Nonlinear Heat Transport Research Articles

Pressure-regulated rotational guests in nano-confined spaces suppress heat transport in methane hydrates

Materials with low lattice thermal conductivity are essential for various heat-related applications like thermoelectrics, and usual approaches for achieving this rely on specific crystalline structures. Here, we report a strategy for thermal conductivity reduction and regulation via guest rotational dynamics and their couplings with lattice vibrations. By applying pressure to manipulate rotational states, we find the intensified rotor-lattice couplings of compressed methane hydrate MH-III can trigger strong phonon scatterings and phonon localizations, enabling an almost three-fold suppression of thermal conductivity. Besides, the disorder in methane rotational dynamics results in anharmonic interactions and nonlinear pressure-dependent heat transport. The overall guest rotational dynamics and heat conduction changes can be flexibly regulated by the rotor-lattice coupling strength. We further underscore that this reduction mechanism can be extended to a wide range of systems with different structures. The results demonstrate a potentially universal method for reducing or controlling heat transport by developing a hybrid system with tailored molecular rotors.

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.

Solid state thermal rectification by chemical pressure tuning of magnetic properties in perovskites

From an efficiency framework, waste heat generation and accumulation place significant limitations on how systems ultimately perform. Particularly, heat buildup leads to a significant loss of efficiency and subsequently system failure. In addition, current insulation and heat removal elements for supporting reliability and efficiency are robust and high power consumption systems that are based entirely on linear thermal elements instead of non-linear elements that would allow a unidirectional heat regulation process, thereby avoiding heat accumulation. In this sense, thermal rectifiers have recently attracted considerable interest due to their ability to manage heat unidirectionally. In this work, with the aim of exploring the potential of perovskites in thermal rectification, the magnon mediated thermal transport in the system La0.7Sr0.3Mn1–xCoxO3 (0 < x < 0.1) obtained by the solid-state ceramic route is investigated. Interestingly, results shows that thermal conductivity and Curie temperature substantially decreases with increasing of Co contents, which is attributed to the fact that positive chemical pressure is created due to smaller Co atoms take the place of some of the Mn atoms in the perovskite, shrinking the crystal structure. Taking advantage of those granted features, two-segment thermal diodes based on La0.7Sr0.3Mn1–xCoxO3/SiO2 have been implemented as a proof of concept devices. Experimental thermal transfer characteristics reveal that thermal diodes have markedly a nonlinear heat transport with rectification factors up to 2.3, meaning that devices control the heat flow via the deactivation of magnons through the Curie temperature; which in turn, controls accurately the on state of the device.

Sensitivity analysis of nonlinear convective heat transport of a hybrid nanoliquid sandwiched by micropolar liquid using RSM

Petroleum and polymer industries utilize a multilayer flow model for efficient heat transfer. In such applications, the linear Boussinesq approximation is not recommended as the devices used in such experiments would work at moderate or extremely high temperatures. Therefore, the flow and heat transfer in a multilayer vertical channel with a magnetic field and the nonlinear (quadratic) Boussinesq approximation are investigated, with the central region filled with a hybrid nanoliquid and the outer regions filled with an oil-based micropolar liquid. The effects of Joule heating and viscous dissipation are taken into account. The effective viscosity and thermal conductivity are modeled using the experimental data based Esfe model. The modeled equations are coupled and nonlinear, they are solved using the Differential Transform Method (DTM). Results are analyzed for various values of the material parameter, quadratic convection parameter, Brinkman number, mixed convection parameter, Hartmann number, nanoparticle volume fraction (NVF) on Nusselt number, skin friction, velocity, microrotation velocity and temperature distributions. Additionally, multi-objective optimization of Nusselt number and friction factor is performed for three different levels of the quadratic convection parameter , material parameter and the NVF using the Response Surface Methodology (RSM). The material parameter diminishes the velocity whereas enhances the microrotation velocity. Also, the quadratic convection parameter increases the flow field. Sensitivity computations reveal that the Nusselt number is more sensitive to material parameter and NVF whereas the skin friction coefficient is more sensitive to quadratic convection parameter.

FEM computations and Taguchi optimization in nonlinear radiative MHD MWCNT-MgO/EG hybrid nanoliquid flow and heat transfer over a 3D wedge surface

The problems concerning to heat transport in hybrid nanofluids on a wedge surfaces are of great interest due to their relevance in applications such as solar panels, drying processes, cooling of electronic equipment, heat exchangers, and air heaters. Therefore, the present study explores the nonlinear thermal radiative heat transport features and three-dimensional rheological characteristics of MWCNT-MgO/EG hybrid nanofluid flowing over a wedge considering the variable magnetic field, and multiple slip boundary conditions. The single-phase model comprising of the experimental data with their dependency on temperature and nanoparticle weight fraction is used for thermal conductivity and viscosity of composite nanomaterial. Rosseland and Boussinesq approximations are accounted. The wedge surface is maintained at thermal jump condition, whereas the ambient state is considered at a constant temperature. The governing conservation laws are transformed into a system of ordinary differential equations via space type similarity transformations, and then are solved using the Galerkin finite element method. The L16 orthogonal array-based Taguchi method is applied to determine the optimal setting of governing parameters are determined for maximum heat transport rate. The contribution of physical parameters in the enhancement of heat transport rate is also estimated. The temperature jump condition has the maximum contribution (51.72%), among the selected four physical parameters whereas the nanoparticle weight fraction has the least (10.02%). The nonlinear thermal radiation has the maximum heat transfer rate compared to the linear one.

Economic topology optimization of District Heating Networks using a pipe penalization approach

In the presented study, a pipe penalization approach for the economic topology optimization of District Heating Networks is proposed, drawing inspiration from density-based topology optimization. For District Heating Networks, the upfront investment is a crucial factor for the rollout of this technology. Today, the pipe routing is usually designed relying on a linearization of the underlying heat transport problem. This study proposes to solve the optimal pipe routing problem as a non-linear topology optimization problem, drawing inspiration from density-based topology optimization. The optimization problem is formulated around a non-linear heat transport model and minimizes a detailed net present value representation of the heating network cost. By relaxing the combinatorial problem of pipe placement, this approach remains scalable for large-scale applications. In a design study on a realistic medium-sized network with 160 houses, a strong influence of economic parameters on the optimal network topology was observed. For this case, the optimization algorithm converges to a discrete network topology and near-discrete pipe design in about 10 min by using the proposed intermediate pipe penalization strategy. The optimal discrete network design found by the algorithm showed to outperform simple rounding post-processing steps by up to 2.8% of their respective net present value.

New and Recent Results for Thermoelectric Energy Conversion in Graded Alloys at Nanoscale.

In this article, we review the main features of nonlocal and nonlinear heat transport in nanosystems and analyze some celebrated differential equations which describe this phenomenon. Then, we present a new heat-transport equation arising within the so-called thermomass theory of heat conduction. We illustrate how such a theory can be applied to the analysis of the efficiency of a thermoelectric energy generator constituted by a Silicon–Germanium alloy, as the application and new results for a nanowire of length nm, are presented as well. The thermal conductivity of the nanowire as a function of composition and temperature is determined in light of the experimental data. Additionally, the best-fit curve is obtained. The dependency of the thermoelectric efficiency of the system on both the composition and the difference of temperature applied to its ends is investigated. For the temperatures K, K, and K, we calculate the values of the composition corresponding to the optimal efficiency, as well as the optimal values of the thermal conductivity. Finally, these new results are compared with recent ones obtained for a system of length mm, in order to point out the benefits due to the miniaturization in thermoelectric energy conversion.

Nonlinear Thermal Transport with Inertia in Thin Wires: Thermal Fronts and Steady States

Abstract In a series of papers we have obtained results for nonlinear heat transport when thin wires exchange heat non-linearly with the surroundings, with particular attention to propagating solitons. Here we obtain and discuss new results related to the propagation of nonlinear heat fronts and some conceptual aspects referring to the application of the second principle of thermodynamics to some nonlinear steady states related to non-propagating solitons.

Numerical Investigation on Low-Salinity Augmented Microbial Flooding within a Sandstone Core for Enhanced Oil Recovery under Nonisothermal and pH Gradient Conditions

Summary In an era of increasing energy demand, declining oil fields, and fluctuating crude oil prices globally, most oil companies are looking forward to implementing cost-effective and environmentally sustainable enhanced oil recovery (EOR) techniques such as low salinity waterflooding (LSWF) and microbial EOR (MEOR). The present study numerically investigates the combined influence of simultaneous LSWF and microbial flooding for in-situ MEOR in tertiary mode within a sandstone core under spatiotemporally varying pH and temperature conditions. The developed black oil model consists of five major coupled submodels: nonlinear heat transport model; ion transport coupled with multiple ion exchange (MIE) involving uncomplexed cations and anions; pH variation with salinity and temperature; coupled reactive transport of injected substrates, Pseudomonas putida and produced biosurfactants with microbial maximum specific growth rate varying with temperature, salinity, and pH; relative permeability and fractional flow curve variations owing to interfacial tension (IFT) reduction and wettability alteration (WA) by LSWF and biofilm deposition. The governing equations are solved using finite difference technique. Operator splitting and bisection methods are adopted to solve the MIE-transport model. The present model is found to be numerically stable and agree well with previously published experimental and analytical results. In the proposed MIE-transport mechanism, decreasing injection water (IW) salinity from 2.52 to 0.32 M causes enhanced Ca2+ desorption rendering rock surface toward more water-wet. Consequently, oil relative permeability (kro) increases with &amp;gt;55% reduction in water fractional flow (fw) at water saturation of 0.5 from the initial oil-wet condition. Further reducing IW salinity to 0.03 M causes Ca2+ adsorption shifting the surface wettability toward more oil-wet, thus increasing fw by 52%. Formation water (FW) salinity showed minor impact on WA with &amp;lt;5% decrease in fw when FW salinity is reduced from 3.15 to 1.05 M. During low-salinity augmented microbial flooding (LSAMF), biosurfactant production is enhanced by &amp;gt;63% on reducing IW salinity from 2.52 to 0.32 M with negligible increase on further reducing IW and FW salinities. This might be owing to limiting nonisothermal condition (40 to 55°C), dispersion, sorption, and microbial decay. During LSAMF, maximum biosurfactant production occurs at microbial maximum specific growth rate of 0.53 h-1, mean fluid velocity of 2.63×10-3 m h-1 and initial oil saturation of 0.6, thus resulting in significant WA, increase in kro by &amp;gt;20%, and corresponding fw reduction by &amp;gt;84%. Moreover, the EOR efficiency of LSAMF is marginally impacted even on increasing the minimum attainable IFT by two orders of magnitude from 10-3 to 10-1 mN m-1. Though pH increased from 8.0 to 8.9, it showed minor impact on microbial metabolism. Formation damage owing to bioplugging observed near injection point causing increase in fw by ~26% can be mitigated by adopting suitable well-stimulation strategies during the LSAMF run time. The present study is a novel attempt to show synergistic effect of LSAMF over LSWF in enhancing oil mobility and recovery at core scale by simultaneously addressing complex crude oil-brine-rock (COBR) chemistry and critical thermodynamic parameters that govern MEOR efficiency within a typical sandstone formation. The present model with relatively lower computational cost and running time improves the predictive capability to preselect potential field candidates for successful LSAMF implementation.

Non-Linear Heat Transport Effects in Systems with Defects

Abstract In this paper we explore several aspects of the influence of fixed and of mobile defects on the thermal conductivity of materials. In particular, we investigate the effects of the temperature and defect concentration dependence of the conductivity on phononic diodes and transistors and on the non-linear thermal conductivity dependent on the heat flux in thermal superlattices.

Two relaxation times and thermal nonlinear waves along wires with lateral heat exchange

We propose a model for studying several nonlinear waves for heat transport along a cylindrical system with lateral non-linear heat transfer to the environment. We consider relaxational equations, each with its own relaxation time, for longitudinal heat transfer and for lateral heat transfer across the wall. We consider two kinds of nonlinear lateral heat transport: radiative heat transport, and flux-limited heat transport. This work generalizes our previous studies in which the relaxation time for the lateral heat transfer was considered equal to that of the longitudinal heat flux. We explore the influence of both relaxation times on the propagation speed of linear and nonlinear waves, and on the form of nonlinear waves.

Peltier effect: From linear to nonlinear

Thermoelectric refrigeration technology is an environment-friendly refrigeration technology with broad application prospects. The Peltier effect plays a central role in the thermoelectric refrigeration process, however, the Peltier coefficient is difficult to measure. So in the actual application process, first, the Seebeck coefficient is usually obtained, and then the Peltier coefficient is achieved by the Kelvin's second relation indirectly. It should be noted that the Kelvin's second relation is obtained under linear conditions (Ohm's law, Fourier's law, etc.), while in practice, nonlinear current-voltage relationships (Schottky junction, pn junction, etc.) and nonlinear heat transport relations are common. And quantum effect plays a leading role in the nano-scaled region, then the Peltier effect must consider the influence of nonlinearity, and the applicability of the Kelvin's second relation must also be reconsidered. This paper first summarizes the theoretical derivation of Peltier coefficient and the Kelvin’s second relation by different methods, then discusses the hypothetical conditions used in the derivation process, and points out that the Kelvin’s second relation can be established only under the hypothetical linear conditions. Then, several experimental methods of determining the Peltier coefficient are summarized. It is found that there are still many problems encountered in the measurement of Peltier coefficient, and the Kelvin’s second relation has not been proved accurately by practical experiments. Various side effects (Fourier effect, Thomson effect, Joule effect and Seebeck effect) in the measurement process affect the temperature distribution of the system directly or indirectly, making it difficult to measure Peltier heat. After that, the theoretical work of nonlinear Peltier effect is briefly introduced. In the process of thermal transport and electrical transport on a microscopic scale, quantum effect plays a leading role, and the nonlinear part of the Peltier coefficient gradually emerges. These studies show the cognition of researchers that the Peltier effect gradually changes from linear to nonlinear. The nonlinear Peltier effect not only exists objectively, but also is very important in the practical applications. However, the current research on the nonlinear Peltier effect is still at the theoretical level, and there is almost no experimental work. Finally, we discuss the research strategy and feasible research direction of Peltier effect under nonlinear conditions. An integrated study of the relationship among various heterojunction band structures, interface properties and interface effects is helpful in comprehensively understanding the Peltier effect. With the continuous improvement of experimental conditions and theoretical research, the study of nonlinear Peltier effect is expected to realize a new breakthrough.

Radiative Thermostat Driven by the Combined Dynamics of Electrons, Phonons, and Photons

Based on the metal-insulator transition of two phase-change materials (PCMs) with asymmetric thermal conductivities and emissivities sensitive to temperature, a radiative thermostat capable of maintaining a constant temperature without consuming energy is proposed. This is done by deriving explicit expressions for the heat flux and temperature profiles of the thermostat surrounded by these PCMs, and demonstrating that the thermostat can be maintained at a temperature nearly equal to the common transition temperature of both PCMs as the environmental temperature changes by more than 20 K. I show that the combined operation of two PCMs is much better than two non-PCMs to develop energy-free thermostats, especially those supporting poor thermal conduction or dominant heat radiation. The obtained results thus establish a fundamental theoretical method that exploits the nonlinear heat transport driven by electrons, phonons, and photons to maximize temperature preservation and thermal insulation.

An adjoint optimization approach for the topological design of large-scale district heating networks based on nonlinear models

This article deals with the problem of finding the best topology, pipe diameter choices, and operation parameters for realistic district heating networks. Present design tools that employ non-linear flow and heat transport models for topological design are limited to small heating networks with up to 20 potential consumers. We introduce an alternative adjoint-based numerical optimization strategy to enable large-scale nonlinear thermal network optimization. In order to avoid a strong computational cost scaling with the network size, we aggregate consumer constraints with a constraint aggregation strategy. Moreover, to align this continuous optimization strategy with the discrete nature of topology optimization and pipe size choices, we present a numerical continuation strategy that gradually forces the design variables towards discrete design choices. As such, optimal network topology and pipe sizes are determined simultaneously. Finally, we demonstrate the scalability of the algorithm by designing a fictitious district heating network with 160 consumers. As a proof-of-concept, the network is optimized for minimal investment cost and pumping power, while keeping the heat supplied to the consumers within a thermal comfort range of 5%. Starting from a uniform distribution of 15 cm wide piping throughout the network, the novel algorithm finds a network lay-out that reduces piping investment by 23% and pump-related costs by a factor of 14 in less than an hour on a standard laptop. Moreover, the importance of embedding the non-linear transport model is clear from a temperature-induced variation in the consumer flow rates of 72%.

Entropy generation minimization and nonlinear heat transport in MHD flow of a couple stress nanofluid through an inclined permeable channel with a porous medium, thermal radiation and slip

AbstractIrreversible losses and heat transport in a magnetohydrodynamic flow of a viscous, steady, incompressible, and fully developed couple stress Al2O3–water nanofluid through a sloping permeable wall channel with porous medium and under the effect of radiation heat flux and slip were analyzed. The fundamental equations were solved numerically by using Runge‐Kutta together with the shooting technique and the results were in qualitative agreement with an exact solution obtained for a limit case. The impacts of couple stress, Darcy number, solid nanoparticle concentrations, conduction‐radiation parameter, Hartmann number and hydrodynamic slip on flow, temperature, heat transport, and entropy production were examined. It was possible to achieve values of minimum entropy production not yet reported in previous studies. In this way, optimal values of couple stress and slip were obtained. The heat transport was also explored and optimal values of slip flow and conduction‐radiation parameter with maximum heat transfer were found. Finally, in addition to the alumina, the distributions of velocity, temperature, and entropy generation in TiO2–water and Cu–water were presented for different solid nanoparticle concentrations. It was obtained that the local entropy of TiO2–water was lower than Cu–water and Al2O3–water in the channel bottom region while it was greater in the upper region.

Transient MHD flow of Maxwell nanofluid subject to non-linear thermal radiation and convective heat transport

The aim of present study is to explore the heat and mass transfer properties in 2D transient flow of Maxwell nanofluid under the influence of magnetic field induced by stretching cylinder. The effects of heat sink/source, convective heat transport at surface and non-linear thermal radiation are contemplated for the analysis of heat transport mechanism in the flow of nanoliquid. Additionally, the aspect of chemical reaction is also reported in the solutal energy transport. The haphazard motion of nanoparticles and thermophoresis effect are studied using well-known Buongiorno theory for nanofluid. In the view of suitable transformations, the governing partial differential equations (PDEs) are transformed into non-linear ordinary differential equations (ODEs). Homotopic approach has been used to compute the series solutions of non-linear differential system. The acquired results are portrayed graphically for pertinent parameters and discussed with physical justification. It is found that the velocity, temperature and concentration fields boost up for higher value of magnetic parameter. The large value of unsteadiness parameter boosts up the both thermal and solutal energy transport in nanoliquid. Moreover, the increase in Brownian motion parameter enhances the temperature field but declines concentration fields. For the confirmation of these results, comparison tables are structured for different parameters.

Nonlinear Heat Transport in Superlattices with Mobile Defects

We consider heat conduction in a superlattice with mobile defects, which reduce the thermal conductivity of the material. If the defects may be dragged by the heat flux, and if they are stopped at the interfaces of the superlattice, it is seen that the effective thermal resistance of the layers will depend on the heat flux. Thus, the concentration dependence of the transport coefficients plus the mobility of the defects lead to a strongly nonlinear behavior of heat transport, which may be used in some cases as a basis for thermal transistors.

Thermal Transport through Single-Molecule Junctions.

Molecular junctions exhibit a rich and tunable set of thermal transport phenomena. However, the predicted high thermoelectric efficiencies, phonon quantum interference effects, rectification, and nonlinear heat transport properties of organic molecules are yet to be verified because suitable experimental techniques have been missing. Here, by combining the break junction technique with suspended heat-flux sensors with picowatt per Kelvin sensitivity, we measured the thermal and electrical conductance of single organic molecules at room temperature simultaneously. We used this method to study the thermal transport properties of two model systems, namely, dithiol-oligo(phenylene ethynylene) and octane dithiol junctions with gold electrodes. In agreement with our density functional theory and phase-coherent transport calculations, we show that heat transport across these systems is governed by the phonon mismatch between the molecules and the metallic electrodes. This work represents the first measurement of thermal transport through single molecules and opens new opportunities for studying heat management at the nanoscale level.

Role of magnons and the size effect in heat transport through an insulating ferromagnet/insulator interface

While recent experiments on the spin Seebeck effect have revealed the decisive role of the magnon contribution to the heat current $Q$ in hybrid systems containing thin ferromagnetic layers, the available acoustic mismatch theory does not account for their magnetic properties. Here, we analyze theoretically the heat transfer through an insulating ferromagnet (F) sandwiched between two insulators (I). Depending on the relation between the F thickness, $d$, and the mean free path of phonons generated by magnons, $l_{ls}$, we reveal two qualitatively different regimes in the nonlinear heat transport through the F/I interfaces. Namely, in thick F layers the regime of conventional "Joule" heating with $Q \propto T_s^4$ is realized, in which the detailed structure of the F/I interfaces is inessential. Here $T_s$ is the magnon temperature. By contrast, in thin F layers with $d\ll l_{ls}$, most of phonons emitted by magnons can leave F without being absorbed in its interior, giving rise to the \emph{magnon overheating} regime with $Q \propto T_s^m$ and $m\gtrsim7$. Conditions for the examination of both regimes and the determination of $T_s$ from experiments are discussed. The reported results are relevant for the theoretical analysis of the spin Seebeck effect and the development of magnon-based spin caloritronic devices.

Experimental and theoretical study of density fluctuations near the stack ends of a thermoacoustic prime mover

This paper proposes the experimental and theoretical study of nonlinear heat transport processes generated by large amplitude acoustic oscillations at the ends of a stack of plates in the presence of a temperature gradient. These processes are notably involved in the operation of thermoacoustic engines. The measurement method, a time-resolved and full-field digital holography interferometry technique, enables to measure the density fluctuations from the optical phase difference between two laser beams. This technique is applied to the analysis of density fluctuations in the vicinity of a stack submitted to a temperature gradient, firstly for the case of (uncontrolled) self-sustained acoustic oscillations generated spontaneously in a standing wave thermoacoustic prime mover, and secondly for the case of an assigned acoustic field whose amplitude is controlled by an external sound source. A theoretical model describing the advective heat transport by sound at the ends of the heated stack is also presented, and numerical simulations are then carried out. The comparison between experimental data and numerical simulations is provided for several stack positions, several sound pressure levels, and several amounts of heat supplied to the stack, and the results show good agreement between the experiments and the model.