Effects Of Temperature-dependent Properties Research Articles

Topology optimization for a water-cooled heat sink in micro-electronics based on Pareto frontier

• An efficient Pareto frontier based design strategy for heat sinks is proposed. • A fitting formula of the Pareto frontiers is introduced to accelerate the design. • The 2D topology design results are validated by 3D CFD simulations. • Effects of temperature dependent properties on the results are significant. Topology optimization has been increasingly adopted as a non-intuitive methodology for heat sink design in the thermal management of microelectronics. In this work, a bi-objective topology optimization method for heat sink design in micro-electronics is suggested by considering the trade-off between two contradicting objectives, i.e., the heat transfer and hydraulic performances. The method in this work focused on the laminar water flow with Reynolds number less than 100 based on the channel width for a wide temperature range that covers different types of micro-electric devices. A series of Pareto frontiers were acquired for heat sink designs with different topologies, which can be used to decide the optimum design in respect of heat transfer and pressure drop. Particularly, an analytical formula in terms of inlet Reynolds numbers was obtained for the fast generation of the Pareto frontiers under different working conditions which help to determine the weight parameters of two contradicting objectives readily. The new strategy for weight parameter determination significantly reduces the workload of trial-and-error during the weight parameter determination in the traditional bi-objective topology optimization and thus accelerates the design process. Besides, the temperature-dependent physical properties (viscosity and thermal conductivity) in the design model were considered and were found to affect the design results significantly. Finally, the 3D heat sink model was reconstructed from the 2D topology optimization, and the thermal-fluid analyses were conducted. The results indicate that the 3D reconstructed model can well satisfy the design objective specified in the topology optimization, thereby confirming the validity and robustness of our design method.

CFD study of Convective Heat Transfer of Water Flow Through Micro-Pipe with Mixed Constant Wall Temperature and Heat Flux Wall Boundary Conditions

The dissipation of heat in tiny engineering systems can be achieved with fluid flow through micro pipes. They have the advantage of less volume to large surface ratio convective heat transfer. There are deep-rooted analytical relations for convective heat transfer available for fluid flow through macro size pipes. But differences exist between the convective heat transfer for fluid flow through macro and micro pipes. Therefore, there is a good scope of work in micro convection heat transfer to study the mechanism of fundamental flow physics. There have been studies with either constant heat flux wall boundary conditions or constant wall temperature boundary conditions with constant and variable property flows. In this article, first, the numerical simulations are validated with the experimental data for 2D axisymmetric conventional pipe with pipe diameter of 8 mm is taken with laminar, steady, and single-phase water flows with constant wall heat flux boundary condition of 1 W/cm2. The computed Nusselt number is compared to the experimental results at different Reynolds numbers of 1350, 1600 and 1700. In the next study, three-dimensional micropipe laminar flow is studied numerically using water with an inlet velocity of 3 m/s and pipe diameter of 100 µm. The mixed wall boundary conditions with upper half pipe surface subjecting to constant wall temperature of 313 K and lower half surface subjecting to 100 W/cm2 are used in the simulations. The focus of research would be to consider the effect of temperature-dependent properties like thermal conductivity, viscosity, specific heat, and density (a combined effect we call it as variable properties) on micro-pipe flow characteristics like Nusselt number at mixed wall boundary conditions and compare it with the constant property flows. The conventional pipe showed no significant difference with variable and constant property flows with different Reynolds numbers. On contrary the flow through 3D micropipe shows that the Nusselt number with variable property flows is less as compared to the constant property flows.

Reflection of plane waves in a nonlocal microstretch thermoelastic medium with temperature dependent properties under three-phase-lag model

Present article is concerned with the propagation of plane waves in a nonlocal, microstretch thermoelastic half-space with temperature dependent properties. Five basic waves consisting of three sets of coupled longitudinal waves and two sets of coupled transverse waves travel with distinct speeds in the considered medium. The numerical values of amplitude ratios are shown graphically to explore the effects of temperature dependent properties, nonlocal and microstretch parameters. The effect of nonlocality on the phase speeds and attenuation coefficients of propagating waves have also been observed. It has also been verified that there is no dissipation of energy during reflection phenomenon.

Nonlinear response for a general form of thermoelasticity equation in mediums under the effect of temperature-dependent properties and short-pulse heating

This article presents an algorithm for nonlinear transient response of an elastic body with temperature-dependent material features in a large deformation domain exposed to short-pulse heating. The principal target of this paper is employing a general form of thermoelasticity equation, including temperature and strain rate-dependent model using finite strain theory (FST). A thermally nonlinear study is conducted considering a significant gradient of temperature in comparison with the reference temperature. Based on FST, to present the couple equations of energy and motion in the reference medium, the second Piola–Kirchhoff stress and the Lagrangian strain–displacement are used. The obtained equations improved integrating temperature and strain rate-dependent technique and then solved using a Hermitian transfinite element technique. Wave propagation analysis under impulsive thermal loadings is also discussed in this work. Analyzing the phase lag in second sound waves and the impacts of temperature dependency of the medium properties are conducted. Based on the obtained results, the temperature dependency of the materials features has a significant influence on the thermoelastic transient responses. Results illustrate an absorbing feature of wave propagation. In addition, it is observed that there is a remarkable difference in the results obtained from using the general form of thermoelasticity and that of obtained from classic model.

An Asymmetric Elasto-Plastic Phase-Field Model for Shape Memory Effect, Pseudoelasticity and Thermomechanical Training in Polycrystalline Shape Memory Alloys

We propose an elasto-plastic phase-field model (PFM) to conduct the first microscopic computational study of shape memory effect (SME), pseudoelasticity, stress assisted two-way memory effect (SATWME), and thermomechanical training of CuAlBe shape memory alloy (SMA). This non-isothermal PFM model considers the effects of temperature dependent properties, latent heat, grain boundaries, and asymmetric transformation and plasticity. PFM simulations demonstrate the capacity of our model to capture the thermomechanical and purely mechanical shape recovery in the SMA. When considering transforming grain boundaries, grain refinement generates a higher transformation stress, a steeper transformation hardening, and smaller hysteresis loops for both SME and pseudoelasticity. The results also point out slightly higher transformation stress when geometrical grain boundaries are used. The simulations of SATWME highlight an augmentation of the residual martensite as the hold stress increases, which is consistent with experimental observations. This is the first PFM that can mimic the thermal training within several SATWME cycles, showing an asymptotic increase of plastic strain and the related retained transformation strain until the fourth cycle, and their stabilization thereafter. The activation of plasticity occurs always after initiation of phase transformation. Although plasticity results in more stress relaxation, it deteriorates the shape recovery for both SME and pseudoelasticity by hindering the reverse transformation. Comparison between tension and compression demonstrates the capacity of this PFM to account for, for the first time, the nonsymmetrical transformation and plastic responses of SMAs.

Reflection of plane waves on generalized thermoelastic medium under effect of temperature dependent properties and initial stress with three-phase-lag model

The present paper investigates the reflection coefficient of thermoelastic plane waves at the free surface of an elastic half-space influenced by initial stress and temperature-dependent properties in the presence of thermal loading bounded by the three-phase-lag (3PHL) thermoelastic model. It revealed three plane waves, i.e. (thermal wave (T-wave), P-wave, and SV-wave). It provided the numerical solution and presented the effect of initial stress and temperature-dependent properties of the reflection coefficient graphically. Moreover, the paper utilized the altered reflected elastic waves because of initial stress and temperature-dependence to identify the more accurate nature of waves reflection, especially seismic waves.

Augmentation and diminution of non-Boussinesq effects due to non-Newtonian power-law behavior in natural convection

This study investigates the extent and significance of augmentation and diminution of non-Oberbeck–Boussinesq (NOB) effects due to power-law rheology in natural convection. The relative significance of each temperature dependent thermophysical property of a non-Newtonian power-law fluid was first evaluated using an order of magnitude analysis. The limiting criteria were derived for a class of fluids having an Arrhenius-type thermodependent consistency index, and a constant power-law index. Significant fluid property dependencies were identified, incorporated into the conservation equations, and solved numerically. The benchmark problem of natural convection around an isothermal vertical flat plate, immersed in a quiescent power-law fluid, was re-investigated from the viewpoint of NOB effects. It was found that power-law rheology significantly augmented or diminished the acceleration of flow caused by NOB effects. Compared to the Newtonian case, strong shear thinning behavior more than doubled the NOB acceleration of the flow field, and shear thickening inhibited the acceleration by nearly half. Numerical solutions facilitated the visualization of velocity and temperature distributions, and thus provided insights to the underlying physics. It is demonstrated that the cumulative effect of the power-law behavior and temperature dependence of properties is more than a mere superposition of the individual effects. Important contributions from the present work include modifications to the OB approximation’s limiting criteria applicable to power-law fluids, insights into the effect of temperature dependent properties on the flow field and consequent heat transfer, and their correspondence to the results of the order of magnitude analysis. The present investigation of the underlying physics of augmentation and diminution facilitate a better understanding for future studies of NOB effects combined with non-Newtonian behavior.

Thermal buckling and vibration of laminated composite plates with temperature dependent properties by an asymptotic numerical method

The objective of this work is the elaboration of analytical and numerical procedures to investigate thermal buckling and vibration analyses of composite plates with thermal dependent material properties. Based on the homotopy and an asymptotic numerical method, a mathematical formulation that may account for various temperature dependent models is elaborated. Power series expansions of the displacement and the temperature are developed, and the finite element method is used for numerical solution. The effects of temperature dependent properties, structural geometry and boundary conditions on the thermal buckling and vibration are analyzed.

Reflection of plane waves in an anisotropic magnetothermoelastic diffusive medium with temperature dependent properties

In this article, a model of two dimensional problem of generalized thermoelasticity for an anisotropic magnetothermoelastic diffusive medium under the effect of temperature dependent properties is established. The enunciation is applied to generalized thermoelasticity theory based on Green-Lindsay model. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD), and quasi-transverse wave (qSV) in the medium. Amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programing. Effects of temperature dependent properties, magnetic and diffusion parameters on the amplitude and energy ratios are depicted graphically. Expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during the reflection phenomenon, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.

Effect of temperature-dependent properties on electroosmotic mobility at arbitrary zeta potentials

• Electroosmotic mobility and volumetric flow rate as temperature-dependent zeta potential are determined. • Analytical solutions for electric and hydrodynamic fields by assuming temperature-dependent zeta potentials are obtained. • The zeta potential is obtained as a function of the temperature field in the electroosmotic flow . • Non-isothermal electroosmotic flow at arbitrary zeta potentials is theoretically analyzed. A theoretical analysis to determine the electroosmotic mobility in an electroosmotic flow (EOF) in a microchannel at arbitrary zeta potentials is conducted in this study. As an important characteristic in this work, we consider that the wall zeta potentials of the microchannel and the viscosity and electrical conductivity of the electrolyte solution vary with temperature. The flow and the electric and temperature fields are obtained using lubrication approximation theory (LAT) together with the application of the regular perturbation technique. The electroosmotic mobility is evaluated, showing an increase higher than 18% (for the values of the physical properties used in this work) when physical properties, including the zeta potential of the microchannel walls, are considered as temperature-dependent functions compared with the isothermal case. Additionally, we show that the volumetric flow rate is drastically influenced when the zeta potential varies with temperature.

Numerical Analysis of a Semi-Infinite Solid with Temperature Dependent Thermal Conductivity using Truly Meshfree Method

This article presents Meshless Local Petrov-Galerkin (MLPG) method to obtain the numerical solution of linear and non-linear heat conduction in a semi-infinite solid object with specific heat flux. Moving least square approximants are used to approximate the unknown function of temperature T(x) with Th(x). These approximants are constructed by using a linear basis, a weight function and a set of non-constant coefficients. Essential boundary condition is imposed by the penalty function method. A predictor-corrector scheme based on direct substitution iteration has been applied to address the non-linearity and two-level  method for temporal discretization. The accuracy of MLPG method is verified by comparing the results for the simplified versions of the present model with the exact solutions. Once the accuracy of MLPG method is established, the method is further extended to investigate the effects of temperature-dependent properties.

Effects of temperature-dependent properties on natural convection of power-law nanofluids in rectangular cavities with sinusoidal temperature distribution

In this paper, the effects of temperature-dependent properties on natural convection of nanofluids in rectangular cavities with sinusoidal temperature distribution are investigated in detail with lattice Boltzmann method. To improve the computational efficiency, all simulations are performed on the Graphics Processing Unit (GPU) using NVIDIA’s CUDA. The fluid in the enclosure is a water-based nanofluid containing Al2O3 nanoparticles. The effects of power-law index (0.5⩽n⩽1.5), thermal Rayleigh number (104⩽Raf⩽106), diameter of nanoparticle (25nm⩽ds⩽100nm), nanoparticle volume fraction (0.0⩽ϕ⩽0.04), temperature of the cooled sidewall (315K⩽Tc⩽335K), temperature difference between the sidewalls (10K⩽ΔT⩽50K), amplitude ratio (0.0⩽A⩽1.0), wave number (0.0⩽ω⩽6.0), phase deviation (0.0⩽θ⩽π) and aspect ratio (0.250⩽AR⩽4.00) on heat and fluid flows are investigated. The results reveal that there is an optimal volume fraction ϕopt at which the maximum heat transfer enhancement is obtained, and the value of ϕopt is found to increase slightly with decreasing the nanoparticle diameter, and to increase remarkably with increasing the temperature of Tc or ΔT. In addition, the average Nusselt number is generally decreased with increasing power-law index, while increased with increasing A and ω. Further, we found that the average Nusselt number behaves nonlinearly with the phase deviation parameter. Moreover, the present results also indicate that there is an optimal value of aspect ratio at which the impact of AR on heat transfer is the most pronounced.

Reflection of plane waves at the initially stressed surface of a fiber-reinforced thermoelastic half space with temperature dependent properties

In this paper, a model of two dimensional problem of generalized thermoelasticity for a fiber-reinforced anisotropic elastic medium under the effect of temperature dependent properties is established. Reflection phenomena of plane waves in an initially stressed thermoelastic medium is studied in the context of two theories proposed by Lord–Shulman and Green–Lindsay. Using proper boundary conditions, the amplitude ratios and energy ratios for various reflected waves are presented. The phase speeds, reflection coefficients and energy ratios are computed numerically with the help of MATLAB programming and are depicted graphically to show the effect of initial stress and temperature dependent properties. It is found that there is no dissipation of energy at the boundary surface during reflection. A comparison between the two theories is also depicted in the present investigation.

Effect of temperature dependent properties on the fin performance under dehumidifying operating conditions

The analysis for fin thermal performance under dehumidifying conditions is conducted using a numerical approach. Finite-Element method is used to account for the non-linear effects due to temperature dependent parameters and humidity-temperature relationship. The temperature profiles, as well as the overall fin efficiency, are studied. The fin efficiency is found to be highly dependent on the operating conditions and the degree to which the heat transfer coefficient is a function of temperature. It is found that the effect of temperature-dependent thermal conductivity on fin performance is less as compared to heat transfer coefficient over the considered range of operating conditions.

Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticity

ABSTRACTIn this work, we consider the problem for an infinite medium with a spherical cavity on temperature-dependent properties subjected to a stress shock and thermal shock under the fractional-order theory of generalized thermoelasticity. The modulus of elasticity and the coefficient of thermal conductivity are taken as linear function of temperature. The governing equations for the problem are formulated and then solved by Laplace transform together with its numerical inversion. The nondimensional temperature, displacement, radial stress, and hoop stress are obtained and illustrated graphically. In the calculation, the emphasis is focused on investigating the effect of temperature-dependent properties on the variations of the considered variables. The graphical results indicate that the temperature-dependent modulus of elasticity plays a significant role on all the physical quantities.

Effects of temperature-dependent properties on natural convection of nanofluids in a partially heated cubic enclosure

In this paper, the effects of temperature-dependent properties on natural convection of nanofluids in a partially heated cubic enclosure are investigated in detail with lattice Boltzmann method. To improve the computational efficiency, all simulations are performed on the Graphics Processing Unit (GPU) using NVIDIA’s CUDA. The fluid in the cuibc cavity is a water-based nanofluid containing Al2O3 nanoparticles. The effects of thermal Rayleigh number (104⩽Raf⩽106), diameter of nanoparticle (25nm⩽ds⩽100nm), nanoparticle volume fraction (0.0⩽ϕ⩽0.04), temperature of the cooled sidewall (315K⩽Tc⩽335K), temperature difference between the sidewalls (10K⩽ΔT⩽50K), aspect ratio (0.50⩽AR⩽1.00) and heating location on temperature field and fluid flows are investigated. The results reveal that the average Nusselt number is decreased with the increase of nanoparticle volume fraction. In addition, it is also observed that there is an optimal volume fraction ϕmax at which the maximum heat transfer enhancement is obtained, and the value of ϕmax is found to increase slightly with decreasing the nanoparticle diameter, and to increase remarkably with increasing the temperature of Tc or ΔT. Moreover, we also find that the average Nusselt number and the heat transfer enhancement are decreased with the increase of aspect ratio.

The effect of temperature-dependent properties on generalized magneto-thermo-elastic medium with two-temperature under three-phase-lag model

PurposeThe purpose of this paper is to investigate the propagation of plane waves in an isotropic elastic medium under the effect of rotation, magnetic field and temperature-dependent properties with two‐temperatures.Design/methodology/approachThe problem has been solved analytically by using the normal mode analysis.FindingsThe numerical results are given and presented graphically when mechanical and thermal force are applied. Comparisons are made with the results predicted by the three-phase-lag (3PHL) model and dual-phase-lag model in the presence and absence of cases where the modulus of elasticity is independent of temperature.Originality/valueIn this work, the authors study the influence of rotation and magnetic field with two‐temperature on thermoelastic isotropic medium when the modulus of elasticity is taken as a linear function of reference temperature in the context of the 3PHL model. The numerical results for the field quantities are obtained and represented graphically.

Propagation of waves in an initially stressed generalized electromicrostretch thermoelastic medium with temperature-dependent properties under the effect of rotation

ABSTRACTIn the present article, a model of the equations of generalized electromicrostretch thermoelasticity in an initially stressed perfectly conducting elastic medium under the effect of temperature-dependent properties is studied. The entire elastic medium is rotating with a uniform angular velocity. Reflection phenomena of plane waves in electromicrostretch thermoelasticity is investigated under two theories proposed by Lord and Shulman (L–S) and Green and Lindsay (G–L). Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the plane boundary of an electromicrostretch thermoelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical examples calculate the amplitude ratios to evince the effects of initial stress parameter, rotation, and temperature-dependent properties, and the results obtained are depicted graphically.

Effects of temperature-dependent properties on wire-coating from a bath of FENE-P fluid

An analysis is carried out to study theoretically the coating of wire by drawing it from a pool of viscoelastic fluid in a pressure type-die under non-isothermal conditions. The constitutive equation of FENE-P model is used to characterize the rheology of the polymer melt. The equations describing the flow and heat transfer inside the die are solved (a) analytically for constant physical properties (b) numerically for temperature-dependent fluid properties. In the former case, the analytical expressions of velocity, volumetric flow rate, final radius of the coated wire and force required to pull the wire are reported. In the latter case, the fluid viscosity and relaxation time are considered as a function of temperature. The well-known Nahme–Griffith law is used to capture such dependence. Shooting method with Runge–Kutta–Fehlberg algorithm is employed to solve the coupled energy and momentum equations. The effects of different parameters on the velocity and the temperature distributions, volumetric flow rate, final thickness of the coated wire and force necessary to pull the wire are illustrated graphically for both the cases of constant and variable physical properties.

Laminar forced convection effectiveness of Al2O3–water nanofluid flow in a circular tube at various operation temperatures: Effects of temperature-dependent properties

In this paper, effects of temperature-dependent thermophysical properties on laminar forced convection effectiveness of Al2O3–water nanofluids in a circular tube imposed to a constant heat flux are investigated numerically. The numerical study is supplemented with a scale analysis based on the integral energy equation. The analysis is conducted for various inlet temperatures and considering two cases for properties including (i) constant-properties, and (ii) temperature-dependent properties. The simulated results are presented for three different concentrations of nanofluids i.e. 0%, 5%, and 9%, volume flow rates in the range of 24–180cm3/min which correspond with Reynolds numbers between 120 and 2000, heat fluxes between 5.51×102 and 1.23×104W/m2, and various inlet temperatures in the range of 25–50°C. The effects of various inlet temperatures of nanofluids and different thermophysical models on the local and average Nusselt numbers in the tube have been investigated in details. It is found that with an increase in both nanofluid concentration and temperature rise in the heated section, the effects of inlet temperature and thermophysical properties on the Nusselt number are more pronounced.