Abstract. Considering the explosive proliferation of small electronic devices, effective heat management now ceases to be an optional feature but a serious design requisite. Power electronic modules, IoT platforms, and modern embedded devices often operate continuously under severe heat stress, with limited airflow and physical space. These is difficult for conventional air-cooling methods to achieve which leads to decreased performance, thermal instability, and long-term reliability problems. This work describes a hybrid adaptive cooling system using a Peltier module for thermoelectric cooling, liquid-based heat extraction, and a proprietary coolant scientifically designed and managed by sophisticated PID and PWM algorithms. The system integrates relay-based fail-safe protection, optocoupler-isolated power electronics, and Bluetooth-enabled real-time telemetry for safe and dependable operation. In parallel, a novel Internet of Things (IoT)-based thermal conductivity testing device was developed to evaluate various distilled water–ethylene glycol (DW–EG) coolant combinations scientifically using Fourier's heat conduction concept. A 70:30 DW–EG mixture provides the optimal balance of thermal conductivity, viscosity, chemical stability, electrical safety, and pump efficiency, according to experimental results. This proposed system represents an advancement of the conventional concept of cooling. The new one offers tighter temperature control, more stability, and fewer operational costs, which make it perfect for compact embedded electronics. Keywords Thermoelectric Cooling, Peltier Module, .Liquid Cooling, PID Control, PWM Control, Thermal Conductivity, Proprietary Coolant, .Embedded Systems & IoT Measurement

A Dual-Branch Boiler Water-Cooled Wall Three-Dimensional Combustion Parameter Prediction Method Based on Multi-Head Latent Attention Mechanism and Fourier's Heat Flux Density Law (M-F Dual NET)

Thermomagnetic Convective Flow of Micropolar Fluid via Extendable Surface With Variable Viscosity Feature and Modified Fourier's Heat Flux Modeling

Establishment and analysis of a piezoelectric actuator dynamic model with temperature-dependent damping, stiffness, and piezoelectric constant

Topology optimization for near-junction thermal spreading of electronics in ballistic-diffusive regime

Molecular dynamic simulations of the heat transfer in double-layered graphene/silicene nanosheets

Thermoelectric hotspot cooling using thermally conductive fillers

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a flexible structure with Fourier's type heat conduction and distributed delay. We prove the wellposedness by using the semigroup theory. Also we establish a decay result by introducing a suitable Lyaponov functional.

The purpose of this investigation is to develop a novel mathematical model for the stagnation point flow of Reiner-Philippoff fluid across an extensible surface, which is accompanied by Cattaneo-Christov double diffusion, thermal radiation, variable molecular diffusivity, and mixed convection. The partial differential expressions governing the flow issues are translated into nonlinear ordinary differential equations via appropriate similarity variables and then numerically treated using the bvp4c MATLAB built-in technique. Tables and graphs are employed to probed the influence of diverse factors on heat and mass transference rates, as well as the density profile of microorganisms. It is revealed that increasing the thermal relaxation time and the concentration relaxation time depreciates the heat transfer and mass transfer processes and that increasing the Peclet quantity and the microbiological concentricity change factor decreases the motile density outline. The current study is original and topical in the sense that the impact of Fourier's heat, as well as mass flux, stagnation point and microorganisms for the case of Reiner-Philippoff fluid, are not interrogated before.

Cattaneo-Christov (C–C) heat flux in Darcy-Forchheimer (D-F) flow of fourth-grade nanomaterial with convective heat and mass conditions

A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo–Christov model is presented in this study. The influence of high-order velocity slip flow, as well as a passive and active control, is also considered. The motive of the research is to develop a computational model, using cobalt ferrite (CoFe2O4) and copper (Cu) nanoparticles (NPs) in the carrier fluid water, to magnify the energy and mass communication rate and boost the efficiency and performance of thermal energy conduction for a variety of commercial and biological purposes. The proposed model becomes more significant, with an additional effect of non-Fick's mass flux and Fourier's heat model to report the energy and mass passage rate. The results are obtained through the computational strategy parametric continuation method. The figures are plotted to reveal the physical sketch of the obtained solution, while the statistical assessment has been evaluated through tables. It has been observed that the dispersion of Cu and CoFe2O4 NPs to the base fluid significantly enhances the velocity and thermal conductivity of water, which is the most remarkable property of these NPs from the industrial point of view.

Nowadays, geothermal resources have become one of the important means for mankind to solve global energy problems and environmental problems, and the exploration and development of geothermal resources are of great significance for sustainable development. However, in view of the complex geological background of the plateau region, the number of heat flow measurement points in this area is small or even blank, thus becoming an important factor limiting the exploration of geothermal resources in this region. In this article, a new model based on Fourier analysis and heat conduction principle is established to process and analyze the long-term monitoring data of soil temperature and eliminate the influence of temperature change on soil temperature as far as possible, so as to improve the calculation accuracy of soil conduction heat dissipation. The experimental results show that the fluctuation range of soil temperature at 20 cm before the correction was large, and the fluctuation range was 2.58°C–14.284°C, which was because the soil here was closer to the land surface and was affected too much by the temperature fluctuation, and as the soil depth deepened, the temperature fluctuation slowly became smaller, and the fluctuation range was 6.67°C–11.15°C at 50 cm, but the effect of temperature fluctuation was still obvious. Also, the fluctuation range was basically reduced within 0.3°C after temperature correction. In this method, the thermal diffusion coefficients of the soil at different depths can be obtained, and the calculated temperatures at the corresponding depths can also be obtained, which can be used to infer the approximate ground temperature gradient of the measured area. This study aims to develop a convenient and fast model for processing soil temperature time series and to provide technical support for developing geothermal resources in highland areas or assessing the geothermal potential of the region.

Currently, when solving problems of heat and mass transfer, linear constitutive equations are used - in hydrodynamics, the viscous stress tensor is proportional to the strain rate tensor (Newton's rheological ratio), in heat transfer, the heat flux density is linearly related to the temperature gradient (Fourier's heat conduction law), in mass transfer, the diffusion flux density proportional to the concentration gradient (Fick's law). When writing these linear governing equations, proportionality coefficients are used, which are called the viscosity coefficient, thermal conductivity coefficient and diffusion coefficient, respectively. Such constitutive equations are widely used to describe the processes of heat and mass transfer in a laminar flow regime. For turbulent flows, these equations are unsuitable, it is necessary to introduce into consideration the empirical turbulent coefficients of viscosity μt, thermal conductivity λt and diffusion Dt. However, to describe turbulent flows, it is possible to go in another way - to modify the linear constitutive relations by giving them a nonlinear power-law form. Two-parameter power-law generalizations of Newton's, Fourier's and Fick's formulas for shear stress, heat flux density and diffusion, which, depending on the value of the exponents, can be used to describe the processes of heat and mass transfer both in laminar and turbulent fluid flow. Also, this generalization can be used to describe the behavior of power-law fluids and flows of polymer solutions exhibiting the Toms effect.

The current article presents a comprehensive investigation of MHD viscous flow of hybrid-nanofluids (Al2O3 − Ag/ water and (Al2O3 − Cu/) over a horizontally irregular 3D plane with non-uniform thickness combined with slip effects. The foremost aim of conducting this study is to enhance thermal transportation. Based on the following novelties, the subject study holds tremendous significance: i. A comparative analysis of two hybrid nanofluids with hybrid-base fluid together with slip effects ii. An exclusive study where the Tiwari and Das nanofluid model is employed combined with Fourier's heat flux model iii. Development of finite-difference code which implements the three-stage Lobatto IIIa approach for the designed problem. We have used suitable scaling transformations to convert the three-dimensional conservation equations of mass, momentum, and energy into a dimensionless system of boundary layer equations. The numerical solution of the coupled non-linear boundary layer problem is determined using the built-in finite-difference code designed to employ the three-stage Lobatto IIIa formula. A comprehensive assessment is carried out in how the velocity components, temperature, skin friction, and heat transfer rate are affected by the physical parameters of interest. The same is presented through graphs and in tabular form to offer a pictorial overview. The fluctuating trends of skin friction coefficients (x, y-directions) and Nusselt number are investigated to explore the physical landscape of the current study. The findings of this study offer a noticeable contrast to their existing counterparts.

The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal properties of fins. This manuscript proposes the fractional modeling of Fourier and non-Fourier heat transfer of longitudinal fin via non-singular fractional approach. The configuration of longitudinal fin in terms of one dimension is developed for the mathematical model of parabolic and hyperbolic heat transfer equations. By considering the Fourier and non-Fourier heat transfer from longitudinal fin, the mathematical techniques of Fourier sine and Laplace transforms have been invoked. An analytic approach is tackled for handling the governing equation through special functions for the fractionalized parabolic and hyperbolic heat transfer equations in longitudinal fin. For the sake of comparative analysis of parabolic verses hyperbolic heat conduction of fin temperature, we depicted the distinct graphical illustrations; for instance, 2-dimensional graph, bar chart, contour graphs, heat graph, 3-dimensional graphs and column graphs on for the variants of different rheological impacts of longitudinal fin.

In the present paper, we study the exponential shock propagation in a self-gravitating rotational axisymmetric perfectly conducting mixture of van der Waal gas and solid particles with magnetic field either axial or azimuthal and radiative and conductive heat fluxes. In our model, the solid particles are distributed continuously in the mixture and are chemically inert, and the equilibrium conditions for flow are preserved in the entire region of flow field behind shock wave. In a thick gray gas model case, the radiation is assumed to be of diffusion type. The Fourier's heat conduction law is used to express the heat conduction. The effects of the problem parameters variations are discussed. It is shown that the density of micro size solid particles to the gas initial density ratio or the gravitational parameter or the rotational parameter or the gas adiabatic index has effects to enhance the shock wave strength. Also, it is derived that an increase in the nonidealness of the gas, Alfvén Mach number, and the mass concentration of solid particles in the mixture have decaying effects on the strength of shock wave. It is shown that the shock wave is stronger when magnetic field is axial and weaker for azimuthal magnetic field.

In this work, a simulation model based on finite element analysis for a one-dimensional p-type segmented semiconductor element with different cross-sectional areas is analyzed to predict transient thermal behavior for thermoelectric coolers (TECs). The proposed model considers all thermoelectric effects, including the Peltier effect, Thomson effect, Joule heating, and Fourier's heat conduction. The supercooling occurs when a pulse current higher than the steady-state optimum current is applied to a TEC. Dynamic characteristics, such as minimum cold side temperature and holding time of transient state, which arise in transient supercooling are very important to be considered for the design and operation of TECs. In this study, we present a new approach of transient performance based on leg geometry shape, considering variable cross-sectional areas, as well as individual element lengths of two different thermoelectric materials using a segmentation model proposed. A variety of model designs are analyzed, considering rectangular, trapezoidal, and inverse trapezoidal legs, where also optimum pulse current is found as a function of the element lengths. It is demonstrated that an improvement of 4.75% in the cooling is possible when using trapezoidal legs compared with conventional rectangular systems. Our presented model is mainly a new alternative in characterizing Peltier supercooling as a function of both pulse current ratio as well as the leg shape.

A new in situ thermal piezocone penetration test (T-CPTU) system is developed to determine the thermal properties of soil. It is expected to overcome most of the shortcomings observed in existing in situ test techniques. Based on Fourier's heat conduction equation and pore pressure dissipation theoretical equation, a method for calculating the thermal conductivity, namely the predicted temperature method, was proposed. The accuracy of the T-CPTU probe testing process and thermal conductivity calculation results were verified by numerical simulation, laboratory large-scale model tank tests, and thermal needle tests. Finally, the field data of T-CPTUs at three sites in Nanjing, China, were collected and compared with the laboratory thermal needle tests. The results indicated that the thermal conductivities obtained using T-CPTU were accurate and closer to those of laboratory thermal needle tests for most soils. The thermal conductivities of the undisturbed soil samples measured in the laboratory were lower than those obtained by T-CPTU.

Abstract With the miniaturization of structures, such as MEMS/NEMS, the size‐dependent effect has become an issue and attracted much attention. The well‐known theories describing the size‐dependent effect mainly include the nonlocal elasticity theory, the strain gradient theory and the modified coupled stress theory. Based on these theories, a number of works have been conducted to explore the size‐dependent behaviors of structures or devices in micro/nano‐scale, among them, majorities are on elastic performances, while, minorities are on thermoelastic performances. It is inevitable for structures suffering changeable temperature, as a consequence, thermal‐induced stress and deformation occur in structures and they are worth being fully concerned. For thermoelastic behaviors limited to small scale problems, the classical Fourier's heat conduction law may fail, meanwhile, new models, for example, fractional order heat conduction model, have been developed to modify Fourier's law. In present paper, the transient thermoelastic response of a nanobeam subjected to a ramp heating is investigated by combining the nonlocal elasticity theory and the fractional order heat conduction model. The governing equations are formulated and then solved by Laplace transform and its numerical inversion. The non‐dimensional temperature, displacement, stress, and deflection in the nanobeam are obtained and illustrated graphically. In calculation, the effects of the ramp‐heating time parameter, the nonlocal parameter and the fractional order parameter on the considered physical quantities are examined and discussed in detail.

Phonon vortex dynamics in graphene ribbon by solving Boltzmann transport equation with ab initio scattering rates