically with the crack length to show the effect of phase-lags and thermal relaxation time through Refined-phase-lag (RPL), simple-phase-lag (SPL), Green-Naghdi (G-N) theory, Lord-Shulman (L-S) theory and the Coupled thermoelasticity (CTE) theory in the presence and absence of rotation.

Bidirectional flow of MHD nanofluid with Hall current and Cattaneo-Christove heat flux toward the stretching surface.

Vacuum pump oil (VPO) is used as a lubricant in pumps of different machines. The rate of heat transport is a fundamental requirement of all phenomena. To enhance the rate of heat transmission and reduce the amount of energy consumed as a result of high temperatures. For this reason, the vacuum pump oil (VPO) is taken as a base fluid and Fe3O4 is the nanoparticles suspended in VPO. That’s why, the present study inspected the consequence of Hall current, Joule heating effect and variable thickness on these three-dimensional magnetohydrodynamics bidirectional flow of nanoliquid past on a stretchable sheet. Further, the Cattaneo-Christove heat flux and radiation impacts are also considered. The VPO−Fe3O4 nanofluid model is composed of momentum equations in x−direction, y−direction and temperature equations. The leading higher-order non-linear PDEs of the current study have been changed into non-linear ODEs with the implementation of appropriate similarity transformations. The procedure of the homotopy analysis method is hired on the resulting higher-order non-linear ODEs along with boundary conditions for the analytical solution. The significance of distinct flow parameters on the velocities in x−direction, y−direction and temperature profiles of the nanofluid have been encountered and briefly explained in a graphical form. Some important findings of the present modelling are that with the increment of nanoparticles volume fraction the nanofluid velocities in x−direction and y−direction are increased. It is also detected that higher estimations of magnetic field parameter, Prandtl number and thermal relaxation time parameter declined the nanofluid temperature. During this examination of the model, it is found that the Fe3O4-Vacuum pump oil (VPO) nanofluid enhanced the rate of heat transfer. Also, the vacuum pump oil (VPO) has many industrial and engineering applications. The current study will help to improve the rate of heat transmission by taking this into account due to which working machines will do better performance and the loss of useful energy will be decayed. Lastly, the skin friction coefficient and Nusselt number are also illustrated in a tabular form. Some major findings according to the numerical computation of the problem are that the enhancing estimations of magnetic parameter, nanoparticles volume fraction and wall thickness parameter augmented the skin friction coefficient in x−direction and Nusselt number. The reduction in skin friction coefficient of the nanofluid in y−direction is examined for Hall current and shape parameter.

Couple stress flow of exponentially stretching sheet with Cattaneo–Christov heat flux model

AbstractThis paper deals with the effect of three‐dimensional magnetohydrodynamic flow for a couple of stress fluids on an exponentially stretching sheet. The magnetic field is implemented normally to the surface. To observe the transfer of heat phenomenon, the Cattaneo–Christov flux model of heat is employed. Using similarity transformation, the substantial differential equations are reformed into ordinary differential equations. Eventually, the effects of different physical parameters are studied graphically. The drawback in Fourier heat flux model is removed by adding a new paramter known as thermal relaxation time by Cattaneo. This perimeter allows heat transportation by way of propagation of waves thermally at a defined speed. After this, the Cattaneo law is further modified by Christov–Christov to replace the ordinary derivative along Oldroyd's upper‐convective derivative.

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

We study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models.

Cattaneo–Christov model for triple diffusive natural convection flows over horizontal plate with entropy analysis embedded in porous regime

This research interprets the features of triple diffusion in naturally convected viscous material flow through a horizontal plate embedded in a porous regime. The heat and mass transmission process is evaluated by the implication of Cattaneo and Christov (CC) models of energy and mass diffusions. Entropy analysis is executed with the help of the second law of thermodynamics. The homogeneous and local thermal equilibrium is assumed for porous medium. The physically modeled expressions are reframed into an ordinary differential system. This re-structured system of expressions is computed numerically by the implication of the Runge–Kutta Fehlberg method. The computed solutions are visualized graphically and in numeric forms. The validation of present solutions is reported by the comparative benchmark with already available results in a limiting sense. It is evident that the opposing and assisting flows show higher entropy generation at the convective wall. An increment in surface entropy generation rate is achieved for higher thermal and solutal relaxation times.

A Petrov–Galerkin finite element approach for the unsteady boundary layer upper-convected rotating Maxwell fluid flow and heat transfer analysis

A numerical investigation is carried out in the present study to view heat transfer framing indifferent Cattaneo–Christov hyperbolic heat flux equation. A numerical scheme built on the Petrov–Galerkin finite element method (PG-FEM) with shooting technique is incorporated successfully to examine the flow regime. In addition, mathematical explanation of energy equation in detail is studied which is in a transient state and unmatched in the accessible literature. Pertinent unsteady parameter for boundary layer flow is analyzed for physical implication. Moreover, momentum and energy profiles are inspected with various physical effects adjacent to thermal relaxation time, rotational parameters, Prandtl and Deborah numbers. A refined numerical strategy based on the PG-FEM scheme is implemented and validated for the results. These results found strong agreement in limiting cases to Mustafa [Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid. AIP AdvAIP Advances. 2015;5:047109] and with other numerical results available in existing literature as well.

A novel magneto-photo-elasto-thermodiffusion electrons-holes model of excited semiconductor

In this investigation, the coupled between electrons and holes is studied during a theoretical mathematical-physical model of semiconductor medium. The elasto-thermodiffusion (ETD) theory during photothermal transport processes is taken into consideration. The governing equations are examined under the effect of external magnetic field. This model is used to improve the outside weak electric of semiconductor medium. The one-dimensional (1D) deformation is constructed when thermoelastic (TD) and electronic (ED) deformation with the holes processes are occurred. The dimensionalized field quantities are obtained algebraically with some mathematical methods for the principle physical fields (hole charge field carrier, elastic, thermal and electrons charge carrier density (plasma) waves). Laplace transform and some initial conditions are used algebraically to solve the system of equations. The conditions are taken at the boundary for the main physical fields subjected to ramp heating type in Laplace domain. Laplace invers transform with approximate technique is used numerically to get the closed form in time domain for the principle fields. Some comparisons are carried out graphically for the waves propagation of the main physical fields under the effect of many different parameters (thermal relaxation times, magnetic field impact and the input parameters of the medium) and discussed.

Bidirectional stretching features on the flow and heat transport of Burgers nanofluid subject to modified heat and mass fluxes

The characteristics of thermal transport in steady 3D flow of viscoelastic nanofluid induced by a bidirectional stretching surface are explored in this study. A new model for heat conduction is established in perspective of Buongiorno's model in combination with Cattaneo–Christov theory. The mathematical formulations in terms of partial differential equations are transformed into ordinary transformations by utilizing suitable dimensionless transformations. The homotopic technique is utilized to inspect the features of velocity components and thermal transport in the flow. The graphical representation of different physical constraints on thermal and solutal profiles is also depicted. It is observed that the transport of thermal energy deteriorates for escalating number of thermal relaxation time parameter. The solutal transport in the flow depreciates by intensifying the effects of stretching strength parameter. Moreover, it is seen that greater thermophoretic force regulates the thermal transport in the flow.

Mechanical and Thermal Properties of Gd-Doped ZnO Nanorods

All the elastic, mechanical and thermal properties of Gd-doped ZnO nanorods (NRs) have studied using interaction potential model. Gd-doped ZnO nanorods are hexagonal wurtzite structure. The characteristic features of elastic characteristics of Gd-doped ZnO NRs imply that this is mechanically stable. For mechanical characterization, bulk modulus (B), shear modulus (G), Young's modulus (Y), Pugh's ratio (B / G), Poisson’s ratio and anisotropic index are evaluated using second order elastic constants. For the investigation of anisotropic behaviour and thermophysical properties, ultrasonic velocities and thermal relaxation time have been also calculated along with different orientations from the unique axis of the crystal. The mechanical properties of the Gd-doped ZnO nanorods are better than at 6% Gd amount due to minimum attenuation. The obtained results are analyzed to explore the characteristic of ZnO nanorods. Computed elastic, ultrasonic and thermal properties are correlated to evaluate the microstructural behaviour of the materials useful for industrial applications

INVESTIGATION OF INTERMETALLIC GdFeAl TERNARY COMPOUND BY ELASTIC, THERMOPHYSICAL AND ULTRASONIC ANALYSIS

Higher order elastic constants were calculated of the intermetallic GdFeAl ternary compound using Lennard Jones potential approach. With the using of second order elastic constants (SOECs), other elastic moduli; shear modulus, bulk modulus, Young’s modulus, Pugh’s ratio, constants of elastic stiffness and Poisson’s ratio are estimated for mechanical and elastic characterization at room temperature. Born stability and Pugh's criteria are used to examine the nature and strength of the intermetallic ternary compound and found that it is mechanically stable compound. For the investigation of anisotropic behaviour and thermophysical properties, ultrasonic velocities and thermal relaxation time have been also calculated along with different orientations from theunique axis of the crystal. The temperature variation of ultrasonic velocities, Debye average velocity and thermal relaxation time along the z axis is evaluated using SOECs. The ultrasonic properties correlated with elastic, thermal and mechanical properties which is temperature dependent is also discussed. Ultrasonic attenuation was calculated at different temperatures due to phonon –phonon (p –p) interactions. The responsible reason of attenuation is p-p interactions; it was got that the thermal conductivity is a core contributor to the characteristic of ultrasonic attenuation as a role of temperature.GdFeAl ternary compound behave as its purest form at lower temperature and are more ductile demonstrated by the minimum attenuation

Particle shape effect on MHD steady flow of water functionalized Al2O3 nanoparticles over wedge

The demand for effectual cooling and heating systems in the automotive, aerospace and chemical industries is driving the growth of heat transfer technology. Keeping in mind the need of efficient cooling and heating systems, the purpose of the current study is to interrogate the outcome of Alumina nanoparticle shapes on the magnetohydrodynamic steady flow of Maxwell liquid, past a wedge existing with a nonlinear thermal radiation impact. A variable magnetic field is applied normal to the wedge surface. Moreover, Catteneo–Christove heat flux impact is considered in the modeling. The similarity transformation technique has been formulated to convert the elementary equations into ordinary differential equations and are then solved with the help of Runge Kutta Fehlberg fourth fifth order (RKF-45) numerical method accompanying the shooting technique. The replica of the output proclaims that more heat transfer enhancement is seen for platelet shaped nanoparticles and the rate of declination in heat transport is faster for the brick case with respect to rise in the values of thermal relaxation time parameter. The rise in values of the radiation parameter improves the heat transport rate, but a reverse trend is seen for increasing values of the magnetic parameter.

Capturing the onset of thermocapillary convection in the Cattaneo–Christov flow of electrically conducting thin film of Welan gum solution

An investigation of heat transfer characteristics of electrically conducting Welan gum solution over a sheet, influenced by thermocapillary convection (thermal Marangoni convection) and magnetic field is carried out. In order to correctly predict the heat transfer characteristics, the more realistic heat flux model i.e. Cattaneo–Christov model has been utilized whereas the Maxwell-power-law model is used to capture the rheological attribute of Welan gum liquid. The Joule dissipation effect produced by the interaction between magnetic field and fluid is also considered in the energy equation. Simplified Navier–Stokes equation under above-mentioned assumptions/considerations have been obtained and are metamorphosed to a set of ODEs using appropriate Lie-group transforms. Set of ODEs are solved by Runge–Kutta fourth-order method facilitated by the shooting technique. Numerical results are displayed via graphs and tables. One of the key findings of this research work is the evidence of Marangoni convection altering the two boundary layers near the interfacial region and having almost no effect on the flow near the sheet. It has been found that the temperature and velocity of Welan gum solution can be decreased by increasing the thermal relaxation time. It has also been observed that the skin friction coefficient, a representative of shear stress is higher for a more solid-like material.

Mechanical and thermophysical properties of 4d-transition metal mononitrides

Abstract The second and third order elastic constants (SOECs and TOECs) of 4d-transition metal mononitrides XN (X: Zr and Nb) have been computed in the temperature range 0 K–500 K using Coulomb and Born–Mayer potential up to second nearest neighbours. In order to investigate the mechanical stability of XN, the computed values of SOECs have been utilized to find out Young’s modulus, bulk modulus, shear modulus, Zener anisotropy and Poisson’s ratio. Furthermore, the SOECs are applied to compute the wave velocities for shear and longitudinal modes of propagation along ⟨100⟩, ⟨110⟩ and ⟨111⟩ crystallographic orientations in the temperature range 100 K–500 K. Temperature dependent Debye average velocity, ultrasonic Grüneisen parameters (UGPs) and Debye temperature have been evaluated. In present work the thermal conductivity of chosen materials has also been evaluated using Morelli-Slack’s approach. Specific heat and total internal thermal energy have been calculated in the temperature range 100 K–500 K on the basis of Debye theory. Thermal relaxation time, acoustic coupling constants and attenuation of ultrasonic waves due to thermo-elastic relaxation and phonon–phonon interaction mechanisms have been calculated in the temperature range 100 K–500 K. The obtained results of present investigation have been compared with available other similar type of materials.

Evaluation of residual stresses in additively produced thermoelastic cylinder. Part I. Thermal fields

The study is aimed at mathematical modeling of non-stationary temperature and stress-strain fields in growing thermoelastic cylinder, which growth is due to the layer-by-layer sintering over its lateral surface. This modeling makes it possible to estimate the reciprocal impact of non-stationary temperature fields, stress-strain state and the scenario of the additive process even in manufacturing of more complicated shapes. The problem is considered in the framework of the theory of thermal stresses with non-linear radiative boundary condition. A distinctive feature of modeling is that the material composition of the body changes over time. Therefore, the mathematical model is represented by the recurrent sequence of initial boundary value problems, formulated for each step of the additive process in different domains with respect to the increments of thermal and stress fields. The domains constitute nested sequence of regions and, together with the sequence of the moments of layer sintering, define the scenario of additive process. Initial values for a step are taken to be equal to the corresponding values at the final moment of previous step. The solution for each step is represented in the form of decomposition over eigenfunctions of differential operator, generated by boundary value problem on this step. Computational modeling of various sintering modes has been carried out. A classification of thermomechanical additive processes, based on the relationship between the characteristic time of the process and the time of thermal relaxation of the attached layer is given. Special attention is paid to non-uniform volume heating, which can be obtained by skin effect during high-frequency induction. Computational simulations based on obtained analytical solution show that auxiliary inductive heating makes it possible to substantially reduce the non-uniformity of the temperature field and thus to reduce the temperature stresses caused by it.

Computational analysis for enhancement of heat and mass transfer in MHD-polymer with hybrid nano-particles using generalized laws

Novel models for heat flux with laws of linear and angular momenta and convection-diffusion equation for heat are used for the formulation of system of problems associated with the flow of polymer (micropolar fluid) over a cylindrical heated body elongating in a radial direction with non-uniform velocity. Spin gradient and vortex effects with couple stresses are taken into account. Problems are solved using the finite element method (FEM) with Galerkin approximation. Grid-independent and convergent solutions are derived. The results for special cases are compared and validated with published benchmarks. Simulations are used to assess the impact of parameters on flow variables based on the convergent solutions. Simulated results are displayed in the form of velocity, temperature and concentration graphs. Thermal relaxation time corresponds to thermal elastic behaviour and is responsible to make the fluid to restore the thermal equilibrium. This thermal relaxation phenomenon helps in reducing the width of the thermal region. The angular motion of fluid particles has been shown to be affected less by vortex viscosity. Vortex viscosity has shown a greater impact on the motion of Cu−Ag− polymer relative that on Cu− polymer. Thermal performance of Cu−Ag− polymer is better than the thermal enhancement of Cu− polymer. Due to Joule heating, hybrid nanofluid dissipates more heat relative to the nanofluid. Vortex viscosity plays vital role in controlling the thermal region. Heat flux has shown an increase as a function of thermal relaxation time.

Machine Learning and Statistical Methods for Studying Voids and Photothermal Effects of a Semiconductor Rotational Medium with Thermal Relaxation Time

Machine learning is the process of creating algorithms that extract useful facts from data automatically. The goal of this paper is to use an artificial neural network and a cubic spline model to predict various physical quantities displacement components in a thermoplastic solid, such as elastic waves, vector form, volume fraction field, thermal waves, stress components, and carrier density concentration (plasma waves). The mean absolute scaled error (MASE), the mean absolute percentage error (MAPE), and the symmetric mean absolute percentage errors (SMAPE) are used to compare the accuracy of two models. The true displacements are given their maximum expected values. These factors have also been described using various descriptive statistics and diagrams. Statistical significance was found in the examination of the correlation between the variables, and a comparison was conducted between the findings and prior results acquired by others. The findings show that voids, rotation, optical temperature, and thermal relaxation all have a significant impact on the phenomena, and they are in line with earlier physical findings. Furthermore, it is demonstrated that certain physical variables describing such systems may display this property, allowing for the development of an analytical criterion for the advent of dynamical chaos.

A numerical approach to interpret melting and activation energy phenomenon on the magnetized transient flow of Prandtl–Eyring fluid with the application of Cattaneo–Christov theory

The current study explores the Impact of activation energy and melting heat transfer on unsteady Prandtl–Eyring model with variable thermal conductivity induced by a stretched cylinder. The Cattaneo–Christov double diffusion theory is used to study heat and mass transfer phenomena. The foremost coupled partial differential equations (PDEs) of the time-dependent Prandtl–Eyring model is transformed to ordinary ones using appropriate local similarity variables. The deduced system is numerically solved using the shooting iterative technique. The characteristics of key flow parameters against fluid concentration, temperature, velocity, skin friction, Sherwood and local Nusselt numbers are examined graphically with justified physical consequences. The comparison with the previously published work showed a fabulous agreement. This investigation presented that the velocity and concentration of fluid are increased by enhancing melting and curvature parameters, while the fluid temperature is diminished due to the impacts of melting and curvature parameters. By raising reaction rate constant, melting, thermal relaxation time, and temperature difference parameters, the fluid temperature is enhanced while the fluid temperature declines with thermal conductivity, activation energy, and unsteadiness parameters. Furthermore, the unsteadiness and activation energy parameters cause a rise in the concentration of a fluid.

Hybrid Finite Element Method to Thermo-Elastic Interactions in a Piezo-Thermo-Elastic Medium under a Fractional Time Derivative Model

In this work, the effect of the fractional time derivative on the piezo-thermo-elastic medium is studied, using the hybrid Laplace transform and finite element methods (LFEM). The generalized fractional piezoelectric–thermoelastic basic equations for piezo-thermo-elastic medium are formulated. The Laplace transforms are used for the time derivatives, and the finite element method is used to discretize for the space derivatives. The inversions process is performed using the Stehfest numerical technique. The finite element approach is used to obtain the solutions of complex coupled formulations of this problem. The effects of fractional time derivative and thermal relaxation time on piezoelectric–thermoelastic mediums are studied. It can be seen from the distribution that the thermal-induced displacement, the temperature and the stress of the medium increase at a high fractional parameter.

Generalized differential quadrature analysis of MHD mixed convective motion of Casson fluids past an isothermal irregular slender geometry via Cattaneo–Christov's approach

AbstractClassical Fourier's theory is well‐known in continuum physics and thermal sciences. However, the primary drawback of this law is that it contradicts the principle of causality. To explore the thermal relaxation time characteristic, Cattaneo–Christov's theory is adopted thermally. In this regard, the features of magnetohydrodynamic (MHD) mixed convective flows of Casson fluids over an impermeable irregular sheet are revealed numerically. In addition, the resulting system of partial differential equations is altered via practical transformations into nonlinear ordinary differential equations. An advanced numerical algorithm is developed in this respect to get higher approximations for temperature and velocity fields, as well as their corresponding wall gradients. For validating our numerical code, the current outcomes are compared with the available literature results. Moreover, it is revealed that the velocity field is more prominent in the suction flow situation as compared with the injection flow case. It is also found that the Casson fluid is hastened in the case of lower yield stress. Larger values of thermal relaxation parameters create a lessening trend in the temperature distribution and its related boundary layer breadth.

Higher Order Chemical Reaction and Radiation Effects on Magnetohydrodynamic Flow of a Maxwell Nanofluid With Cattaneo–Christov Heat Flux Model Over a Stretching Sheet in a Porous Medium

Abstract In this paper, we investigated the heat and mass transfer analysis of an MHD convection flow of Maxwell nanofluid with Cattaneo–Christov heat flux model along with a porous stretching sheet. The effects of thermal radiation, viscous dissipation, suction/injection, and higher-order chemical reaction are taken into consideration. By using similarity transformations the governing equations of the study are reduced into a system of ordinary differential equations and solved numerically by using the BVP5C matlab package. The effects of dimensionless parameters on the present study are deliberated with the aid of graphs and tables. It is found that an increase in thermal Grashof number, thermal radiation, and thermal relaxation time parameter drops the temperature field. The heat transfer rate is declined with enhancing heat source, Brownian motion and thermophoresis parameters. Also, observed that the concentration field reduces with the rising value of chemical reaction. The numerically computed values of Nusselt number and Sherwood number are validated with existing literature and found a good agreement.