Thermal Relaxation Time Research Articles

Intelligent adaptive nonlinear autoregressive eXogeneous neuro‐structure for ferromagnetic Powell‐Eyring fluidic involving cubic autocatalysis chemical reaction

AbstractThe scope of artificial intelligence in the field of fluid mechanics has been expanded with the development sophisticated technology to enhance the efficiency, reliability, solve complexities, introduced alternate transformation and enabling more dependable solutions with their analysis. The goal of this study is to investigate the ferromagnetic Powell‐Eyring fluids (FMPEFs) model with non‐Fourier heat flux by using artificial intelligence‐based scheme by exploiting the adaptive nonlinear autoregressive eXogenous (NARX) neuro‐architecture with backpropagation of Levenberg Marquart (LM), that is, NARX‐LM. The developed NARX‐LM methodology applied on synthetic datasets acquired with the help of Adams numerical method for FMPEF system by prudently changing physical quantities that is, material parameters of Eyring Powell, homogeneous reaction, heterogeneous reaction, dimensionless thermal relaxation time, Prandtl number, Schmidt number with fixed values parameter of ferrohydrodynamic interaction, rate of diffusion coefficient. Outcomes of NARX‐LM are regularly overlapping with the numerical results for the FMPEFs system having reasonable small error magnitude for each variant. The proficiency of intelligent computing anticipated on FMPEFs is depicted exhaustively with iterative mean squared error based iconvergence curves, analysis of adaptive controlling factors, error frequency distribution on the histograms, auto‐correlation, and correlation measures.

Shadows Wreak Havoc in Transition Disks

We demonstrate that shadows cast on a protoplanetary disk can drive it eccentric. Stellar irradiation dominates heating across much of these disks, so an uneven illumination can have interesting dynamical effects. Here, we focus on transition disks. We carry out 3D Athena++ simulations, using a constant thermal relaxation time to describe the disk’s response to changing stellar illumination. We find that an asymmetric shadow, a feature commonly observed in real disks, perturbs the radial pressure gradient and distorts the fluid streamlines into a set of twisted ellipses. Interactions between these streamlines have a range of consequences. For a narrow ring, an asymmetric shadow can sharply truncate its inner edge, possibly explaining the steep density drop-offs observed in some disks and obviating the need for massive perturbers. For a wide ring, such a shadow can dismantle it into two (or possibly more) eccentric rings. These rings continuously exert torque on each other and drive gas accretion at a healthy rate, even in the absence of disk viscosity. Signatures of such twisted eccentric rings may have already been observed as, e.g., twisted velocity maps inside gas cavities. We advocate for more targeted observations and for a better understanding on the origin of such shadows.

Role of chemical processes and porous media in thermal transport of Casson nanofluid flow: A study with Riga plates

A Riga plate is an electro-magnetic instrument working with anodes and magnets on plates. The Riga plate has numerous advantages in geophysical sciences, the field of engineering, sensors,and astrophysics.The present work investigated the transitory Electromagnetohydrodynamic radiative squeezing unsteady motion of Casson nanofluid through a parallel channel impacted by the Riga plate with endothermic/exothermic chemical processes and porous media. The PDEs transform into non-linear ODEs using the appropriate similarity transformations. The RKF-45 method and Shooting techniques are utilized to compute the solutions to these non-linear ODEs and related boundary conditions. The consequences of non-dimensional parameters on the corresponding profiles are illustrated graphically. And also studied some significant engineering coefficients. The primary findings of the present study are a rise in the thermal relaxation time parameter, temperature increases for the exothermic chemical reaction case, and opposite behavior in the endothermic chemical reaction case. Enhancement in activation energy parameter, the temperature drops for exothermic and increases for the endothermic case. The value of the modified Hartmann number rises, the velocity profile is also increased in the lower plate and the opposite behavior in the upper plate. Increase in Biot number, temperature decreases in the exothermic case and increases in the endothermic case.

Thermal performance of a hybrid nanofluid flow through a stretchable stationary disk featuring the Cattaneo-Christov heat flux theory

A hybrid nanofluid is comprised of a (Ethylene glycol) base fluid component and (Copper and Aluminium oxide) nanoparticles, and the nanoparticles are scattered inside the Ethylene glycol. Integrating nanoparticles into a base fluid (Ethylene glycol) can significantly enhance its thermal conductivity, which in turn can boost the base fluid's rate of heat transfer. In addition, the dynamics of viscous fluid together with nanoparticles is quite interesting and has a large of applications in the industrial sector. The current predominately predictive modeling investigates the flow of the hybrid nanofluid via a stretchable stationary disk in the presence of heat source/sink. A progressive modification in he energy equation is done by utilizing the Cattaneo-Christov heat flux expressions. This theory provides predictions for the features of the thermal relaxation time of the liquid on the boundary layer flow. Further, the study focuses on the features of the Lorentz force resulting from the applied of a magnetic field perpendicular to the disk. The similarity approach is used to obtained the dimensionless ordinary differential equations.The bvp4c approach in Matlab is utilized as a numerical method for the solution. All the solutions are obtained through graphical form. According to the results, the thermal profile is reduced by adjusting the thermal relaxation time parameter. Motion of the hybrid nanofluid slows down by enlarging the magnetic force parameter. Additionally, the effect of the heat source significantly increases the thermal profile. It is noted that the temperature field is enhanced in the case of a larger Lorentz force. Moreover, the increase in volume fraction concentration intensifies the thermal distribution, but the velocity is diminished due to the effect of viscosity.

Modeling with generalized flux theory for computational investigation of thermal enhancement in fluid with tri‐, di‐, and mono‐nanoparticles

AbstractTo study the influence of several factors (tri‐nanoparticles and relaxation time related to momentum, thermal, and concentration) on non‐Fourier transport of heat and mass, mathematical models are developed. The cases of tri‐, di‐, and mono‐nanofluids are considered. Flow and transport scenarios are translated into mathematical equations for which conservation laws and correlations for thermophysical properties are used. Boundary layer simplifications are used to approximate these mathematical models. The nondimensional set of problems is numerically solved using the finite element method (FEM). The solutions that are convergent and mesh‐free are obtained. The outcomes are compared to existing benchmarks. There is excellent consistency between the current and published results. The viscoelastic behaviors related to momentum, thermal, and solutal relaxation times are examined. It is also investigated how tri‐nanoparticles improve heat transmission in flow. The wall shear stresses for the mono‐, di‐, and tri‐nanofluids are calculated against momentum relaxation time. It is observed that tri‐nanofluid exerts the highest stress on the surfaces over which it flows. Therefore, while using these fluids, the surface should be ensured to bear the stresses; otherwise, failure of the system may take place. Thus, industrial applications and additional capability of surface be ensured. This looks at influence the Deborah number on the fluid motion. Deborah number is straightforwardly connected with relaxation time and it is found that higher is Deborah number lower will be the speed of fluid. As a consequence, viscous region will be narrow down. Thus, viscous dominant region is controllable by the using fluid of higher relaxation time. A significant enhancement in the thermal performance of Maxwell fluid occurs via the dispersion of tri‐nanoparticles ().

Multiple edge cracks in a coated semi-infinite medium due to non-Fourier thermal shock

In this wok, based on the non-Fourier C-V model, the problem for multiple edge cracks is investigated for a coating-substrate pair subjected to a sudden temperature drop at the surface of coating. The temperature and resulting thermal stresses without cracks are obtained by the method of Laplace transform. By numerically solving the singular integral equations, the thermal stress intensity factors (SIFs) are evaluated. The results from the Fourier model and C-V heat conduction model are presented for comparison. Two dimensionless quantities are proposed to account for the coupling effects of heat conduction parameters (i.e., thermal conductivity, thermal diffusivity, and thermal relaxation time). Numerical results are presented for the thermal SIF as a function of normalized quantities such as time, crack depth, material constants and crack spacing. The findings in this work are expected to provide references for maintaining the integrity of the coating-substrate pair in the extreme heat transfer applications.

Cattaneo-Christov fluxes for nonlinear mixed convective entropy generated Reiner-Rivlin material flow

Thermal and solutal transportation processes involve in tremendous useful applications related to heat exchanger, scientific, micro-electronic device technologies and industry sectors like nuclear reactors cooling, marine engineering, nanotechnology, thin-film technology, biomedical applications and thermal conduction in soft tissue. In view of such useful applications the Cattaneo-Christov analysis for nonlinear mixed convective Reiner-Rivlin material flow in presence of constant applied magnetic field is considered. Heat source, magnetohydrodynamics and radiation are incorporated in energy equation. Cattaneo-Christov flux is employed to discuss the thermal and mass transport characteristics. Entropy calculation in radiating flow is discussed. The proposed non-linear systems are transformed into dimensionless ordinary systems through appropriate transformation. Non-linear ordinary expressions are computed for convergent series solutions through Optimal homotopy analysis technique (OHAM). Graphical interpretations for quantities under interest against pertinent variables are explored. Large magnetic parameter has opposite impact for entropy and fluid flow. An increase of temperature through thermal relaxation time parameter is noticed. Velocity has same trend for both mixed convection and Reiner-Rivlin fluid variables. Reduction in concentration is seen for solutal relaxation time parameter. Temperature enhancement is witnessed in presence of heat generation. Entropy rate enhancement for radiation is observed. Decrease in concentration is noticed for reaction. Entropy rate increases against diffusion variable is enhanced.

Active Brownian information engine: Self-propulsion induced colossal performance.

The information engine is a feedback mechanism that extorts work from a single heat bath using the mutual information earned during the measurement. We consider an overdamped active Ornstein-Uhlenbeck particle trapped in a 1D harmonic oscillator. The particle experiences fluctuations from an inherent thermal bath with a diffusion coefficient (D) and an active reservoir, with characteristic correlation time (τa) and strength (Da). We design a feedback-driven active Brownian information engine (ABIE) and analyze its best performance criteria. The optimal functioning criteria, the information gained during measurement, and the excess output work are reliant on the dispersion of the steady-state distribution of the particle's position. The extent of enhanced performance of such ABIE depends on the relative values of two underlying time scales of the process, namely, thermal relaxation time (τr) and the characteristic correlation time (τa). In the limit of τa/τr → 0, one can achieve the upper bound on colossal work extraction as ∼0.202γ(D+Da) (γ is the friction coefficient). The excess amount of extracted work reduces and converges to its passive counterpart (∼0.202γD) in the limit of τa/τr → high. Interestingly, when τa/τr = 1, half the upper bound of excess work is achieved irrespective of the strength of either reservoirs, thermal or active. Finally, we look into the average displacement of active Brownian particles in each feedback cycle, which surpasses its thermal analog due to the broader marginal probability distribution.

Thermal relaxation time and photothermal optomechanical force in sliced photonic crystal silicon nanobeams

Thermal relaxation time and photothermal optomechanical force in sliced photonic crystal silicon nanobeams

Comparison of two nonlinear formulations of the Maxwell-Cattaneo equation in heat pulse transmission

The nonlinear terms resulting from temperature dependence of thermal conductivity and relaxation time must be considered when studying systems undergoing very short thermal pulses with non-negligible amplitude of the temperature perturbation. Two nonlinear formulations of the Maxwell-Cattaneo-Vernotte equation for thermal transport with relaxation effects are introduced. A comparison of the consequences of these two different nonlinear Cattaneo type equations on thermal pulse propagation is obtained and discussed. The differences in the corresponding velocities and in the corresponding heights of the perturbation peaks turn out to be significant and could be experimentally detected.

Local high temperature phenomena near the complex interfaces of thermal barrier coatings based on non-Fourier model

Thermal barrier coatings (TBCs) consist of a metal substrate (Sub), a bond coat (BC), and a ceramic top coat (TC). The ceramic coating is a porous dielectric layer with a significant relaxation time that cannot be ignored. In high-temperature environments, an irregularly shaped thermally grown oxide layer (TGO) forms between the BC and the TC. Therefore, using non-Fourier model to describe the thermal contact process of TBCs with complex interface can get more accurate results. However, it is difficult to obtain the analytical solution of this model. This paper introduces a finite volume method based on unstructured meshes to address the non-Fourier heat transfer process in the complex interfaces of multilayer TBCs. The gradient reconstruction technique is employed to calculate the cell derivatives on the surface. The method's reliability is confirmed through a comparison with a two-dimensional analytical solution. The results indicate that the thermal wave travels at a limited speed within the TC layer. After passing through the interface, the thermal wave travels very fast within the BC and Sub layers, due to the influence of thermal wave reflection and superposition, obvious local high temperature will be formed near the interface. In addition, the effects of thermal conductivity, relaxation time and interface shapes on the non-Fourier heat conduction process of TBCs are also discussed. The results of this paper are useful for the structural design and failure mechanism research in TBCs.

Stagnation point radiative flow with Cattaneo-Christov theory and heat generation

Heat generation and magnetohydrodynamics for flow of Burgers liquid. Stagnation point flow towards stretched wall is considered. Radiation aspect is nonlinear. Cattaneo-Christov theory and boundary layer approximations are utilized. Related differential systems are formulated. Computations by Optimal homotopy analysis method (OHAM) are implemented. Total residual error is arranged. Graphical illustrations lead to the impacts of sundry parameters. Important points have been concluded. Higher Deborah number lead to velocity enhancement. Decrease in velocity occurs for magnetic field whereas reverse trend witnessed regarding thermal field. Temperature upsurges for higher radiation and heat generation variables. Higher radiation results in Nusselt number enhancement. Mass transport rate enhancement versus Schmidt number is observed. Reduction of thermal distribution occurs for thermal relaxation time.

Passive control of bio-convective flow on Eyring–Powell nanofluid over a slippery surface with activation energy and magnetic impact

The current communication deliberates the consequences of the Darcy–Forchheimer flow of Eyring–Powell nanofluid past a slippery surface containing activation energy and motile microorganisms. The flow is influenced by the consequences of Brownian motion, thermal radiation, the Cattaneo–Christov heat-mass flux theory, and thermophoresis. The framed flow models are transformed into ordinary derivative equations by adopting appropriate conversion variables. The transformed equations are numerically tackled by using the bvp4c scheme in MATLAB. The study is remarkable for its comprehensive analysis of the interplay of several flow factors, such as the Forchheimer number, Richardson number, bioconvection Rayleigh number, radiation, thermophoresis, Brownian motion, thermal and mass relaxation time parameters. The outcomes are visualized through tables and diagrams, which provide significant insights into the intricate physical mechanisms involved in this multifaceted subject. Evidently, the velocity profile declines when there is a rise in the buoyancy ratio parameter and the opposite trend is obtained for the Richardson number. The temperature grows when there is a larger magnitude of the thermophoresis parameter and it reduces for greater values of the time relaxation parameter. The activation energy and mass relaxation parameters enhance the concentration profile. The microbe density increases when enhancing the quantity of Peclet number and it declines for bioconvection Lewis number.

Numerical analysis for Cattaneo-Christov heat flux on convective viscous non-Newtonian fluid flow through porous medium with nonuniform heat source

This work investigates the Ohmic heating, nonuniform heat generation, and Hall effects with Cattaneo-Christov model (CCM) on flow and heat transfer of power-low non-Newtonian fluids (NNFs) past stretching surface embedded in a porous medium. Runge-Kutta method is used to solve non-linear ODEs numerically using a shooting procedure. We study non-Newtonian fluids for power law values of 0.7 and 1.2, respectively. Innovation of this work lies in studying the effect of Hall currents in presence of buoyancy force and an irregular heat source on slip flow of NNFs moving through Darcy porous medium. Varying velocities, surface frictional forces, and Nusselt numbers are examined. Resulting entropy is also examined using computational flow problem investigation. Model-simulated results suggested that various factors play critical role in constructing thermal systems. It is asserted that Hall parameter, mixed convection parameter, Biot numbers, and thermal relaxation time improve heat transference rates by directly affecting fluid molecules temperature.

Non-Fourier computations of heat and mass transport in nanoscale solid-fluid interactions using the Galerkin finite element method

PurposeTo improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and development of models. The thermal performance of sample fluids is compared to determine which types of combination of nanoparticles are the best for an optimized enhancement in thermal performance of fluids. This article aims to: (i) investigate the impact of nanoparticles on thermal performance; and (ii) implement the Galerkin finite element method (GFEM) to thermal problems.Design/methodology/approachThe mathematical models are developed using novel non-Fourier heat flux theory, conservation laws of computational fluid dynamics (CFD) and no-slip thermal boundary conditions. The models are approximated using thermal boundary layer approximations, and transformed models are solved numerically using GFEM. A grid-sensitivity test is performed. The accuracy, correction and stability of solutions is ensured. The numerical method adopted for the calculations is validated with published data. Quantities of engineering interest, i.e. wall shear stress, wall mass flow rate and wall heat flux, are calculated and examined versus emerging rheological parameters and thermal relaxation time.FindingsThe thermal relaxation time measures the ability of a fluid to restore its original thermal state, called thermal equilibrium and therefore, simulations have shown that the thermal relaxation time associated with a mono nanofluid has the most substantial effect on the temperature of fluid, whereas a ternary nanofluid has the smallest thermal relaxation time. A ternary nanofluid has a wider thermal boundary thickness in comparison with base and di- and mono nanofluids. The wall heat flux (in the case of the ternary nanofluids) has the most significant value compared with the wall shear stresses for the mono and hybrid nanofluids. The wall heat and mass fluxes have the highest values for the case of non-Fourier heat and mass diffusion compared to the case of Fourier heat and mass transfer.Originality/valueAn extensive literature review reveals that no study has considered thermal and concentration memory effects on transport mechanisms in fluids of cross-rheological liquid using novel theory of heat and mass [presented by Cattaneo (Cattaneo, 1958) and Christov (Christov, 2009)] so far. Moreover, the finite element method for coupled and nonlinear CFD problems has not been implemented so far. To the best of the authors’ knowledge for the first time, the dynamics of wall heat flow rate and mass flow rate under simultaneous effects of thermal and solute relaxation times, Ohmic dissipation and first-order chemical reactions are studied.

Impact of chemical reaction on the Cattaneo–Christov heat flux model for viscoelastic flow over an exponentially stretching sheet

In this article, the numerical solutions for the heat transfer flow of an upper-convected Maxwell fluid across an exponentially stretched sheet with a chemical reaction on the Cattaneo–Christov heat flux model have been investigated. Using similarity transformation, the controlling system of nonlinear partial differential equations was transformed into a system of ordinary differential equations. The resulting converted equations were solved numerically by a successive linearization method with the help of MATLAB software. A graphic representation was created to analyze the physical insights of the relevant flow characteristics. The findings were presented in the form of velocity, temperature, and concentration profiles. As the relaxation time parameter varied, the local Nusselt number increased. The thermal relaxation time was shown to have an inverse relationship with fluid temperature. Furthermore, the concentration boundary layer becomes thinner as the levels of the reaction rate parameter increase. The results of this model can be applicable in biological fluids and industrial situations. Excellent agreement exists between the analysis's findings and those of the previous studies.

A Semi-Explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of a dual-phase-lag heat conduction model with Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag–Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

Vertical shear instability with dust evolution and consistent cooling times

Context. Gas in protoplanetary disks mostly cools via thermal accommodation with dust particles. Thermal relaxation is thus highly sensitive to the local dust size distributions and the spatial distribution of the grains. So far, the interplay between thermal relaxation and gas turbulence has not been dynamically modeled in hydrodynamic simulations of protoplanetary disks with dust. Aims. We aim to study the effects of the vertical shear instability (VSI) on the thermal relaxation times, and vice versa. We are particularly interested in the influence of the initial dust grain size on the VSI and whether the emerging turbulence is sustained over long timescales. Methods. We ran three axisymmetric hydrodynamic simulations of a protoplanetary disk including four dust fluids that initially resemble MRN size distributions of different initial grain sizes. From the local dust densities, we calculated the thermal accommodation timescale of dust and gas and used the result as the thermal relaxation time of the gas in our simulation. We included the effect of dust growth by applying the monodisperse dust growth rate and the typical growth limits. Results. We find that the emergence of the VSI is strongly dependent on the initial dust grain size. Coagulation also counteracts the emergence of hydrodynamic turbulence in our simulations, as shown by others before. Starting a simulation with larger grains (100 μm) generally leads to a less turbulent outcome. While the inner disk regions (within ∼70 au) develop turbulence in all three simulations, we find that the simulations with larger particles do not develop VSI in the outer disk. Conclusions. Our simulations with dynamically calculated thermal accommodation times based on the drifting and settling dust distribution show that the VSI, once developed in a disk, can be sustained over long timescales, even if grain growth is occurring. The VSI corrugates the dust layer and even diffuses the smaller grains into the upper atmosphere, where they can cool the gas. Whether the instability can emerge for a specific stratification depends on the initial dust grain sizes and the initial dust scale height. If the grains are initially ≳100 μm and if the level of turbulence is initially assumed to be low, we find no VSI turbulence in the outer disk regions.

Full operating parameter recording as an essential component of the reproducibility of laser-tissue interaction and treatments.

The number and diversity of published peer-reviewed studies in the discipline of laser dentistry have grown considerably during the past 10 years. Within primary research, the development of protocols to guide and formulate clinical practice demands precision and ease of reproducibility. Errors in data acquisition and management may become amplified as the applied randomized clinical trials (RCTs) forge new levels of clinical diversity and predictability in the use of laser photonic energy in both ablative (surgical) and sub-ablative (photobiomodulation (PBM) or photodynamic therapy (PDT)) applications. A comprehensive range of empirical and computational operating parameters must be included in published studies to facilitate the uniformity of powerand time-related values of laser irradiation. Choosing the correct "tissue irradiation parameters" is difficult and depends on the pathology and symptoms, the surface area to be treated, laser wavelength, the thermal relaxation time of each targeted tissue, and controlling penetration depth of the light into tissues. Therefore, to allow the reproducibility of the results, it is recommended that authors mention with the greatest care and clarity the irradiation parameters used in their study. This paper outlines the concerns felt regarding the general shortfalls and proposes a minimum range of laser operating parameters that should be represented in future peer-reviewed publications.

Thermal effects of electromagnetic radiation on the skin tissue by considering fourth‐order MGT bioheat model

AbstractUnderstanding the biothermal response of skin tissue exposed to electromagnetic (EM) radiation and variable thermal fields is crucial for mitigating risks associated with such exposures. This knowledge can empower the development of safe and efficacious evidence‐based treatments for various skin conditions within the medical field. This study employs the fourth‐order Moore–Gibson–Thomson (MGT) concept to establish a theoretical framework for biothermal analysis. This investigation aims to elucidate the biothermal response of skin tissues to EM radiation. The developed model facilitates the prediction of thermal reactions within human skin and the subsequent evaluation of bioheat transfer efficiency in biological tissues. The proposed model is implemented on a one‐dimensional representation of a skin layer and incorporates the effects of an induced electric field and a time‐harmonic heat source. Additionally, a linear dependence of metabolic heat generation on tissue temperature is considered. By employing Laplace transforms, the analytical solutions for tissue temperature are presented. The derived analytical solutions are compared with established theories to assess the accuracy of the proposed model. The results reveal that the modified MGT bioheat transfer model predicts lower temperatures compared to the conventional Pennes model, attributable to the incorporation of the thermal relaxation time constant.