non-Fourier Model Research Articles

Relationship Between Heat and Troughs During a Transport Process of Heating the Pet Films

Understanding the troughs caused during a heat treatment process is important for ensuring process stability and product quality in roll-to-roll (R2R) productions methodology. The purpose of this study is to confirm the relationship between heat and troughs during a transport process of heating where heat is applied over a wide range of area. The temperature and tension applied to the web during the heated transport process were measured in the experimental analysis. Results showed that the web were stretched in the web transport direction during the heat transfer process. However, troughs did not occur because the experiment was conducted below the glass transition temperature. The comparison between the web temperature obtained in the experimental analysis with the one-dimensional thermal conduction simulation for the temperature distribution of the web are also conducted in this paper. This simulation was performed using a non-Fourier model that can be used on microscales. Simulation results show that when the temperature is gradually raised, the amount of thermal conduction is reduced during transportation of the web. The thermal conduction of ballistic phonon is smaller than that of the diffuse phonon when compared at same distance. Even though there were differences between the experimental values and the simulation results, this is because it ignores the heat transfer and radiant heat transfer.

Thermal analysis of magnetohydrodynamics (MHD) Casson fluid with suspended iron (II, III) oxide-aluminum oxide-titanium dioxide ternary-hybrid nanostructures

This study is carried out to enhance and analyze the thermal performance of non-Newtonian Casson fluid by immersing Ternary hybrid nanoparticles Fe3O4-Al2O3-TiO2 uniformly. To model the behaviour of such complex phenomena mathematically, a system of complex transport differential equations is developed by utilizing a non-Fourier heat transfer model for energy transport. The non-dimensional system of transport equations involving physical parameters is analyzed numerically by employing the Galerkin finite element methodology (G-FEM). The simulations predicted promising enhanced heat transfer characteristics in Ternary hybrid Casson fluid. The Casson fluid parameter has shown remarkable behavior on temperature distribution. Ternary hybrid nanoparticles have increased the overall thermal conductivity of the fluid and consequently, the temperature distribution is significantly raised. Hence ternary hybridity of nano-structures in Casson fluid is shown as an effective technique in improving the thermal performance of complex fluid.

Biomedical aspects of entropy generation on MHD flow of TiO2-Ag/blood hybrid nanofluid in a porous cylinder

This study aims to analyze the heat transfer behavior of the magnetohydrodynamic blood-based Casson hybrid nanofluid in the occurrence of a non-Fourier heat flux model and linear thermal radiation over a horizontal porous stretching cylinder with potential applications in biomedical engineering. The present investigation utilised titanium dioxide and silver nanoparticles, which exhibit considerable potential in the realm of cancer therapy. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. Suitable self-similarity variables are employed to transform the nonlinear mathematical equations such as velocity, temperature, skin friction coefficient, and heat transfer rate, which are computed via homotopy perturbation method (HPM). HPM computations have been executed to solve the influences of various parameters such as porosity parameter ( K = 0.0 , 1.0 , 2.0 ) , Curvature parameter ( α = 0.0 , 1.0 , 3.0 , 5.0 ) , Casson parameter ( β = 0.0 , 0.5 , 1.5 ) , inertia coefficient ( Fr = 0.5 , 1.5 , 2.5 ) , thermal relaxation parameter ( δ ∗ = 0.0 , 0.5 , 1.0 ) , radiation ( Rd = 0.0 , 0.5 , 1.0 ) , Eckert number ( Ec = 0.0 , 0.1 , 0.2 ) , Brinkman number ( Br = 0.5 , 1.0 , 1.5 ) and temperature difference parameter ( α 1 = 0.0 , 0.5 , 1.0 ) . The comparison using the homotopy perturbation technique produces a more accurate and reliable consequence than the numerical method (Runge-Kutta method). The higher values of the Casson and Curvature parameters decrease the velocity profile. The temperature profile of M = 1 and M = 0 increases with improving values of the thermal relaxation parameter. Entropy generation rises to enhance Brinkman number values, whereas Bejan number exhibits the reverse influence. Improving the value of the heat source parameter declines the Nusselt number.

Effects of different nanoparticles Cu, TiO2, and Ag on fluid flow and heat transfer over cylindrical surface subject to non-fourier heat flux model

The significance of this investigation is to optimize the heat transfer rate of magnetohydrodynamic bioconvective hybrid nanofluid flow in the presence of heat source and thermal convection. The main focus is to examine the two-dimensional incompressible MHD and / hybrid nanofluid flow across the stretching cylinder with the Cattaneo–Christov heat flux model. The response surface methodological approach and sensitivity analysis have been employed to statistically scrutinize the influences of concentration, bioconvection, and thermo-diffusion on heat transfer rate. By applying suitable similarity vectors in controlling the partial differential equations, a system of equations (ODEs) is formed. A well-known method Runge Kutta with shooting has used for numerical simulations. The role of various involving factors on heat and mass transfer rate and skin friction factor is illustrated using tables, figures, and surface plots. The three-dimensional graphs displayed the synchronized effect of involving factors on physical quantities. The heat transfer rate is least responsive to variations in the magnetic parameter and most sensitive to the fluctuations of the Biot number. It is perceived that the nanoparticle concentration and motile concentration profiles declined with the increasing effect of chemical reaction parameters. The legitimacy of the current conclusions is established by the excellent agreement concerning present and previous consequences.

Double diffusion Forchheimer flow of Carreau-Yasuda nanofluid with bioconvection and entropy generation: Thermal optimized analysis via non-Fourier model

The entropy generation phenomenon is important in thermodynamic systems, chemical engineering, industrial systems, reducing the energy consumptions and optimizing the resource utilization. Owing to such motivated applications, aim of current research is to present the applications entropy generation phenomenon in double diffusion flow Carreau-Yasuda nanofluid due to bidirectional stretched surface. The rheology of non-Newtonian fluid is observed by using the Carreau-Yasuda (CY) nonlinear model. The analysis is further supported with suspension of microorganisms with Carreau-Yasuda nanofluid. The formulated model is extended by entertaining the viscous dissipation, thermal radiation and activation energy consequences. The inertial effects are supported with Darcy Forchheimer approach. Additionally, non-Fourier and Fick theories are implanted to observe the thermal phenomenon. The equations resulted from the given model are analytically entertained via homotopy analysis scheme. The physical insight of thermal model is graphically presented. Moreover, the streamlines are plotted for flow model. An enhancing outcomes for entropy generation phenomenon are noted due to diffusion parameter and magnetic parameter. Moreover, the optimized phenomenon also increases due to Brinkman number.

Dynamics of unsteady axisymmetric of Oldroyd-B material with homogeneous-heterogeneous reactions subject to Cattaneo-Christov heat transfer

In several industrial and engineering applications, the Catteno-Christov heat flux plays a major role in the flow and heat transport of non-Newtonian fluids. Therefore, the goal of this study is to investigate the characteristics of homogeneous-heterogeneous reactions in the axisymmetric flow of Oldroyd-B materials using heat conduction analysis. The heat transfer phenomenon is examined from the non-Fourier heat flux model perspective. The governing flow field equations are developed using the rheological formulation of the Oldroyd-B fluid model, which is transformed into a set of nonlinear differential equations by utilizing the proper similarity conversions. The series solutions for the velocity, thermal, and solutal distribution are derived. The physical behaviors of relevant parameters are discussed in detail. The findings reveal that for the curvature parameter, the fluid velocity improves near the cylinder surface and no motion occurs away from the surface, while this predicts the dual behavior on temperature and concentration distributions. Further, fluid relaxation and retardation time exhibit opposite behavior on fluid velocity. Additionally, the results demonstrate that the homogeneous response parameter exhibits contradicting behavior on the concentration field while the thermal relaxation parameter lowers the temperature field.

Entropy minimization of the non-Newtonian bio-hybrid (Fe3O4-CuO/blood) nanofluid flow over a linear extending sheet by means of induced magnetic field

The physiological system loses heat energy through the bloodstream to nearby cells. Such energy loss can lead to a quick death, anemia, severe hypothermia and high or low blood pressure to heart surgery. As a result, biomedical engineers and physicians are increasingly attracted to the study of entropy production to calculate the energy loss of biological systems. Furthermore, the thermodynamic state of entropy production is used to access cancer cells during chemotherapy treatment and heat transfer in tissues. The current model intends to explore the significance of the non-Fourier heat flux model on Eyring–Powell/Maxwell hybrid nanofluid (Fe3O4–CuO/blood) flow in a linear extending sheet with induced magnetic field and entropy generation. Suitable self-similarity variables are performed to convert momentum and thermal equations determined using the homotopy perturbation method into ordinary differential equations. The significance of distinct physical parameters such as thermal relaxation parameter, volume fraction, fluid parameter, magnetic Prandtl number, Biot number, Brinkman number, heat source, Eckert number, radiation and heat source on velocity, temperature, skin friction coefficient, Nusselt number, entropy production, streamlines and isotherm are represented through figures. It is recognized that the fluid friction irreversibility is comparatively higher than thermal irreversibility and highly dominates the total entropy generation. The nanoparticle volume fraction diminishes the velocity and induced magnetic field of both Eyring–Powell and Maxwell hybrid nanofluid. Fluid friction irreversibility is more in Maxwell fluid compared to the Eyring–Powell fluid.

Investigation of inherent irreversibility and wall friction using non-Fourier model in converging/diverging flow of Power-law fluid

The comparative analysis of heat and mass transfer of power-law fluid past convergent conduit with the perspective of modified and conventional Fourier’s law is revisited in this paper. To consolidate the mathematical modelling for the physical flow problem through wedge shaped channel the cylindrical coordinates are used. The governing equations are normalized and solved with an efficient built-in numerical code Bvp4c. The thermal distribution against various parameters depletes with thermal relaxation and can be adjusted as controlling toll to optimize the thermal performance of the system. Comparison to classical heat flux model the non-Fourier and Fick’s law has a better performance. The functioning of channel fluidic systems is improved by low values of the power-law index and the lubricated walls.

Onset about isothermal flow of Carreau liquid over converging channel with Cattaneo-Christov heat and mass fluxes

In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.

Homotopy analysis of mixed convection flow of a magnetized viscoelastic nanofluid from a stretching surface in non-Darcy porous media with revised Fourier and Fickian approaches

This article addresses theoretically the mixed convection hydromagnetic flow of electrically conducting viscoelastic nanofluid from a vertical permeable stretching sheet in a non-Darcy porous medium with Cattaneo–Christov double-diffusion model to evaluate the heat transfer phenomena in steady boundary layer flow on a stretchable surface. In this regard, thermal and solutal hyperbolic wave relaxation effects are included for non-Fourier and non-Fickian models. Heat absorption is also included in the analysis. The Buongiorno two-component nanoscale model is adopted for simulating Brownian motion and thermophoretic body force effects. A non-Darcy drag force model is employed for the porous medium and the Reiner–Rivlin second-grade model for non-Newtonian characteristics. Via appropriate dimensionless similarity variables, the nonlinear dimensional partial differential conservation equations for momentum, energy and concentration with associated boundary conditions are rendered into a nonlinear dimensionless ordinary differential boundary value problem. The homotopy analysis method (HAM) is utilized to solve the boundary value problem and the impact of emerging parameters including thermal relaxation parameters, non-Newtonian material parameter, Darcy permeability parameter, porous inertial parameter and Hartmann magnetic number on the momentum, heat and mass transfer characteristics are visualized graphically and in tables. A 30th-order approximation for HAM is shown to produce sufficient accuracy for the velocity and temperature fields and a 40th-order estimates is adequate for the concentration field. It is observed that increasing the magnitude of thermal and solutal relaxation parameters has the opposite effect on the thermal and concentration distributions. The novelty of the work is the simultaneous inclusion of multiple effects (non-Fourier and non-Fickian thermal relaxation hyperbolic wave models, non-Darcy drag effects and heat generation/absorption) which are relevant to rheological nanomaterials processing and also the deployment of homotopy analysis as an alternative to conventional numerical methods such as finite differences, finite elements and MATLAB solvers. The study is relevant to the manufacture of electro-conductive polymers (ECPs) and smart (functional) magnetic nano-liquids.

A general non-Fourier Stefan problem formulation that accounts for memory effects

The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a general model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. On shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in contrast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result confirmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.

Analytical Model for Thermoelastic Dissipation in Oscillations of Toroidal Micro/Nanorings in the Context of Guyer–Krumhansl Heat Equation

Thermoelastic dissipation or thermoelastic damping (TED) can restrict the quality factor of micro/nanoring resonators seriously. This paper employs the non-Fourier model of Guyer–Krumhansl (GK model) to render a size-dependent formulation and analytical solution for approximating the amount of TED in micro/nanorings with circular cross-section by inclusion of nonlocal and single-phase-lagging effects. To fulfill this objective, the equation of heat conduction in the ring is first established according to GK model. Then, by placing the temperature distribution obtained from the heat conduction equation in the TED relation defined on the basis of thermal energy approach, an expression in the form of infinite series is given for TED, which includes non-classical parameters of GK model. Finally, after checking the validity of the model through a comparative study, several simulation results are prepared to emphasize on the influence of different factors such as non-classical parameters of GK model, geometry of ring, vibrational mode and ambient temperature on TED value. Numerical examples reveal that the mentioned factors along with the two- or three-dimensional heat transfer (2D or 3D) model have major influences on TED variations.

An MHD Casson fluid flow past a porous stretching sheet with threshold Non-Fourier heat flux model

The present paper investigates the magnetohydrodynamics Casson fluid flow with porous medium. The Cu-water nanofluid is used to investigate further analytical results. Thermal radiation is considered along with the Cattaneo-Christov heat flux model and then solved analytically, then expresses the closed forms analytical solution in terms of two variables of hypergeometric function. The special form of Appell hypergeometric solutions are closed form of analytical solutions. The results of normalized shear stress at the wall and temperature profile, and rate of heat flux can be analyzed with suitable parameters, Viz., relaxation time parameter, Prandtl number, Radiation parameter, Magnetic parameter, and so on. The newness of the current work's novelty is to explain a solution to issues with stretching sheets on the basis of Appell hypergeometric form and also investigation takes place on a time relaxation parameter. The shear stress fηη0 is also calculated analytically. This problem has many industrial applications and engineering processes, namely glass-fiber production, extrusion of rubber sheets and so on. Finding that an increase in the thermal relaxation parameter and Prandtl number keeps the fluid temperature constant is the primary physical application.

Insights into the 3D Slip Dynamics of Jeffrey Fluid Due to a Rotating Disk with Exponential Space-Dependent Heat Generation: A Case Involving a Non-Fourier Heat Flux Model

The dynamics of non-Newtonian Jeffrey fluid in conjunction with a spinning disk surface can be problematic in heating systems, polymer technology, microelectronics, advanced technology, and substantive disciplines. Therefore, the significance of the Hall current and Coriolis forces in terms of the dynamics of Jeffrey fluid flowing across a gyrating disk subject to non-Fourier heat flux was investigated in this study. A temperature-related heat source (TRHS) and exponential-related heat source (ERHS) were incorporated into the model to improve the thermal characteristics. Thermal radiation and multiple slip effects were employed in the flow system. The connected non-linear PDEs governing the transport were transmuted into non-linear ODEs and solved using the Runge–Kutta shooting technique (RKST). The results of the RKST were substantiated in previous studies and found to have adequate reliability. The numerical values of the coefficient of friction and the Nusselt number were simulated. The non-Fourier heat flux was found to have a higher rate of heat transfer (HTR) than with traditional Fourier heat flux. Furthermore, both TRHS and ERHS phenomena support the progression of HTR. The swelling effects of the Hall current influence the velocities, whilst the temperature of the Jeffrey fluid shows the opposite tendency. Furthermore, asymptotic variances were detected for larger Hall parameter values.

Temperature response in skin tissue during hyperthermia based on three-phase-lag bioheat model using RBF meshfree method

Various non-Fourier heat conduction models have been proposed to overcome the paradox of the infinite propagation speed of heat signals in Fourier’s law. The three-phase-lag (TPL) heat model is a non-Fourier model based on the linearized theory of coupled thermoelasticity that combines heat flux, temperature gradient, and thermal displacement gradient. The present paper proposes a novel method with meshfree and spectral nature to solve the two-dimensional three-phase lag (TPL) bioheat model for tissue heating during hyperthermia. In the space domain, radial basis functions (RBFs) and, in the time direction, shifted Chebyshev polynomials are employed to solve the model. The use of Chebyshev polynomials in the time direction enables one to get the solution in the whole time domain simultaneously with fewer nodes. Further, there is no need for background meshes in space due to the meshless nature of RBFs, and the proposed method is equally applicable to irregular domains. The proposed method is validated with the existing semi-analytical solution of the TPL model in one spatial dimension and found to be in good agreement. The temperature profile and the impact of various parameters, such as phase lag times, blood perfusion rate, and heat source parameters on heat transfer in tissue, have also been discussed.

Backpropagated Neural Network Modeling for the Non-Fourier Thermal Analysis of a Moving Plate

The present article mainly focuses on the transient thermal dispersal within a moving plate using the non-Fourier heat flux model. Furthermore, the innovative, sophisticated artificial neural network strategy with the Levenberg-Marquardt backpropagated scheme (ANNS-LMBS) is proposed for determining the transient temperature in the convective-radiative plate. Using dimensionless terms, the energy model for transient heat exchange is simplified into a non-dimensional form. The arising partial differential equation (PDE) is then numerically tackled using the finite difference method (FDM). A data set for the various scenarios of the thermal parameters influencing the thermal variation through the plate has been generated using the FDM. In addition, the effect of the dimensionless physical variables on the thermal profile of a moving plate has been examined and discussed in detail. Increments in the convection-conduction and radiation-conduction parameters are figured to yield a reduction in the transient thermal dispersion. An upsurge in the Peclet number caused the improvement of thermal dispersal in the plate.

Computation of Sakiadis flow of an Eyring-Powell rheological fluid from a moving porous surface with a non-Fourier heat flux model

This article examines theoretically and numerically the effect of non-Fourier heat flux on non-Newtonian (Eyring-Powell) Sakiadis convective flow from a moving permeable surface accompanied by a parallel free-stream velocity, as a simulation of polymeric coating processes. The Cattaneo-Christov model is deployed which features thermal relaxation effects as these are important in thermal polymer processing. The physical flow problem is modeled in a Cartesian coordinate system and the governing conservation differential equations and associated boundary conditions are rendered dimensionless by applying suitable transformations. Liquid velocity and thermal distributions are computed considering numerical procedure namely, a shooting method in conjunction with the 5th order Runge–Kutta algorithm (R-K5) executed in a symbolic software. Validation with the three-stage Lobatto IIIA algorithm in MATLAB is included. The impact of key parameters on streamline distributions is also computed. Velocity is increased with increment in Eyring-Powell first parameter for the Sakiadis case whereas it is reduced with Eyring-Powell second parameter for the case where sheet and liquid are inspiring in the similar direction. The special case of Blasius flow is also examined (stationary sheet). For higher injection, there is a solid dampening in the boundary-layer flow for both Sakiadis and Blasius scenarios.

Thermal shock fracture analysis of auxetic honeycomb layer based on non-Fourier heat conduction

Auxetic honeycomb layer (HL) is a typical metamaterial with a negative Poisson's ratio. In this paper, the thermal shock fracture problem of the auxetic HL is investigated based on non-Fourier heat conduction. The uncracked non-Fourier temperature and thermal stress field are determined by the separation of variables method and the constitutive model of auxetic HL. The corresponding thermal stress intensity factor (TSIF) is obtained in numerical form. Based on the TSIF and the fracture toughness criterion, the critical temperature of auxetic HL is predicted. There is a clear difference between the results based on the non-Fourier and Fourier models. The maximum thermal stress and TSIF of the auxetic HL obtained from the non-Fourier model are both significantly higher than those obtained from the Fourier model. If non-Fourier effects are not taken into account, the critical temperature of the auxetic HL is also overestimated. In addition, the auxetic property can increase the critical temperature of the HL, whether based on the non-Fourier or Fourier model. The results demonstrate the good potential of the auxetic HL in the thermal protection system application.

Temperature and Motion Analysis of a Rotational Maxwell Fluid with non-Constant Thermal Conductivity and non-Fourier Heat Transfer Model, Using Homotopy Perturbation Method

Temperature and Motion Analysis of a Rotational Maxwell Fluid with non-Constant Thermal Conductivity and non-Fourier Heat Transfer Model, Using Homotopy Perturbation Method

Non-Fourier heat transfer in a moving longitudinal radiative-convective dovetail fin

The purpose of this research is to estimate the non-Fourier temperature distribution in dovetail fin. The Cattaneo-Vernotte heat model is utilized to estimate heat conduction behavioral patterns in dovetail fin. In addition, the variation in the temperature profile has been inspected for both non-Fourier and Fourier models. The governing equation involves the linear variance of thermal conductivity, the power-law dependence of the heat transfer coefficient, and the constant surface emissivity. This equation is transmuted by using dimensionless variables, yielding a dimensionless partial differential equation (PDE). To solve the obtained PDE, a numerical technique called the finite difference method (FDM) is employed. The graphical illustration is provided to explain the upshot of thermal parameters on the temperature gradient. The significant findings of this investigation exhibit that as the scale of the convection and radiation variables rises, the thermal response in the fin gradually decreases. Also, the temperature field enhances for Peclet number and ambient temperature parameter. Moreover, the temperature drops from the fin's base to its tip for the Fourier effect. The temperature drops quickly at a point on the fin in comparison to the surrounding value, and this minimal temperature is preserved throughout the rest of the fin.