Part Of Heat Flux Research Articles

Thermal Performance Investigation of Vapor Chamber Under Partial Heating and Different Heat Flux Conditions: Effects of Inclination Angle

Abstract The need for cooling technologies increases tremendously with raising demand on the powerful and compact electronics. There, it pushes the research and technology to the new investigations on varying heat transfer mechanisms and devices. While one of these devices is vapor chamber (VC), an experimental study has been carried out to investigate the heat transfer performance of a VC under partial heating, varying heat fluxes, and different inclination angles for different temperatures, in the current study. For this purpose, a VC with a dimension of 90 mm × 90 mm × 3 mm is evaluated via its resulting thermal resistance, performance, and the temperature distribution over the VC surface. There, the limited effect of inclination angle is observed on the performance, while the highest change is obtained with decreasing local heating surface area, thus increasing heat fluxes. Moreover, this trend is seen almost similar with a reasonable shift up or down according to the different temperature differences.

DEVELOPMENT OF HEAT EXCHANGER WITH TWO-PASS DIVERGING MICROCHANNELS FOR EVAPORATION COOLING SYSTEMS

This study developed a two-pass diverging microchannel heat exchanger to avoid flow reversal and partial dry out of HFC-245fa flow boiling in the evaporation cooling systems. It is aimed to improve the diverging microchannel heat exchangers designed by previous studies and to effectively accommodate diverging channels on a limited heating base surface. The test results showed that the maximum heat transfer coefficients in a diverging channel heat exchanger were as much as 20% higher than those in straight channel heat exchanger, while the maximum partial dry-out heat flux is 42% higher in diverging channel heat exchanger. There is no significant difference for the pressure drops in two heat exchangers at low heat fluxes before it reached the partial dry-out condition. For higher flux, the pressure drops in straight channels were higher than those in divergent channels while partial dry out. It is concluded that the two-pass diverging channel design provided higher maximum heat transfer coefficients and higher maximum heat fluxes with lower penalties of pressure drops. It could be a good design to replace the conventional straight channel heat exchanger for evaporation cooling systems.

A COMBINED ACTIVE (PIEZOS) AND PASSIVE (MICROSTRUCTURING) PARTIAL FLOW-BOILING APPROACH FOR STABLE HIGH HEAT-FLUX COOLING WITH DIELECTRIC FLUIDS

Controlled but explosive growth in vaporization rates is made feasible by ultrasonic acoustothermal heating of the microlayers associated with microscale nucleating bubbles within the microstructured boiling surface/region of a millimeter-scale heat exchanger (HX). The HX is 5 cm long and has a 1 cm × 5 mm rectangular cross section that uses saturated partial flow-boiling operations of HFE-7000. Experiments use layers of woven copper mesh to form a microstructured boiling surface/region and its nano/microscale amplitude ultrasonic (~1-6 MHz) and sonic (< 2 kHz, typically) vibrations induced by a pair of very thin ultrasonic piezoelectric-transducers (termed piezos) that are placed and actuated from outside the heat-sink. The ultrasonic frequencies are for substructural microvibrations whereas the lower sonic frequencies are for suitable resonant structural microvibrations that assist in bubble removal and liquid filling processes. The flow and the piezos' actuation control allow an approximately 5-fold increase in heat transfer coefficient value, going from about 9000 W/m<sup>2</sup>-°C associated with microstructured no-piezos cases to 50,000 W/ m<sup>2</sup>-°C at a representative heat flux of about 25 W/cm<sup>2</sup>. The partial boiling approach is enabled by one inlet and two exit ports. Further, significant increases to current critical heat flux values (~70 W/cm<sup>2</sup>) are possible and are being reported elsewhere. The electrical energy consumed (in W) for generating nano/micrometer amplitude vibrations is a small percentage (currently < 3%, eventually < 1% by design) of the total heat removed (in W), which is a heat removal rate of 125 W for the case reported here.

Reconstruction of Timewise Term for the Nonlocal Diffusion Equation from an Additional Condition

The inverse problem of reconstructing the timewise term along with the temperature in the nonlocal diffusion equation with initial and boundary conditions and additional measurement (an integral and partial heat flux) is, for the first time, numerically investigated. This inverse problem appears extensively in the modeling of various phenomena in engineering and physics. The inverse problem considered in this paper has a unique solution. A Crank–Nicolson FDM is applied as a direct solver. The resulting nonlinear problem is solved using the MATLAB subroutine to minimize the objective functional. The Tikhonov regularization method is applied where necessary. A pair of examples, with smooth and non-smooth continuous timewise term, are discussed to assess the accuracy and stability of the numerical solutions.

A simple numerical scheme to linear radiative transfer in hollow and solid spheres

Nesse trabalho consideramos a transferência radiativa linear em esferas ocas e maciças, bem como a solução em um meio com fronteiras refletoras difusas e com fonte de energia. O método de ordenadas discretas com a técnica de diamond difference é utilizado para calcular as intensidades de radiação e os fluxos de calor parciais nas fronteiras. Nossos resultados foram obtidos para os espalhamentos para frente, isotrópico e para trás e foram comparados com os dados da literatura.

3D modeling and simulation of high-current vacuum arc subjected to real external transverse magnetic field

Vacuum circuit breakers (VCBs) are widely used in power distribution systems. When the VCB in a switchgear interrupts the short circuit current, the U type loop, which consists of a vacuum interrupter, an external busbar and a conductive rod, generates an external transverse magnetic field (ETMF). This field deflects the vacuum arc and affects the interruption performance of the VCB. In this paper, the real magnetic field data of the arc region are obtained by establishing a simulation model of an electrode system, taking into account the real ETMF and real axial magnetic field (AMF). Furthermore, the three dimensional steady magnetohydrodynamic model of the vacuum arc is established by using real magnetic field data as the boundary condition. The vacuum arc characteristics under the combined effect of AMF and the asymmetric transverse magnetic field (TMF) are studied. The simulation results show that the ETMF considerably changes the Bx of the arc column, which demonstrates asymmetry in the positive and negative directions, whereas By demonstrates a weaker asymmetry. Moreover, the asymmetric TMF deflects the distributions of the vacuum arc plasma and increases the partial heat flux density and axial current density. With the increase in the severity of the short circuit, the TMF asymmetry of the arc region is enhanced and the deflection of the vacuum arc plasma is also enhanced.

Weakly nonlocal thermodynamics of binary mixtures of Korteweg fluids with two velocities and two temperatures

We provide a thermodynamic framework for binary mixtures of Korteweg fluids with two velocities and two temperatures. The constitutive functions are allowed to depend on the diffusion velocity and the specific internal energy of both constituents, together with their first gradients, as well as on the mass density of the mixture and the concentration of one of the constituents, the latters together with their first and second gradients. Compatibility with second law of thermodynamics is investigated by applying a generalized Liu procedure. In the one-dimensional case, a complete solution of the set of thermodynamic restrictions is obtained by postulating a possible form of the constitutive equations for the partial heat fluxes and stress tensors. Taking a first order expansion in the gradients of the specific entropy, the expression of the entropy flux is determined. This contains the classical terms (namely, the sum of the ratios between the heat fluxes and the temperatures of the constituents) and some additional contributions accounting for nonlocal effects.

A Hamiltonian-based analytical approach for three-dimensional heat conduction of cylinders with specific mixed boundary conditions

A novel analytical symplectic method is introduced to investigate the three-dimensional steady-state heat conduction of cylinders with specific mixed boundary conditions (partial temperature and partial heat flux density). By defining the temperature and heat flux density as the mutually dual variables, the Hamiltonian form of governing equations are established. The original problem is reduced into a symplectic eigenproblem which can be solved by the method of separation of variables and a symplectic sub-system. Exact analytical solution is obtained and expressed in terms of symplectic eigensolutions. Comparison studies demonstrate the accuracy of the proposed method. Some new results are given also.

NANOFLUID SLIP FLOW THROUGH POROUS MEDIUM WITH ELASTIC DEFORMATION AND UNIFORM HEAT SOURCE/SINK EFFECTS

The uniform heat source/sink effect on second-grade nanofluid flow over a stretching sheet embedded in Darcian porous medium is studied with elastic deformation. The partial slip, heat flux, and mass flux boundary conditions are considered. The magnetic field is applied in various directions. The nanofluid model is considered with viscoelasticity, Brownian motion and theromophosis mechanisms. Mathematical equations governing the problem are solved numerically using the fourth-order Runge-Kutta method with shooting iteration technique. The flow and heat transfer phenomena are analyzed through plots for various sets of physical parameters. It is found that the presence of elastic deformation and the uniform heat source increase the thickness of the nanofluid thermal and concentration boundary layers.

Experimental investigation of circumferentially non-uniform heat flux on the heat transfer coefficient in a smooth horizontal tube with buoyancy driven secondary flow

In this experimental investigation the influence of non-uniform heat flux distributions on the internal heat transfer coefficient in a horizontal circular tube was studied for liquid water. The tube had an inner diameter of 27.8 mm and a length to diameter ratio of 72. Different outer wall heat flux conditions were studied for Reynolds numbers ranging from 650 to 2600 at a Prandtl number of approximately 6.5. Heat flux distributions included fully uniform heating (which had a circumferential angle span of 360°) and different partial uniform heat flux distributions with angle spans of 180° or 90° at different circumferential positions. Depending on the angle span, local heat flux intensities ranging from 1658 W/m2 to 6631 W/m2 were tested. Results indicate that the average steady state Nusselt number is greatly influenced by the applied heat flux position and intensity. Highest average heat transfer coefficients were achieved for cases where the applied heat flux was positioned on the lower half (in terms of gravity) of the tube circumference, while the lowest heat transfer coefficients were achieved when the heating was applied to the upper half of the tube. Smaller angle spans produced lower heat transfer coefficients. The relative thermal performance of the different heating scenarios where characterised and described by means of newly developed heat transfer coefficient correlations for angle spans of 180° and 90° which correlated 92% and 96% of the data respectively within 3% of the measured Nusselt number.

Conductive heat transfer in rarefied binary gas mixtures confined between parallel plates based on kinetic modeling

The kinetic model introduced by Kosuge (2009) is implemented to solve heat transfer through rarefied binary gas mixtures confined between two parallel plates maintained at different temperatures. The results have been found to be in very good agreement with corresponding ones obtained by the Boltzmann equation, the DSMC method and the Chapman-Enskog analysis. The efficiency of the Kosuge model for this problem is clearly demonstrated in the whole range of the Knudsen number for various heat flow setups, even when the temperature difference between the plates is large. The following three intermolecular models have been implemented: Hard Sphere (HS), Lennard Jones (LJ), Realistic Potential (RP). The computed HS heat fluxes in the transition and viscous regimes vary significantly with the corresponding ones of the LJ and RP models, which are close to each other. Also, the intermolecular model has a significant effect on the distribution of the mole fraction between the plates, while it has a minor effect on the density and temperature distributions. Concerning the partial heat flux distributions of the light and heavy species it has been found that moving from the hot towards the cold plate the former one is decreasing, while the latter one is increasing with the total heat flux being always constant. Heat fluxes with partial thermal accommodation at the walls are reported for He-Ne and He-Xe. For the same mixtures dimensional heat fluxes in terms of the reference pressure are plotted indicating that the total heat fluxes of the mixture with various mole fractions are always bounded from below and above by the heat flux of the heavy and light species respectively. These data may be useful for comparisons with experiments. Applying the equivalent single gas approach, it is deduced that this concept is not useful in rarefied binary gas mixture heat flow problems, which should be treated by two coupled kinetic equations. Finally, the effective thermal conductivity approximation has been successfully applied, provided that the system Knudsen number remains adequately small.

Entropy-based mixed three-moment description of fermionic radiation transport in slab and spherical geometries

The mixed three-moment hydrodynamic description of fermionic radiation transport based on the Boltzmann entropy optimization procedure is considered for the case of one-dimensional flows. The conditions for realizability of the mixed three moments chosen as the energy density and two partial heat fluxes are established. The domain of admissible values of those moments is determined and the existence of the solution to the optimization problem is proved. Here, the standard approaches related to either the truncated Hausdorff or Markov moment problems do not apply because the non-negative fermionic distribution function, denoted \begin{document}$f$\end{document} , must satisfy the inequality \begin{document}$f≤q 1$\end{document} and, at the same time, there are three different intervals of integration in the integral formulae defining the mixed moments. The hydrodynamic equations are obtained in the form of the symmetric hyperbolic system for the Lagrange multipliers of the optimization problem with constraints. The potentials generating this system are explicitly determined as dilogarithm and trilogarithm functions of the Lagrange multipliers. The invertibility of the relation between moments and Lagrange multipliers is proved. However, the inverse relation cannot be determined in a closed analytic form. Using the \begin{document}$H$\end{document} -theorem for the radiative transfer equation, it is shown that the derived system of hydrodynamic radiation equations has as a consequence an additional balance law with a non-negative source term.

A novel Hamiltonian-based method for two-dimensional transient heat conduction in a rectangle with specific mixed boundary conditions

A novel Hamiltonian-based method is introduced to the two-dimensional (2-D) transient heat conduction in a rectangular domain with partial temperature and partial heat flux density on one boundary. This boundary condition is very difficult to deal with in the classical Lagrangian solving system. Because of this, a total unknown vector consisting of both temperature and heat flux density is regarded as the primary unknown so that the problem is converted to the Hamiltonian form. By using the Laplace transform and method of separation of variables, the total unknown vector is solved and expressed in terms of symplectic eigensolutions in the complex frequency domain (s-domain). The undetermined coefficients of the symplectic series are obtained according to a generalized adjoint symplectic orthogonality. In this manner, analytical expressions for the rectangular domain with specific mixed boundary conditions are achieved in the s-domain. Highly accurate numerical results in the time domain (t-domain) are then obtained by using inverse Laplace transform. Numerical examples are given to demonstrate the efficiency and accuracy of the proposed method.

A simplified energy dissipation based model of heat transfer for subcooled flow boiling

In the paper a model is presented based on energetic considerations for subcooled flow boiling heat transfer. The model is the extension of authors own model developed earlier for saturated flow boiling and condensation. In the former version of the model we used the heat transfer coefficient for the liquid single-phase as a reference level, due to the lack of the appropriate model for heat transfer coefficient for the subcooled flow boiling. That issue was a fundamental weakness of the that approach. The purpose of present investigation is to fulfil this drawback. Now the reference heat transfer coefficient for the saturated flow boiling in terms of the value taking into account the subcooled flow conditions. The wall heat flux is based on partitioning and constitutes of two principal components, namely the convective heat flux and partial evaporation heat flux of the liquid replacing the detached bubble. Both terms are accordingly modeled. The convective heat flux is regarding vapour bubbles travelling longitudinally and the liquid moving radially – liquid pumping. The results of calculations have been compared with some experimental data from literature showing a good consistency.

Random variable transformation for generalized stochastic radiative transfer in finite participating slab media

The stochastic radiative transfer problem is studied in a participating planar finite continuously fluctuating medium. The problem is considered for specular- and diffusly-reflecting boundaries with linear anisotropic scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions, that are represented by the probability-density function (PDF) of the solution process. In the RVT algorithm, a simple integral transformation to the input stochastic process (the extinction function of the medium) is applied. This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the transport equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity and transmissivity at the medium boundaries. In terms of the average reflectivity and transmissivity, the average of the partial heat fluxes for the generalized problem with internal source of radiation are obtained and represented graphically.

Temperature distribution profiles during vertical continuous casting process

A vertical continuous casting model is considered to analysis the temperature distribution profiles during the casting process. Heat flux is applied at the interface between the liquid layer and the solid layer to overcome the deficient of insufficiency boundary conditions. By combining the general solution of time dependent heat transfer partial differential equation and heat flux at the interface generate linear systems, and linear systems determine the temperature distribution profiles at each layer. The width of liquid layer and enough time interval are important factors in controlling the casting process and yield profound influence on the mechanisms.

Radiative transfer in finite participating atmospheric aerosol media

The properties of radiation transfer through a plane-parallel atmospheric aerosol medium has been studied. It has been done by employing Mie theory to calculate the radiation transfer scattering parameters of the medium in the form of extinction, scattering, and absorption efficiencies. Then, the equation of radiative transfer through a plane-parallel atmosphere of aerosol has been solved for partial heat fluxes using two different analytical techniques, namely, the Variational Pomraning -Eddington approximation and Galerkin technique. Average efficiencies over log-normal and modified gamma size distributions are calculated. Therefore, the radiative properties of Carbon, Anthracite, Bituminous, Lignite, and Fly ash have been calculated. The obtained numerical results show very good agreement with each other in addition to the previous published work.

Radiative transfer in absorbing, emitting and isotropically scattering segregated two-layered, 3D rectangular enclosures

The exact 3-D radiative integral transfer equations (RITEs) for a rectangular absorbing, emitting and isotropically scattering, vertically segregated two-layered media are solved. The subtraction of singularity technique is used to handle singularities and to obtain the numerical solution of the RITEs. The surface and the volume integrals that arise in this method are evaluated analytically to handle the singular integrals and to reduce computational time. The enclosure is composed of two vertically-stacked layers in which the medium properties are discontinuous at the interface. The numerical integrations are carried out using sixth order Newton–Cotes quadratures along with the composite rule which assures highly accurate integration. In the numerical simulations, the optical thickness of layer-1 (τzp=0.25, 0.5, 0.75mfp) and the medium properties of both layers are varied over a wide range, and the net partial radiative heat fluxes and the incident energy distributions are obtained along the vertical centerline and specified boundary lines of the enclosures for the extinction ratios of βr=0.25 and 4. For selected enclosures and medium, five-significant-digit accurate exact solutions for the incident energy and the partial heat fluxes are also provided in tabular forms for benchmarking purposes.

Radiation transfer through atmospheric aerosol media with anisotropic scattering

Radiation transfer in atmospheric aerosol media with general boundary conditions has been studied for anisotropic scattering. The considered aerosol medium assumed to have specular and diffused reflecting boundary surfaces and in the presence of internal source. The radiation transfer scattering parameters as single scattering albedo, asymmetry factor, scattering, absorption, extinction efficiencies and anisotropic scattering coefficient have been calculated using the Mie theory. The problem with general boundary conditions is solved in terms of the solution of source-free problem with simply boundary conditions. Pomraning-Eddington approximation is used to solve the source-free problem. For the sake of comparison, a weight function is introduced and used in two special forms. The calculated partial heat fluxes with the two methods are compared and showed good agreement. Some of our results are found in a good agreement with published data.

Nodal synthetic kernel (N-SKN) method for solving radiative heat transfer problems in one- and two-dimensional participating medium with isotropic scattering

In this study, a nodal method based on the synthetic kernel (SKN) approximation is developed for solving the radiative transfer equation (RTE) in one- and two-dimensional cartesian geometries. The RTE for a two-dimensional node is transformed to one-dimensional RTE, based on face-averaged radiation intensity. At the node interfaces, double P1 expansion is employed to the surface angular intensities with the isotropic transverse leakage assumption. The one-dimensional radiative integral transfer equation (RITE) is obtained in terms of the node-face-averaged incoming/outgoing incident energy and partial heat fluxes. The synthetic kernel approximation is employed to the transfer kernels and nodal-face contributions. The resulting SKN equations are solved analytically. One-dimensional interface-coupling nodal SK1 and SK2 equations (incoming/outgoing incident energy and net partial heat flux) are derived for the small nodal-mesh limit. These equations have simple algebraic and recursive forms which impose burden on neither the memory nor the computational time. The method was applied to one- and two-dimensional benchmark problems including hot/cold medium with transparent/emitting walls. The 2D results are free of ray effect and the results, for geometries of a few mean-free-paths or more, are in excellent agreement with the exact solutions.