Time-dependent Thermal Conductivity Research Articles

Bioconvective flow of a variable properties hybrid nanofluid over a spinning disk with Arrhenius activation energy, Soret and Dufour impacts

This paper explores the heat and mass transfer by hybrid nanofluids flow over a spinning disk in the presence of oxytactic microorganisms. During this study, the Soret and Dufour together with Lorentz force impacts are considered. The worked nano-mixture is assumed to be having time-dependent dynamic viscosity and thermal conductivity and its components are methanol-based hybrid nanofluid comprising CuO and MgO nanoparticles. The disk surface is permeable and various aspects such as thermal radiation, heat generation and Arrhenius activation energy are taken into account. The governing equations are treated numerically and suitable similar transformations are introduced. The obtained results revealed that both of the velocity and temperature gradients are enhanced as the absolute values of unsteadiness parameter and nanoparticles concentrations are rising. However, the flow is slowdown as the temperature-dependent variable viscosity parameter is growing.

Influence of thermal conductivity on transient mixed convection in a vented cavity with a hollow cylinder and filled with CNT-water nanofluid

This study is aimed to perform a numerical time-dependent investigation thermal conductivity effect of the annular cylinder within a vented cavity using CNT based-water nanofluid. For demonstrating the effect of thermal conductivity, four distinct hollow cylinder materials such as Ks = 0.5(Plastic tiles), Ks = 0.84(Clay tiles), Ks = 1.1(Concrete tiles), and Ks = 2(Slate tiles) are introduced together with a suitable variation of dimensionless time (0 ≤ τ ≤ 1). The governing equations of the model with associated boundary conditions is solved using finite element based Galerkin's weighted residual method. Different contour plots for thermal and flow field transformation and mean Nusselt number, mean fluid temperature, bulk convective field temperature, temperature gradient, pressure gradient, vortices, and fluid velocity magnitude are presented for qualitative and quantitative thermal performance analysis. With the decrease of solid thermal conductivity, 27.3% thermal transport enhancement is noted from the heated surface of the cylinder. However, a 16.3% increase in the bulk fluid temperature has been recorded with the increase in cylinder conductivity. The numerical outcomes from this investigation propose a better thermo-fluid efficiency compared to the existing methodology which can be suggestive to engineers and researchers for designing heat exchangers, heat pipes, and other thermal systems.

An inverse boundary value problem for isotropic nonautonomous heat flows

We study an inverse boundary value problem on the determination of principal order coefficients in isotropic nonautonomous heat flows stated as follows; given a medium, and in the absence of heat sources and sinks, can the time-dependent thermal conductivity and volumetric heat capacity of the medium be uniquely determined from the Cauchy data of temperature and heat flux measurements on its boundary? We prove uniqueness in all dimensions under an assumption on the thermal diffusivity of the medium, which is defined as the ratio of the thermal conductivity and volumetric heat capacity. Our assumption on the thermal diffusivity is related to construction of certain families of exponential solutions to the heat equation.

Fractional analysis of Jeffrey fluid over a vertical plate with time-dependent conductivity and diffusivity: A low-cost spectral approach

The development of a new method to solve nonlinear models and compatible with increasing the efficiency and optimizing the results with high accuracy is difficult. Herein, we developed two novel algorithms: linearized spectral method (LSM) and semi-discrete method (SDM). We successfully applied them to investigate the fractional-order MHD Jeffery fluid model's solution over a vertically moving surface with constant heat flux. The model consists of a nonlinear coupled differential equation, which is solved with proposed techniques. To attain the influence of emerging parameters on velocity and temperature distributions, emerging parameters, namely: nonlinear thermal radiation, time-dependent thermal conductivity and diffusivity, are variates for numerical values. Viable dimensionless variables are used to nondimensionalized the governing problem. Linearized spectral scheme based on function approximation and operational-matrices of fractional and integer order derivatives using shifted Gegenbauer polynomials (SGPs). Picard-iterative method is adopted to linearize the governing set of equations. The time-based derivative is estimated utilizing a forward difference scheme while spatial derivatives are evaluated with operational matrices' help to present the semi-discrete method. The significant part of the proposed method is to convert the highly nonlinear problems into a set of linear equations that surely help to deal efficiently. Nusselt number exhibits a direct relation with temperature ratio and heat absorption parameters. Numerical justification provided of the proposed algorithms through convergence and error bound. Furthermore, the established algorithms can inspect the accurate solution of more fractional problems which is highly nonlinear of physical nature.

Heat-current filtering for Green–Kubo and Helfand-moment molecular dynamics predictions of thermal conductivity: Application to the organic crystal [formula omitted]-HMX

The closely related Green–Kubo and Helfand moment approaches are applied to obtain the thermal conductivity tensor of β-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (β-HMX) at T=300 K and P=1 atm from equilibrium molecular dynamics (MD) simulations. Direct application of the Green–Kubo formula exhibits slow convergence of the integrated thermal conductivity values even for long (120 ns) simulation times. To partially mitigate this slow convergence we developed a numerical procedure that involves filtering of the MD-calculated heat current. The filtering is accomplished by physically justified removal of the heat-current component which is given by a linear function of atomic velocities. A double-exponential function is fitted to the integrated time-dependent thermal conductivity, calculated using the filtered current, to obtain the asymptotic values for the thermal conductivity. In the Helfand moment approach the thermal conductivity is obtained from the rates of change of the averaged squared Helfand moments. Both methods are applied to periodic β-HMX supercells of four different sizes and estimates for the thermal conductivity of the infinitely large crystal are obtained using Matthiessen’s rule. Both approaches yield similar although not identical thermal conductivity values. These predictions are compared to experimental and other theoretically determined values for the thermal conductivity of β-HMX.

Fractional Analysis of Dissipative Viscous Fluid Flow with Mixed Convection and Variable Viscosity

Time‐dependent viscosity and thermal conductivity have been studied in relation to flow and thermal energy propagation along a vertical turning cone. Except the density variance, the other fluid’s properties are assumed to be constant. Using the similarities procedure, the nonlinear system of differential equations is simplified to dimensionless ODEs. The resultant nonlinear ODEs system is computed while using fractional code FDE12, and the findings are quantitatively examined using the bvp4c approach for accuracy and consistency. In form of figures and tables, the behavior of momentum, energy, and mass is interpreted versus the physical constraints. The axial and radial velocity, both declines with the variation of unsteadiness parameter S. The axial velocity of the fluid is considerably increased when the mixed convection parameter is elevated, but the radial velocity is reduced. Similarly, when the variable viscosity increases, the velocity profile develops.

Simultaneous Identification of Thermal Conductivity and Heat Source in the Heat Equation

This paper presents a numerical solution to the inverse problem consisting of recovering time-dependent thermal conductivity and heat source coefficients in the one-dimensional parabolic heat equation. This mathematical formulation ensures that the inverse problem has a unique solution. However, the problem is still ill-posed since small errors in the input data lead to a drastic amount of errors in the output coefficients. The finite difference method with the Crank-Nicolson scheme is adopted as a direct solver of the problem in a fixed domain. The inverse problem is solved subjected to both exact and noisy measurements by using the MATLAB optimization toolbox routine lsqnonlin , which is also applied to minimize the nonlinear Tikhonov regularization functional. The thermal conductivity and heat source coefficients are reconstructed using heat flux measurements. The root mean squares error is used to assess the accuracy of the approximate solutions of the problem. A couple of numerical examples are presented to verify the accuracy and stability of the solutions.

Simultaneous reconstruction of thermal boundary condition and physical properties of participating medium

A hybrid optimization technique, which combines decentralized fuzzy inference method (DFIM) and sequential quadratic programming (SQP) algorithm, is developed to reconstruct the thermal boundary condition and physical properties of participating medium simultaneously. The coupled radiation-conduction heat transfer in the medium is solved by finite volume method in combination with discrete ordinate method. The reconstruction task is formulated as an inverse problem which is solved by the hybrid DFIM-SQP technique from the knowledge of surface temperature and exit radiative intensity. Retrieval results demonstrate that the time-dependent heat flux, absorption coefficient, scattering coefficient and thermal conductivity of participating medium can be accurately retrieved by the present methodology. The proposed DFIM-SQP technique is more accurate and efficient in solving the simultaneous reconstruction problem than DFIM, conjugate gradient method, SQP, particle swarm optimization and krill herd algorithms.

Reconstructing the Time-Dependent Thermal Coefficient in 2D Free Boundary Problems

The inverse problem of reconstructing the time-dependent thermal conductivity and free boundary coefficients along with the temperature in a two-dimensional parabolic equation with initial and boundary conditions and additional measurements is, for the first time, numerically investigated. This inverse problem appears extensively in the modelling of various phenomena in engineering and physics. For instance, steel annealing, vacuum-arc welding, fusion welding, continuous casting, metallurgy, aircraft, oil and gas production during drilling and operation of wells. From literature we already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, we apply the alternating direction explicit method along with the Tikhonov regularization to find a stable and accurate numerical solution of finite differences. The root mean square error (rmse) values for various noise levels p for both smooth and non-smooth continuous time-dependent coefficients Examples are compared. The resulting nonlinear minimization problem is solved numerically using the MATLAB subroutine lsqnonlin. Both exact and numerically simulated noisy input data are inverted. Numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.

Thermo diffusion aspects in Jeffrey nanofluid over periodically moving surface with time dependent thermal conductivity

Double diffusion flow of Jeffrey fluid in presence of nanoparticles is studied theoretically under time dependent thermal conductivity. The considered nanoparticles are evaporated over convectively heated surface which moves periodically in its own plane. The appropriate dimensionless variables are employed to obtain the dimensionless forms of governing equations. We computed the analytical solution of non-linear differential equations by utilizing homotopy analysis method. The present investigation reveals the features of various emerging parameters like Deborah number, combined parameter, oscillation frequency to stretching rate ratio, Prandtl number, Lewis number, thermophoresis parameter, Brownian motion parameter, nano Lewis number, modified Dufour parameter, and Dufour solutal Lewis number. A useful enhancement in movement of nanoparticles is observed by utilizing the combined magnetic and porosity effects. Unlike traditional studies, present analysis is confined with the unsteady transportation phenomenon from periodically moving surfaces. Such computation may be attributable in flow results from tensional vibrations due to stretching and elastic surfaces. The simulation presented here can be attractable significance in the bioengineered nanoparticles manufacturing. It is observed that the heat transportation of nanoparticles may efficiently enhance through the utilization of variable thermal conductivity. The solutal concentration decreases with increasing Deborah number and Lewis number. It is further noted that the nano Lewis number causes reduction of nanoparticles concentration.

Heat Transfer of Semicrystalline Nylon Nanofibers.

Polymers are generally regarded as thermal insulators. The efficient heat transfer observed in the low-dimensional polymers in the literature mainly result from the larger crystallinity or improved polymer chain orientation in the low-dimensional polymers. However, the role of the amorphous domain on heat transfer in polymers remains unexplored. In this work, we report that the semicrystalline nylon polymer nanofibers can exhibit a very large thermal conductivity of 59.1 ± 3.1 W m-1 K-1 and the heat transfer in the semicrystalline polymer nanofibers was time-dependent. The thermal conductivity of the nanofibers could be modulated to span 3 orders of magnitude from being nearly insulated (∼0.27 ± 0.02 W m-1 K-1) to being highly thermal conductive after annealing (∼59.1 ± 3.1 W m-1 K-1). The time-dependent thermal conductivity was observed at a temperature lower than the gamma transition temperature of the polymer and was a result of the physical aging of the semicrystalline polymer. A phenomenological model was adopted to explain the time-dependent heat transfer of the semicrystalline nanofibers. The physical aging reduced the configuration disorder in the polymer and caused the heat transfer of the semicrystalline polymer to increase during the annealing process.

A superstatistical model for anomalous heat conduction and diffusion

We propose a superstatistical model for anomalous heat conduction and diffusion, which is formulated by the thermal conductivity distribution, overall temperature and heat flux distributions. Our model obeys Fourier's law and the continuity equation at the individual level. The evolution of the thermal conductivity distribution is described by an advection-diffusion equation. We show that the superstatistical model predict anomalous behaviors including the time-dependent effective thermal conductivity and slow long-time asymptotics. The time-dependence of the effective thermal conductivity is determined by the mean square displacement (MSD), which coincides with existing investigations. The superstatistical structure can also be extended into other non-Fourier models including the Cattaneo and fractional-order heat conduction models.

Recovery of temporal coefficient for heat equation from non-local overdetermination conditions

Recovery of time-dependent thermal conductivity has been numerically investigated. The problem of identification in one-dimensional heat equation from Cauchy boundary data and mass/energy specification has been considered. The inverse problem recasted as a nonlinear optimization problem. The regularized least-squares functional is minimised through lsqnonlin routine from MATLAB to retrieve the unknown coefficient. We investigate the stability and accuracy for numerical solution for two examples with various noise level and regularization parameter.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

Cu-Al2O3/Water hybrid nanofluid through a permeable surface in the presence of nonlinear radiation and variable thermal conductivity via LSM

This paper scrutinizes the significant effects of nonlinear thermal radiation and time-dependent thermal conductivity due to rotating flow of Cu-Al2O3-water hybrid nanofluid over a three-dimension stretching sheet. The influence of bouncy forces and magnetic field are also considered. The obtained set of partial differential equations (PDEs) converted to a simplified set of ordinary differential equations (ODEs) by introducing the feasible similarity transformation. Least square method (LSM) is adopted to examine the solution of developed model. The obtained solutions are compared with the well-known numerical technique: Runge-Kutta method of order fourth (RK-4). Significant influence of various physical parameters on the velocities and temperature are explained in detailed through graphical representations. Behavior of skin friction coefficient and local Nusselt number due the variation of numerous parameters also discussed in detail. The velocity profiles F′(η) and G′(η) for the case of Cu-Al2O3-water are dominant as compare to Cu-water and Al2O3-water while the fluid temperature is dropped for Cu-Al2O3-water case as compare to Cu-water and Al2O3-water. It is noticed that, variation in the Hartmann, porosity and suction/injection parameters cause to increase the friction at the surface. Opposite behavior of skin friction coefficient is observed by increasing the strength of rotational, Grashof number and slip parameter. Obtained results and comparative study witnesses that the least square technique is well-matched with existing results and it can be applied for complex nature models.

TC Study of Manufacturable Nano Grease: Evidence of 3D Network Structure

Surfactant-free grease made from carbon nanotube and carbon nanofibers has shown improvement in thermal conductivity. Time-dependent thermal conductivity (TC) magnetic study with different (Fe2O3 concentrations and Ni-coated carbon nanotubes) was performed. The results show that under the influence of a strong magnetic field, the TC value remains constant even with different processing times, magnetic fields, and Fe2O3 concentrations. An explanation for these results could be that for a high loading of CNTs (> 10 wt%), CNTs become associated strongly with each other by van der Waals forces and form a three-dimensional network (3D), which makes magnetic alignment of nanotubes very unlikely. A slight change on the TC of carbon nanofibers grease was noticed, which is probably because of the weak Van der Waals forces among the nanofibers. Mixing the CNFs with SWNTs produced a stable grease as SWNTs help to create the 3D network structure; however, the TC has dropped to 0.37 W/mK which is attributed to the lower TC of the SWNTs grease itself. The scientific merit of this paper is that the results provide further support that the CNTs form a 3D network structure and move forward the R&D work of manufacturable carbon nano grease.

A Stefan problem with temperature and time dependent thermal conductivity

In this paper, a one phase Stefan problem with time and temperature dependent thermal conductivity is investigated. With the help of similarity transformation and tau method based on shifted Chebyshev operational matrix of differentiation, an approximate solution of the problem is discussed. For a particular case, an exact solution of the proposed problem is also discussed and it is used to check the accuracy of the obtained approximate results. The effect of some parameters involved in the model on temperature distribution and movement of phase front is also analysed.

Dynamic analysis of material ejection from cathodic metal nano-tips due to local heating and field generated stress

The potential for explosive cathode emission due to nanoprotrusions subjected to Maxwell stress and heating from strong electric fields is probed self-consistently based on non-equilibrium molecular-dynamics. The focus is on determining the electric field magnitudes that could lead to material ejection, assessing dependencies of the instability on the nanoprotrusion height and cross-sectional area, and the role of time-dependent thermal conductivity and local temperature changes. Our results indicate that large aspect ratios would facilitate mass ejection, with protrusion break up occurring over times in the 25 ns range, in agreement with experimental reports on explosive emission.

Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations

The problem of identifying the time-dependent thermal conductivity coefficient in the initial–boundary-value problem for the quasi-stationary two-dimensional heat conduction equation in a bounded cylinder is considered. It is assumed that the temperature field in the cylinder is independent of the angular coordinate. To solve the given problem, which is related to a class of inverse problems, a mathematical approach based on the method of conjugate gradients in a functional form is being developed.

Implementation of the equivalent-homogeneous-layers-set method in whole-building simulations: Experimental validation

This work presents the experimental validation of the equivalent-homogeneous-layers-set method (EHLS) implemented in EnergyPlus, a whole-building energy simulation program. The EHLS method generates a constructive system that is thermally equivalent, under time-dependent heat transfer, to a wall/roof constructive system that has air-cavities inside. The equivalent constructive system is a set of homogeneous layers, some of them with time-dependent equivalent thermal conductivity. The EHLS method takes into account the heat transfer through the constructive system by two-dimensional conduction, natural convection inside the air-cavities and radiation between the air-cavity surfaces. To validate the EHLS method implemented in EnergyPlus, a whole year of experimental results were taken from a non-air-conditioned test-hut constructed with concrete hollow-block walls and the roof comprised of concrete hollow-blocks and T-beams. The numerical results show a good agreement with the experimental ones. The differences between EnergyPlus simulation results and experimental results are of the same order of magnitude as the differences between EnergyPlus simulation and experimental results from two adjacent test-huts made of homogenous constructive systems over the same time-period and reported previously.