Periodic Temperature Boundary Conditions Research Articles

Multiscale modeling and thermal conductivity evaluation of nano-reinforced composite materials with pore defect

The performance of resin-based composite materials often exhibits diversity due to the designability of various components. Thermal conductivity, an important thermal parameter of the composite, plays a significant role in thermal-chemical reactions, thermal stress analysis, temperature conduction, etc. However, it is relatively difficult to experimentally explore the thermal conduction mechanism of hybrid composite materials, mainly due to the relatively difficult control of various components. Therefore, this paper proposes a sequentially coupled cross-scale numerical method to characterize the thermal conductivity of nano-reinforced composite materials with pores by a multiscale periodic Representative Volume Element model generated by an improved Random Sequential Absorption algorithm. Firstly, periodic temperature boundary conditions are described, and the thermal conductivity performances of nano-reinforced matrix and composite with pores are investigated based on the finite element homogenization theory. Then, the proposed modes are validated and grid sensitivity analysis is conducted, indicating that the optimal grid sizes for the RVE models are 1.9 nm for the nano-reinforced matrix and 0.14 μm for the composite with pores based on a comprehensive comparison of four pore characterization methods, respectively. Furthermore, the study explored the effect of multiple parameters including nanoparticle content, pore content, and pore shape on thermal conductivity. Numerical findings reveal that the thermal conductivity of the nanocomposite matrix exhibits a linear increase with higher particle content. Specifically, compared to 0 % particle content, the thermal conductivity rises by 141.92 % at 12 % particle content. While the composite material's transverse thermal conductivity is sensitive to porosity content, it is less influenced by pore shape. The method proposed in this paper provides an effective approach for studying the thermal conduction of nano-reinforced composite materials with pores, and the research findings also offer theoretical guidance for process engineers.

Multi-scale Modeling and Finite Element Analyses of Thermal Conductivity of 3D C/SiC Composites Fabricating by Flexible-Oriented Woven Process

Thermal conductivity is one of the most significant criterion of three-dimensional carbon fiber-reinforced SiC matrix composites (3D C/SiC). Represent volume element (RVE) models of microscale, void/matrix and mesoscale proposed in this work are used to simulate the thermal conductivity behaviors of the 3D C/SiC composites. An entirely new process is introduced to weave the preform with three-dimensional orthogonal architecture. The 3D steady-state analysis step is created for assessing the thermal conductivity behaviors of the composites by applying periodic temperature boundary conditions. Three RVE models of cuboid, hexagonal and fiber random distribution are respectively developed to comparatively study the influence of fiber package pattern on the thermal conductivities at the microscale. Besides, the effect of void morphology on the thermal conductivity of the matrix is analyzed by the void/matrix models. The prediction results at the mesoscale correspond closely to the experimental values. The effect of the porosities and fiber volume fractions on the thermal conductivities is also taken into consideration. The multi-scale models mentioned in this paper can be used to predict the thermal conductivity behaviors of other composites with complex structures.

Thermo-bioconvection performance of nanofluid containing oxytactic microorganisms inside a square porous cavity under constant and periodic temperature boundary conditions

Thermo-bioconvection performance of nanofluid containing oxytactic microorganisms inside a square porous cavity under constant and periodic temperature boundary conditions

Transient thermal rectification effect of one-dimensional heterostructure

Like an electric diode, thermal diode transmits heat in a specific direction, and thermal rectification is also a fundamental phenomenon for active heat flow control. However, in practical applications, thermal rectification needs to be operated under transient conditions. In this study, transient thermal rectification ratio of a one-dimensional heterostructure is numerically investigated by using the finite element method. The effects of interface thermal resistance, interface initial gap, periodic boundary condition and geometric and material parameters on the transient thermal resistance ratio are obtained. Research indicates that the interface thermal resistance can enhance the thermal rectification effect of the system, and the introduction of the initial interface gap improves the transient thermal rectification ratio by an order of magnitude. The ability to engineer the thermal diffusivity of materials allows us to control the heat flux and improve transient thermal rectification ratio. Since interface thermal resistance can enlarge the difference in heat transfer capability between forward case and reverse case, it is reasonable to suggest that adjusting the interface thermal resistance may also enhance the thermal rectification effect, but excessive interface thermal resistance will reduce it. Under the periodic temperature boundary conditions, the larger the temperature difference in boundary fluctuation, the larger the fluctuation amplitude of the transient thermal rectification ratio is. The fluctuation frequency of thermal rectification changes with the periodic boundary frequency, which also affects the amplitude of the fluctuation. Furthermore, by adjusting the initial interface gap, the gap is closed during heat transfer and the interface thermal resistance is reduced in the forward case, while the interface gap is kept open in the reverse case, thereby improving the overall thermal rectification ratio by an order of magnitude. For different transient stages, the equivalent thermal conductivity can be changed by adjusting the material and geometrical properties to improve the thermal rectification ratio.Therefore, the proposed numerical approach and results can guide the optimal design of the transient thermal rectifier.

Comparative investigation of phase change material on heat transfer characteristics under theoretical and practical periodic temperature boundary

In this paper, heat transfer characteristics of phase change material in rectangular containers are numerically analyzed. The inclination angles of the container refer to 0?, 90?, and 180?. Both theoretical and practical periodic temperature boundary conditions are taken into consideration, in which the periodic temperature boundary conditions include 50-80?C and 65-80?C. The comparison study is carried out through the liquid fraction and temperature histories during the heat transfer process under these different boundary conditions. It is indicated that there are large differences between the calculated results under the theoretical and the practical periodic temperature boundary conditions when the temperature boundary is 50-80?C, while the theoretical and the practical periodic temperature boundary conditions of 65-80?C have relatively little effect on the numerical results of the heat transfer process of the phase change material. Furthermore, compared with the temperature increasing stage, the numerical results calculated under the theoretical and the practical boundary conditions have more significant differences in the temperature decreasing stage. The research conclusion of this paper can provide a theoretical basis for the application of phase change material under periodic temperature boundary conditions.

Thermo-Bioconvection Performance of Nanofluid Containing Oxytactic Microorganisms Inside a Square Porous Cavity Under Constant and Periodic Temperature Boundary Conditions

Thermo-Bioconvection Performance of Nanofluid Containing Oxytactic Microorganisms Inside a Square Porous Cavity Under Constant and Periodic Temperature Boundary Conditions

Influence of snow cover on temperature field of frozen ground

Research on the effect of snow on the temperature field of frozen ground is of great significance to the laying of underground oil pipelines, design of roads, and control of frost damage in cold regions. The heat transport laws of frozen ground with phase changes under periodic temperature boundary conditions were analyzed based on data monitoring in this paper. Based on the boundary conditions determined by the monitoring data, the numerical calculations of frozen ground and subgrade with/without snow cover were carried out, and the effects of snow cover on the temperature fields of frozen ground and subgrade in cold regions were explored. Monitoring results demonstrate that the temperature at different sections of frozen ground with phase change presents a sine-like function under the periodic temperature boundary condition. According to monitoring data, when the thickness of the natural surface snow cover is about 25 cm, the daily average minimum temperature of soil at 0.1 m from the surface will rise by about 10 °C compared to that without snow cover during a year (in a cycle); nevertheless, when combined with numerical calculation, the permafrost table increases by about 2.87 m, and the permafrost base decreases by more than 5.59 m. Under the boundary conditions set in this paper, the permafrost under the subgrade disappears in a greater area due to the construction of the subgrade in the snow-covered area. In addition, the elliptical thawing soil area produced by the lower part of the slope of a snow-covered subgrade will adversely affect its stability.

Analysis of time-dependent heat transfer with periodic excitation in microscale systems

• Analytical, experimental and numerical study of heat transfer on microscale. • Time-dependent temperature distribution with periodic excitation. • Penetration depth at which the periodic-thermal excitations are still noticeable. • A round impinging water jet used to cool a surface heated by pulsing laser. • System reaction for time scales and material properties typical for micro-systems. This study investigates time-dependent heat transfer with periodic excitation in micro-scale systems. Specifically, this study sheds light on time and length scales relevant to periodic heat transfer in micro systems. First, a system's substrate is modeled as a slab of finite thickness, in which the heat conduction equation is solved analytically for a periodic temperature boundary condition over the entire range of transient-periodic process. Using the analytical solutions, the system reaction in time is characterized for time scales and material properties typical for micro-systems. A “penetration depth” is defined as a parameter which indicates the maximum distance from the periodically-heated boundary/surface at which the periodic-thermal excitations are still noticeable. Then, as a case study, an experimental device is examined that uses a round, impinging water jet to cool a surface heated by pulsing laser. Finally, a three-dimensional numerical simulation, validated versus experiments, is used to elucidate the system's expected thermal behavior, including spatial and temporal temperature field variation, relevant time scales for measurements, and the spatial distribution of the heat transfer coefficient. It is demonstrated that the analytical findings can serve to characterize the real behavior rather accurately. The findings can assist in the design of systems with unsteady heating, and in future studies aiming at understanding more complex physically-driven transient phenomena, like flow boiling in micro-systems.

MHD nanofluid free convection inside the wavy triangular cavity considering periodic temperature boundary condition and velocity slip mechanisms

Recent studies have shown that the two-phase modeling of nanofluid in natural convection is more compatible with the experimental results. This numerical study is applied to Buongiorno's model for solving the volume fraction of iron oxide nanoparticles inside a triangular chamber with a hot wavy wall using the finite volume method. Also, a uniform magnetic field is used to improve the heat transfer rate and entropy generation. The periodic temperature boundary condition is considered for the wavy side of the chamber while the other side is at the constant temperature. Hartmann number (Ha), Rayleigh number (Ra), undulation number (n), and inclination angle of magnetic field (ξ) variations are investigated. The results show that n has significant effects on heat transfer. Also, the Nusselt number is inversely related to the undulation number and is directly associated with the Rayleigh number. Moreover, the heat transfer rate is inversely related to the total entropy generation. Due to the magnetic field in high Ra, entropy generation first increases and then remains constant with increasing Ha.

A comparative study for the thermal conductivities of C/SiC composites with different preform architectures fabricating by flexible oriented woven process

Thermal conductivity behaviors are one of the most important evaluations of C/SiC composites in the field of thermal protective structures. Represent volume element (RVE) models of microscale, void/matrix, and mesoscale proposed in this work are used to investigate the thermal conductivity behaviors of the C/SiC composites with different preform architectures. The thermal conductivities of 2.5D woven composites (2.5D), 3D woven orthogonal composites (3D), 3D five-directional woven composites (3DFD) and the combination of three structures fabricating by the flexible oriented woven process (FOWP) are comparatively discussed. The periodic temperature boundary conditions are applied to the RVE models to predict the thermal conductivities (TCs). The proposed analytical methods are validated by the values from the experiment and the literature. In addition, the effect of porosity and structure combination sequences on TCs is also taken into consideration. The results show that the 3D woven orthogonal composites have the lowest TCs and the structure combination sequences have little effect on TCs of C/SiC composites. The present work can potentially help to improve the design process and provide a significant reference to select the appropriate preform architectures.

Fractional Modeling of Fin on non-Fourier Heat Conduction via Modern Fractional Differential Operators

The enhancement of heat transfer for electronic kits and automobiles has become highly dependent on the finned heat exchangers; this is because fin provides high heat transfer rate and superior performance with a significant temperature reduction. In this manuscript, a fractional modeling of non-Fourier heat conduction problem of a fin is proposed within the periodic temperature boundary condition. The mathematical modeling is performed via classical theory of heat conduction that is directly proportional to temperature gradient through which hyperbolic heat conduction equation for a fin is generated. The hyperbolic heat conduction equation for a fin is fractionalized via modern approaches of fractional differentiations, namely Atangana–Baleanu and Caputo–Fabrizio differential operators. In order to have analyticity of hyperbolic heat conduction equation for a fin, we invoked the mathematical techniques of Laplace transform. The exact solutions of temperature distribution have been obtained in terms of Fox-H and Mittag–Leffler functions with the product of convolution. The solutions of temperature distribution have been classified into integer verses non-integer theories by making fractional parameters $$ \alpha = \beta = 1 $$ and $$ \alpha \ne \beta \ne 1 $$ , respectively. Our results suggest that due to variability of different rheological parameters on temperature distribution, the cooling process is faster via fractional models in comparison to non-fractional model. Additionally, it is also observed that thermal wave propagates at a specific time results the reciprocal trend in temperature distribution.

Effect of periodic surface temperature on heat transfer in layered saturated soil

This paper presents numerical analyses of one-dimensional heat transfer in layered saturated soil with effective porosity and under a periodic temperature boundary condition using the numerical model HT1. The model characterizes the soil layer using separate columns to represent solid matrix and mobile pore fluid components, and a series-parallel approach to model soil thermal conductivity. Numerical simulations are presented to illustrate the effect of fluid velocity, thermal retardation factor, thermal conductivity of solid particles, effective porosity and layer heterogeneity. Numerical results indicate that increasing downward fluid velocity and decreasing retardation factor can increase the distance that temperature oscillations from the surface can propagate into the layer. In addition, decreasing fluid velocity, increasing retardation factor, and increasing thermal conductivity of solid particles can decrease the temperature oscillation amplitude in the soil. Temperature profiles also indicate the significance of soil effective porosity and multiple soil layers on heat transfer behavior.

Buoyancy-assisted mixed convection in a vertical channel with spatially periodic wall temperature

The influence of a spatially periodic temperature boundary condition on the laminar mixed convection in an upward flow between two vertical parallel plates is numerically studied. A detailed assessment is presented of the effects of the Grashof and Reynolds numbers, the channel length, and the wavelength of the periodic temperature distribution at the colder wall on the flow and thermal characteristics. It is found that, above a critical ratio of Grashof-to-Reynolds numbers, the flow gradually changes into a multi-cellular regime, with periodic features that match the periodicity of the boundary temperature distribution. Local recirculating zones are formed near the colder wall with size and strength that are increased with increasing ratio of Grashof-to-Reynolds numbers, periodicity of the flow domain and/or wavelength of the spatially periodic wall temperature. The temperature field exhibits a variation in the vertical direction affecting the wall heat transfer with increasing Grashof and Reynolds numbers. The wall heat fluxes are initially decreased acquiring a local minimum value and are subsequently increased with increasing ratio of Grashof-to-Reynolds numbers, while they are reduced with increasing the channel length.

Natural convection and heat transfer in attics subject to periodic thermal forcing

The heat transfer through the attics of buildings under realistic thermal forcing has been considered in this study. A periodic temperature boundary condition is applied on the sloping walls of the attic to show the basic flow features in the attic space over diurnal cycles. The numerical results reveal that, during the daytime heating stage, the flow in the attic space is stratified; whereas at the night-time cooling stage, the flow becomes unstable. A symmetrical solution is seen for relatively low Rayleigh numbers. However, as the Ra gradually increases, a transition occurs at a critical value of Ra. Above this critical value, an asymmetrical solution exhibiting a pitchfork bifurcation arises at the night-time. It is also found that the calculated heat transfer rate at the night-time cooling stage is much higher than that during the daytime heating stage.

Conjugate Heat Transfer in an Enclosure with a Centered Conducting Body Imposed Sinusoidal Temperature Profiles on One Side

The present work is concerned with natural convection heat transfer and fluid flow in a vertical enclosure subject to periodic temperature boundary condition imposed at the right sidewall with a conducting body placed at the center of the enclosure. A close inspection is concentrated to the effects of the body size and thermal conductivity ratio on the resonant frequencies for unsteady state. The body size varies from 0.1 to 0.9 the height of the enclosure, and the thermal conductivity ratio from 0.1 to 20. The results are presented in terms of amplitude of cycle averaged Nusselt number, fluctuating velocity and temperature contours and its intensity. The vertical and horizontal temperature excursions are also shown. It is found that the resonant frequency decreases with increasing the body size and thermal conductivity ratio. The disturbance of hot wall travels the core region, and will be interrupted by the centered body. Double-peak structure of the vertical velocity intensity would be observed at resonance.

A three-dimensional instability in mixed convection with streamwise periodic heating

Three-dimensional numerical simulations of flow through a channel with spatially periodic temperature boundary conditions in the streamwise direction have been carried out. A spectral method employing Fourier series expansion in the streamwise and spanwise directions and Chebyshev expansion in the vertical direction is used. A supercritical bifurcation to three-dimensional flow is found to occur before the onset of unsteadiness. The bifurcation to unsteady three-dimensional flow is also found to be supercritical. The unsteady three-dimensional flow oscillates at a slightly lower frequency than the two-dimensional flow, and introduces a slightly higher incommensurate frequency causing quasiperiodic flow and a slow spanwise wave motion.

Flow regimes in two-dimensional mixed convection with spatially periodic lower wall heating

Two-dimensional numerical simulations of flow through a channel with spatially periodic temperature boundary conditions at the lower wall have been carried out. A spectral method with a Fourier series expansion in the streamwise direction and a Chebyshev expansion in the vertical direction is employed. A bifurcation to a limit cycle occurs at Reynolds numbers as low as Re=4 and Rayleigh numbers as low as Ra=14 500. The frequency of oscillation decreases with Re and is essentially independent of Ra. Maps of flow regimes for varying periodicities have been created. Regimes with periodicities longer than the imposed temperature boundary condition have been found.

Deduction of fluidized bed heat transfer coefficients using one- and two-dimensional analyses

Prior calculations of heat transfer coefficients for an experimental horizontal tube in a bubbling fluidized bed have assumed that heat conduction through the tube wall is a one-dimensional problem. However, a comparison between one-dimensional (1D) and two-dimensional (2D) analyses using experimental data shows that there exists a significant difference between 1D and 2D calculations, especially at the side of the tube. In addition, because of the periodic character of the bubbling fluidized beds, a theoretical analysis of a horizontal tube subjected to a periodic temperature boundary condition which varies in the circumferential direction is presented. The 2D analysis was accomplished by solving the unsteady two-dimensional heat conduction equation numerically, where the boundary conditions were taken from temperature data measured at five different locations of the tube simultaneously.

Moisture diffusion due to periodic moisture and temperature boundary conditions—an approximate steady analytical solution with non-constant diffusion coefficients

An approximate steady analytical solution is given to the moisture diffusion equation with periodic moisture and temperature boundary conditions, where the moisture flux is determined by both temperature and moisture gradients, specifically F = −D m( ∂m/ ∂x)−D T( ∂T/ ∂x) and which has nonconstant diffusion coefficients. The key physical assumptions made are that the thermal conductivity is constant and that the Fourier number is ⪢1 so that the internal temperature gradient is linear but periodic in response to the periodic temperature boundary conditions. The key mathematical approximation made is to ignore second and higher harmonic terms in the time-dependent part of the solution. The solution agrees with a numerical model over a wide range of parameters to within 10%, and reduces in special cases to well known existing analytical solutions. The solution has applications in a wide number of moisture diffusion problems in building physics.

A two-dimensional instability in a mixed convection flow with spatially periodic temperature boundary conditions

Two-dimensional numerical simulations of combined forced and natural convection have been carried out in a periodic channel with spatially periodic temperature boundary conditions at the lower wall and an insulated upper wall. The resulting flow separates from the lower wall just downstream of the hot section of the wall. At Re=45 and Ra=20 000 a weakly damped oscillatory flow is found in which the vortex periodically separates from the wall sending a plume of hot fluid to the center of the channel. After this periodic motion has died away, the upper half of the channel is at a uniform temperature and the vortex is again fixed to the wall. At Re=60 and Ra=100 000, self-sustained oscillations occur, but the plume motion is unable to reach the upper half of the channel. All of these flows show inflectional velocity profiles indicating that this is a Kelvin–Helmholtz type of instability.