Thermal Relaxation Time Research Articles

Flow Dynamics of Eyring–Powell Nanofluid on Porous Stretching Cylinder under Magnetic Field and Viscous Dissipation Effects

The current paper scrutinized the flow dynamics of Eyring–Powell nanofluid on porous stretching cylinder under the effects of magnetic field and viscous dissipation by employing Cattaneo–Christov theory. In order to study impacts of thermophoretic force and Brownian motion, the two-phase (Buongiorno) model is considered. As a consequence, very nonlinear PDEs that govern flow problem were formulated, transformed into ODEs via relevant similarity variables, as well as tackled by utilizing R-K-45 integration scheme along with the shooting technique in the MATLAB R2018a software. Consequently, the numerical simulations reveal that Eyring–Powell fluid, curvature, velocity ratio parameters have the propensity to raise nanofluid velocity. Nanofluid temperature shows an increasing pattern with magnetic, curvature, dissipative heating, and thermophoresis parameters. Besides, Prandtl number, Eyring–Powell fluid, velocity ratio, thermal relaxation time, and porous parameters indicate the declining impact against the nanofluid temperature. Hence, the porous medium reasonably and successfully managed nanofluid temperature as well as the overall thermal system in terms of system cooling. The concentration profile gets fall down with escalating values of Schmidt number, magnetic, curvature, dissipative heating, thermophoresis, Brownian motion, and solutal relaxation time parameters. Moreover, coefficient of the skin friction gets rise for larger values of Eyring–Powell fluid, magnetic and curvature parameters however porous medium and velocity ratio parameters reveal the opposite trends on it. The magnetic, curvature, Eyring–Powell fluid, velocity ratio, and dissipative heating parameters indicate increasing impacts on both Nusselt N u and Sherwood S h numbers even though both N u and S h get cut down with the porous medium parameter. Moreover, an excellent and sound agreement was attained up on comparing coefficients of the skin friction for the current result against that of previously published literatures under some limiting cases.

Percutaneous laser coagulation of dilated intradermal veins: from theory to practice

Review authors consider the current possibilities of percutaneous laser coagulation for telangiectasias and reticular veins, which are the most common cosmetic defects of vascular genesis, occurring in more than 80% of women of different age groups. This vascular pathology constituting an aesthetic defect and causing local physical discomfort is one of the most common indications for phlebosclerosing therapy and percutaneous laser coagulation. The authors present the most effective and safe guidelines for percutaneous laser coagulation based on analyses of a large volume of specialized literature. Due to the use of state-of-the-art Nd:YAG lasers, percutaneous laser coagulation is increasingly used in patients with various types of intradermal vein lesions and, owing to high efficiency and safety, has advantages over compression sclerotherapy by several criteria. Nd:YAG lasers can be divided into long- and short-pulse ones according to their technical characteristics. Long-pulse lasers provide coagulation of the target vessel due to a single pulse with a high energy density (fluence), while short-pulse lasers, on the contrary, generate a series of pulses to the target vein with a running time of fractions of a millisecond, which ensures the conversion of hemoglobin into methemoglobin with a ten-fold increased ability to absorb laser energy and convert it to heat. As the duration of the pulses generated by the device is a priori shorter than the thermal relaxation time, the risk of burns to the skin and paravasal structures almost completely disappears. The authors provide clinical examples of the application of Aerolase Neo device that utilizes MicroPulse technology to confirm the effectiveness and safety of shortpulse Nd:YAG lasers.

Entropy analysis on EMHD 3D micropolar tri-hybrid nanofluid flow of solar radiative slendering sheet by a machine learning algorithm

The purpose of this paper is to analyze the heat transfer behavior of the electromagnetic 3D micropolar tri-hybrid nanofluid flow of a solar radiative slendering sheet with non-Fourier heat flux model. The conversion of solar radiation into thermal energy is an area of significant interest as the demand for renewable heat and power continues to grow. Due to their enhanced ability to promote heat transmission, nanofluids can significantly contribute to enhancing the efficiency of solar-thermal systems. The combination of silicon oil-based silicon (Si), magnesium oxide (MgO), and titanium (Ti) nanofluids has attracted attention for their ability to improve the performance of solar-thermal systems. The present study discloses a new approach for intelligent numerical computing solving, which utilizes an MLP feed-forward back-propagation ANN and the Levenberg-Marquard algorithm. The collection of data was conducted for the purpose of testing, certifying, and training the ANN model. The Bvp4c solver in MATLAB is utilized to solve the nonlinear equations governing the momentum, temperature, skin-friction coefficient, and Nusselt number. The characteristics of numerous dimensionless parameters such as porosity parameter left(K={0.0,2.0,4.0}right), vortex viscosity parameter left({R}_{1}={0.5,1.0,1.5}right), electric field parameter left(E={0.0,0.1,0.2}right), thermal relaxation time left(Lambda ={0.01,0.10,0.20}right), heat source/sink parameter, left(Q=-{0.3,0.0,0.3}right) thermal radiation parameter left(R={0.5,1}.{0,1.5}right), temperature ratio parameter left({theta }_{w}={0.5,1.0,1.5}right),nanoparticle volume fraction left(phi ={0.00,0.02,0.04}right) on Si + MgO + Ti/silicon oil micropolar tri-hybrid nanofluida are analyzed. The ANN model engages in a process of data selection, network construction, training, and evaluation of its effectiveness through the utilization of mean square error. Tables and graphs are used to show how essential parameters affect fluid transport properties. The velocity profile is decreased by higher values of the porosity parameter, whereas the temperature profile is increased. The temperature profile is inversely proportional to higher values of the electric field parameter. The micro-rotation profiles reduced by expanding values vortex viscosity parameter. It has been determined that entropy generation and Bejan number intensifications for enlarged nanoparticle volume fraction.

Nonlinear thermal analysis of two-dimensional materials with memory

A nonlinear hyperbolic heat transport equation has been proposed based on the Cattaneo model without mechanical effects. We analyze the two-dimensional Maxwell-Cattaneo-Vernotte heat equation in a medium subjected to homogeneous and non-homogeneous boundary conditions and with thermal conductivity and relaxation time linearly dependent on temperature. Since these nonlinearities are essential from an experimental point of view, it is necessary to establish an effective and reliable way to solve the system of partial differential equations and study the behavior of temperature evolution. A numerical scheme of finite differences for the solution of the two-dimensional non-Fourier heat transfer equation is introduced and studied. We also investigate the attributes of the numerical method from the aspects of stability, dissipation and dispersive errors.

Phonon non-equilibrium effects on interface thermal resistance between graphene and substrates

Accurate measurement and deep understanding of interfacial thermal transport through interfaces where two-dimensional (2D) materials are involved are crucial for efficient thermal management in nanodevices. However, there is still a large discrepancy in the measurement on the interfacial thermal resistance (ITR) at interfaces between 2D materials and substrates. In this study, two kinds of molecular dynamics techniques are utilized to investigate the ITR of graphene/silicon interfaces under steady-state and transient conditions. Our results indicate that, in both conditions, phonon non-equilibrium phenomena could lead to an overestimation of the interfacial thermal resistance. In the steady state, the overestimation of ITR arises from an exaggerated interfacial temperature difference when using specific vibrational modes as indicators of the sample temperature. In the transient regime, it is attributed to the extended thermal relaxation time of flexural acoustic modes in graphene caused by weak phonon coupling when recording the temperature evolution to extract the ITR. These findings provide a comprehensive understanding of thermal transport across the graphene/silicon interface, aiding in the optimization of graphene-based nanodevices. The study also underlines the necessity of considering the specific experimental setup and physical processes involved when interpreting ITR data obtained from measurements.

Exponential stability and numerical analysis of Timoshenko system with dual‐phase‐lag thermoelasticity

AbstractThis study aims to investigate the well‐posedness and stability of a thermoelastic Timoshenko system with non‐Fourier heat conduction. Specifically, we analyze the system using the dual‐phase‐lag (DPL) model, which incorporates two thermal relaxation times, and , to model non‐instantaneous heat propagation. Applying the semigroup approach, we demonstrate the existence and uniqueness of the solutions. Subsequently, we introduce a novel stability parameter using the multiplier method. Exponential decay is proven for the case of with . Using Gearhart–Prüss theorem, we show the lack of exponential stability when and . Numerically, we present a fully discrete approximation using the finite element method and the backward Euler scheme, and we provide some numerical simulations to show the discrete energy decay and the behavior of solutions.

Cell cycle parameters and ornithine decarboxylase activity in the red bone marrow of hibernating ground squirrels Urocitellus undulatus

During the hibernation season, the values for the parameters of the cell cycle of red bone marrow cells in the hibernating ground squirrels Urocitellus undulatus, when they return to an active-like state between periods of torpor and interbout arousal, do not differ from those observed in summer-active animals. In animals that enter a state of torpor, the cumulative percentage of cells in the resting phase (G0 phase) and pre-synthesis phase (G1 phase) increased from 71.8 to 76.0%, the percentage of cells in the synthesis phase (S phase) decreased from 19.3 to 15.3% compared to those animals that return to an active-like state between periods of torpor and interbout arousal. The cumulative percentage of cells in the post DNA synthesis phase (G2 phase) and mitosis (M) does not change, but (G2 + M)/S ratio increases. When animals enter a state of torpor, changes in parameter values are observed when the animal’s body temperature drops below 25°C, this effect refers to a system whose thermal relaxation time is a nonmonotonic function of the initial temperature. The activity of the key enzyme of polyamine synthesis ornithine decarboxylase, a marker of cell activation and proliferation during interbout arousal does not significantly differ from that observed in summer-active animals; the enzymatic activity decreases sharply, when animals decrease their body temperature below 25°C and enter a state of torpor, and this activity remains at a low level during hibernation and arousal until body temperature reaches 30°C. The role of changes in the parameter values associated with proliferative activity in adaptation of hematopoietic tissue during hibernation of the Yakutian ground squirrel is discussed.

Influence of thermal relaxation time on thermomechanical interactions in biological tissue during hyperthermia treatment

This study presents an analytical analysis of thermo-mechanical interactions within living tissues using a generalized biothermoelastic model with one thermal relaxation time. Utilizing Laplace transforms and associated techniques, we investigate the response of living tissue to a pulse boundary heat flux that decays exponentially on a traction-free surface. Through detailed graphical illustrations, we elucidate the influence of key parameters such as thermal relaxation time, blood perfusion rate, and the characteristic time of the pulsing heat flux on temperature distribution, displacement, and thermal strain. Our results are presented through comprehensive graphical representations. Furthermore, a parametric analysis is conducted to guide the selection of optimal design factors, enhancing the accuracy of hyperthermia treatments.

Oblique stagnation point flow of magnetized Maxwell fluid over a stretchable Riga plate with Cattaneo-Christov heat flux and convective conditions

The current work deals with the oblique stagnation point flow phenomenon of a rate-type Maxwell fluid with the significance of the Cattaneo-Christov double diffusion theory. The Cattaneo-Christov theory is illustrated through the modified form of Fourier’s and Fick’s laws. The steady magnetized flow mechanism is observed in two dimensions through a stretchable convective Riga plate. In the mass and heat transfer analysis, the consequences of chemical reactions and thermal radiation are also incorporated. With the contribution of relevant dimensionless quantities, the setup of dimensionless equations is acquired which further takes the form of nonlinear equations. The physical significance of the numerous parameters on different features of the flow phenomenon is graphically exhibited. The interesting physical quantities are computed and numerically evaluated relative to the pertinent parameters. This study reveals that the thermal relaxation time parameter lowers the rate of heat transfer, and the thermal Biot number enhances the rate of heat transport. Moreover, the Deborah number minimizes the flow field of both tangential and axial velocities.

Theoretical Investigation on Thermal, Mechanical and Ultrasonic Properties of Zirconium Metal with Pressure

Zirconium (Zr), a metal with an hcp structure, has been investigated for the transmission of acoustic wave in the 0 to 25 GPa operating pressure. For this, the Lennard-Jones interaction potential approach has been used to estimate the higher order elastic coefficients (SOECs and TOECs). This model is used to calculate the 2nd and 3rd order elastic parameters for zirconium metal. With the help of SOECs, other elastic moduli such as bulk modulus (B), Young’s modulus (Y) and shear modulus (G) have been calculated for Zr metal using Voigt-Reuss-Hill (VRH) approximations. Later, applying SOECs as well as zirconium density under the same pressure range, three orientation dependent acoustic velocities, comprising Debye average velocities, have been studied. Basic thermal characteristics such as specific heat at constant volume, thermal conductivity associated with lattice, thermal energy density, thermal relaxation time as well as acoustic coupling coefficients of zirconium metal have been also calculated at same pressure range. The computation is also satisfactory in estimating the ultrasonic attenuation coefficients, arises due to the interaction of phonons, hardness as well as melting temperature under various pressures in this research work.

Cattaneo-Christov heat-mass flux model on mixed convection of Casson nanofluid in a porous medium microchannel with thermal radiation and chemical reaction

This article presents mixed convection of radiating and reacting Casson nanofluid in microchannel filed with a saturated porous medium with Cattaneo-Christov heat-mass flux model. The Buongiorno’s nanofluid flow model is used to study the effects of the Brownian motion and the thermophoresis whereas the Darcy-Forchheimer model is considered to examine the nanofluid and porous medium interaction. Thereafter, the highly nonlinear system of equations for momentum, energy and concentration are formulated and solved numerically by utilizing the Runge-Kutta-Fehlberg integration scheme with shooting technique. Consequently, the numerical simulation indicates that the Casson fluid parameter and the variable viscosity parameter play a great role in escalating the velocity field and temperature profile however chemical reaction, porous medium, radiation, thermal relaxation time and convective heating control over the temperature profile. Besides, an increase in the thermal relaxation time causes more transfer of heat from the hot microchannel wall to the fluid and thus, fluid temperature distribution is higher for Hence, the Cattaneo-Christov heat flux model is constructive in cooling process as compared to that of the classical Fourier’s law of heat conduction. Furthermore, heat and mass transfer rates are enhancing because of the thermal radiation and solutal Grashof number at both sides of the microchannel walls. Also, the current findings are compared with that of the existing literature and a sound agreement was established.

Numerical investigation of heat and mass transfer of variable viscosity Casson nanofluid flow through a microchannel filled with a porous medium

Thermal behaviours and hydrodynamics of non-Newtonian nanofluids flow through permeable microchannels have large scale utilizations in industries, engineering and bio-medicals. Therefore, this paper presents the numerical investigation of heat and mass transfer of variable viscosity Casson nanofluid flow through a porous medium microchannel with the Cattaneo-Christov heat flux theory. The highly nonlinear PDEs corresponding to the continuity, momentum, energy and concentration equations are formulated and solved numerically via the second order implicit finite difference scheme known as the Keller-Box method. Accordingly, the numerical simulations reveal that variable viscosity parameter, thermal Grashof number, solutal Grashof number, thermophoresis parameter, Schmidt number and Casson fluid parameter show increasing effects on both velocity and temperature of the nanofluid. Furthermore, the temperature profile escalates with increasing values of the Eckert number and the thermal relaxation time parameter. Thus, the Cattaneo-Christov heat flux model is beneficial in warming the transport system of microfluidics when compared to that of the classical Fourier heat conduction law. The temperature profile however, indicates a retarding behavior with increasing values of the Brownian motion parameter, Prandtl number and porous medium parameters namely Forchheimer number and porous medium shape parameter and hence, the porous medium quite effectively controls the nanofluid temperature distribution which plays substantial roles in cooling the transport system of microfluidics. Moreover, the concentration profile shows an increasing pattern with escalating values of the Prandtl number, Schmidt number and thermophoresis parameter but it demonstrates a decreasing trend with the Casson fluid, variable viscosity, thermal relaxation time and solutal relaxation time parameters. It is also observed that coefficient of the skin friction increases with increasing values of the pressure gradient parameter, Eckert number, Forchheimer number and injection/suction Reynolds number. Besides, the heat transfer rate at both walls of the microchannel enhances with rising values of the Eckert number, variable viscosity, parameter and injection/suction Reynolds number. The Casson fluid and thermal relaxation time parameters reveal opposite scenarios on the heat transfer rate at the left and right walls of the microchannel. In addition, the mass transfer rate at both walls of the microchannel shows an increasing pattern as the Eckert number, variable viscosity parameter, Schmidt number and suction/injection Reynolds number increase.

Synthesis and cis-trans kinetics of an azobenzene-based molecular switch for light-responsive silica surfaces

Light-responsive materials design is an attractive research field that stimulates demand for the synthesis of novel molecular photoswitches. The novel photoswitches should be capable of being attached to a desired surface in order to provide it with light-responsive properties. The switchback to its ground state is expected to be gradual, with the possibility of acceleration. This study presents a comprehensive description of a chemical route to a molecular photoswitch based on an azobenzene derivative with a trifluoromethoxy group and a long alkyl chain. The photoswitch is capable of modifying submicrometer silica particles and silicon wafers as models of curved and flat surfaces, respectively. The thermal relaxation times of the synthesized azobenzene were studied in three different solvents: ethanol, chloroform, and toluene. The results reveal a significantly delayed relaxation process lasting for several days. This observation is found to be related to the polarity of the solvents used. To characterize the extensive thermal relaxation process, a methodology including the use of white-light pulses to accelerate cis-trans isomerization is suggested. The white light spectrum used in pulses affects thermal relaxation but does not alter the relaxation time extrapolated to zero. The density of the photoswitch molecules attached to particles varies from 0.7 to 1.7 molecules/nm2 as the initial amount of azobenzene in the reaction increases. Surface-attached photoswitches demonstrate reversible cis-trans isomerization behavior when exposed to UV and white light irradiation. A 14° contact angle change is observed when flat surfaces modified with photoswitches are irradiated with UV light.

ATSS model based upon applications of Cattaneo-Christov thermal analysis for entropy optimized ternary nanomaterial flow with homogeneous-heterogeneous chemical reactions

ATSS model for magnetohydrodynamic Darcy-Forchheimer radiative ternary nanoliquid flow by curved stretched sheet is constructed. Ternary nanoliquid consists of three different nanoparticles (gold (Au), zinc oxide (ZnO) and multi-walled carbon nanotube (MWCNT)) in ordinary liquid (Carboxymethylcellulose water (CMC-H2O)). Cattaneo-Christov heat flux and convective condition are discussed. Thermal equation has Ohmic heating, heat generation/absorption and radiation. Entropy production along with cubic autocatalysis chemical reaction is discussed. The obtained differential nonlinear systems are numerically computed by using ND-solve method. Graphical discussion for liquid flow, entropy rate and temperature via influential parameters for nanomaterial (Au/CMC-H2O), hybrid nanomaterial (Au+ZnO/CMC-H2O) and ternary nanomaterial (Au+ZnO+MWCNT/CMC-H2O) is organized. Computational outcomes for coefficient of skin friction and Nusselt number are studied. Opposite trend of velocity and skin friction for curvature is noticed. Velocity reduces against higher magnetic field. Augmentation for temperature against Eckert and thermal Biot numbers is noticed. Entropy production enhancement for radiation and diffusion parameter is observed. Thermal transport rate for radiation and thermal relaxation time has an increasing effect.

Role of bioconvection and activation energy on MHD flow of Maxwell’s nanofluid with gyrotactic microorganisms in porous media: The Cattaneo–Christov model

This study examines and analyzes the impact of MHD and bioconvection on Maxwell’s nanofluid flow in a porous medium that contains gyrotactic microorganisms. In addition, more study on chemically reactive activation energy and Cattaneo–Christov heat flux is conducted, and the conclusions from this research are presented. The bioconvection flow of Maxwell nanofluids over a stretched sheet is presented by highly nonlinear partial differential equations, which are reduced to ordinary differential equations using suitable similarity transformations. A shooting method based on the Runge–Kutta technique is used to overcome the issue. The outcomes are graphically represented and explored numerically in detail for the relevant parameters’ impact on the velocity, temperature, concentration, and motile microorganisms profiles. Results reveal that the velocity profile is decreased by increasing the magnetic parameter, while those enhanced by the mixed convection parameters. The thermal boundary thickness and temperature profile negatively correlate with the thermal relaxation time and Prandtl number and are proportional to the magnetic parameter. Boosting the Brownian motion parameter, Deborah number, and thermophoresis parameter improves heat transport. The activation energy and Prandtl parameters show an upward trend in concentration profiles. The density of the motile microorganisms is a decreasing function of Lewis and Peclet numbers.

Numerical study of Cattaneo‐Christov heat transfer in MHD Carreau‐Yasuda hybrid nanofluid subjected to Buoyancy force

AbstractHybrid nanofluids (HNFs) have potentials applications in automotive industry, heating and cooling systems, biomedical and other fields due to their ability to introduce higher thermal conductivity than standard nanofluids. The purpose of this study is to investigate and compare the thermal transport performance (in the presence of buoyancy force) of two sets of HNFs. The hybrid nanoparticles which is the combination of titanium carbide and aluminium oxide, and the combination of titanium carbide‐copper oxide are taken into account. Both types of hybrid nanoparticles are dispersed in as a subjective fluid over a vertical nonlinear stretching sheet embedded in a porous medium. This will be the first study on the MXene base material , making it possible for MXene‐based materials to enter the fluid dynamics field. Further, MXene material as heat transporting material is studied less and much more is needed for explore its various aspect. The specific combination of , and is considered because of their promising thermophysical and thermal transport properties. Moreover, considered combination of nanoparticles and the base fluid form a mixture which has thermal relaxation characteristics due to which its deviates from classical Fourier law of heat conduction. Therefore, instead of conventional Fourier's law of heat conduction, the non‐Fourier law of heat conduction is used to formulate the energy equation. It is first time that fhe finite element of method (FEM) is used for such a coupled and nonlinear complex problems of computational fluid dynamics (CFD). The numerical and graphical impacts of magnetic fields, Grashof number, permeable parameter, and thermal relaxation time parameter on velocity, and heat transport are investigated by applying FEM on formulated boundary value problems. In each studied system, increasing the Hartmann number causes an increase the skin friction coefficient and a decrease in the Nusselt number. Moreover, by increasing the thermal relaxation parameter, the temperature of the fluid decreases significantly. The velocity of the modified nanofluids is directly proportional to the Grashof number. The thermal boundary layer thickness (TBLT) and momentum boundary layer thickness (MBLT) of Carreau‐Yasuda (CY)‐HNF (Set II) is greater than CY hybrid nanofluid (CY‐HNF) (Set I) and CY‐Nanofluid (NF), respectively. We believe that the current research work provides new insights to improve the heat transport of nanofluid using appropriate combination of hybrid nanoparticles for practical application.

Modified thermal and solutal fluxes through convective flow of Reiner-Rivlin material

Heat transport in mixed convection Reiner-Rivlin liquid flow due to stretching cylinder is addressed. Cattaneo-Christov double diffusive relation is utilized to discuss heat and solutal transport features. Variable thermal conductivity and mass diffusivity impacts are incorporated. Adequate transformations are used to reduce non-linear differential expressions for dimensionless expressions. The given non-dimensional expressions are solved through implementation of Optimal homotopy analysis technique (OHAM). Physical features of fluid flow, concentration and temperature against influential parameters are examined. Clearly higher mixed convection parameter boost the liquid flow. Decay in temperature is detected against thermal relaxation time. Similar impact of temperature is witnessed by curvature and thermal conductivity variables. Velocity enhances against Reiner-Rivlin material variable. Decline in concentration is detected for higher Schmidt number. Concentration boosts against mass diffusivity parameter. Higher solutal relaxation time parameter leads to decline concentration. Reduction in temperature is noticed for Prandtl number whereas opposite behavior witnessed for heat transport rate. An increment in mass transport rate occurs for mass diffusivity and solutal relaxation time variables.

Comprehensive analysis of magnetized second-grade nanofluid via Fourier's and Cataneo-Christove models past a curved surface

This study presents the computer simulations of the magnetized effects of Cattaneo-Christov double diffusion models on the heat and mass transport behavior of a second-grade nanofluid flowing in two dimensions across a curved stretching and shrinking surface. Moreover, the features of convective heat transfer, slip velocity, viscous dissipation, porosity, and heat source/sink with a chemical reaction are also used. Considering the concentration and thermal relaxation times, the classical models of heat and mass diffusion (Fourier and Fick's laws) are extended to the generalized form in regard to the double diffusion Cattaneo-Christov models. Evaluating the current physical study including the Lorentz forces allows us to better understand how the magnetic field affects the process of double diffusion coupled with Joule heating. The system of highly nonlinear, two-dimensional, coupled partial differential equations caused by the moment of second-grade fluid across a curved sheet is solved using the bvp4c scheme. The key findings proves that the concentration and temperature of classical Fourier and Fick's law causes to rise faster than that of Cattaneo-Christov heat and mass flux model respectively as well as the concentration and temperature of Newtonian fluid causes to rise faster than that of second grade nanofluid. The generalized Fourier and Fick's law respectively generate greater heat and mass transport than the classical Fourier and Fick's law as well as the second-grade nanofluid generate greater heat and mass transport than the Newtonian fluid.

Analysis of a viscoelastic fluid flow with Cattaneo–Christov heat flux and Soret–Dufour effects

The present study concentrates on the motion of a third-grade fluid with magneto-hydrodynamics (MHD) over a stretching surface. Additionally, the Cattaneo–Christov model is employed to derive information about the heat flux, which is subsequently utilized to ascertain the heat transmission properties. The inquiry involves an assessment of the impact of thermal relaxation time on the boundary layer. The considered fluid is a type of non-Newtonian fluid that deal with both shear thinning and shear thickening behaviors. The study also involved calculating all normal stress components that are not accounted for by either the power law model or the second grade model. The motion of fluid is attributed by linear stretching, and the momentum flow is observed with the help of Soret–Dufour effects. The Cattaneo and Christov model is particularly beneficial for describing transmission of heat in materials with high thermal conductivity, where the classical Fourier’s law may not be accurate. The examination of the transport properties of velocity, heat, and mass involves the consideration of the temperature effect on variable viscosity and thermal conductivity, which are linearly associated with each other. A set of partial differential equations (PDEs) that are nonlinear in nature has been derived, and some boundary conditions have been identified that yield satisfactory results. Using similarity transformation a system of nonlinear PDE’s are modify into dimensionless system of ordinary differential equations (ODE’s). The homotopy analysis method (HAM) is applied in a convenient manner to obtain solutions for transform equations, while the impact of relevant flow parameters is visually demonstrated. Adequate graphical and tabular results are achieved using a semi-analytical approach. Moreover, the Cattaneo–Christov equation can provide a better understanding of the thermal behavior. It allows for a more comprehensive analysis of the thermal response, ensuring that the heat transfer models used are appropriate for such conditions.

Thermal properties of the core of magnetar

During very early age of neutron stars, the core cools down faster compared to the crust creating a large thermal gradient in the interior of the star. During 10−100 years, a cooling wave propagates from the core to the crust causing the interior of the star to thermalize. During this duration thermal properties of the core material is of great importance to understand the dynamics of the interior of the star. The heat capacity and thermal conductivity of the core depends on the behaviour of matter inside the core. We investigate these two properties in case of magnetars. Due to presence of large magnetic field, the proton superconductivity is quenched partially inside the magnetars depending upon the comparative values of upper critical field and the strength of the magnetic field present. This produces non-uniformity in the behaviour of matter throughout the star. Moreover, such non-uniformity arises from the variation of nature of the pairing and values of the pairing gap energy. We find that the heat capacity is substantially reduced due to the presence of superfluidity. On the other hand, the thermal conductivity of neutron is enhanced due to proton superconductivity and gets reduced due to neutron superfluidity. Hence, the variation of the thermal properties due to superfluidity in presence of magnetic field is different at different radius inside the star. However, in all the cases the maximum variation is of the order one. This affects the thermal relaxation time of the star and eventually its the thermal evolution.