Difference Scheme for Hyperbolic Heat Conduction Equation with Pulsed Heating Boundary

horotctionIt is well known that the basic law of heatconduction is the Fourier law. It has the formq = --k' vT, and one-dimensional heat conduchondifferenhal equation is. The aboveequations are derived from the hypothesis that thevelocity to establish the thermal balance is infinitelygreat. In the modem heat conduchon theory heattransacts in materials in a licited velocity. The factorsto affect the velocity are the thermal propelles of thematerials. In order tO describe this Problem, the sch…     

Study on local resistance of non-Newtonian power law fluid in elbow pipes

This paper focuses on the flow characteristic and local resistance of non-Newtonian power law fluid in a curved90° bend pipe with circular cross-sections,which are widely used in industrial applications.By employing numerical simulation and theoretical analysis the properties of the flow and local resistance of power law fluid under different working conditions are obtained.To explore the change rule the experiment is carried out by changing the Reynolds number,the wall roughness and different diameter ratio of elbow pipe.The variation of the local resistance coefficient with the Reynolds number,the diameter ratio and the wall roughness is presented comprehensively in the paper.The results show that the local resistance force coefficient hardly changes with Reynolds number of the power law fluid;the wall roughness has a significant impact on the local resistance coefficient.As the pipe wall roughness increasing,the coefficient of local resistance force will increase.The main reason of the influence of the roughness on the local resistance coefficient is the increase of the eddy current region in the power law fluid flow,which increases the kinetic energy dissipation of the main flow.This paper provides theoretical and numerical methods to understand the local resistance property of non-Newtonian power law fluid in elbow pipes.     

Heat Transfer and Fluid Flow over a Single Disk in a Fluid Rotating as a Rigid Body

Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a solid body at β= Ω/ω= const. Radial variation of the disk's surface temperature follows a power law. An exact numerical solution of the problem is obtained basing on the self-similar profiles of the local temperature of fluid, its static pressure and velocity components. Numerical computations were done at the Prandtl numbers Pr = 1(?)0.71. It is shown that with increasing βboth radial and tangential components of shear stresses decrease, and to zero value at β= 1. Nusselt number is practically constant at β= 0(?) 0.3 (and even has a point of a maximum in this region); Nu decrease noticeably for larger βvalues.     

Quantification on the Effects of Liquid-Vapor Separation in Air-Conditioning System by using Advanced Exergy Analysis

Air-conditioning system consumes a large amount of electricity in residential sections,and its efficiency has drawn extensive concerns in energy-conscious era.Liquid-vapor separation is a heat transfer enhancement technology that can effectively improve the performance of the heat exchanger as well as the system.In this paper,a regular air-conditioning system as the baseline(system-A)and other two air-conditioning systems with liquid-vapor separation heat exchanger(system-B and system-C)are comparatively studied.The component behaviors and system performances are deeply explored by using advanced exergy analysis with a focus on quantifying how much consequences come from the variants,i.e.liquid-vapor separation.The results indicate that the system-B has large reduced exergy destruction from the compressor and condenser at cooling mode relative to the system-A.The system-C has mainly diminished exergy destruction in the compressor caused by other components relative to the system-B.At heating mode,the system-C has an enhanced system exergy efficiency of 9.6%over the system-A,and it also has the decreased avoidable exergy destruction which is dominantly contributed by the compressor and evaporator.Furthermore,it is found that liquid-vapor separation mainly benefits the compressor and outdoor heat exchanger where it locates,leading to the system performance improvements.     

Experimental Study on Jet Blast at Laboratory Scale

The flow field of 3D （three-dimensional） wall-jet is investigated. Jet-blast from airplane is simulated by wall-jet setup using a sonic nozzle at a laboratory scale. Farfield velocity and fluctuation distributions are measured by using X-type hot wire anemometer at four measurement planes. As a result, the flow properties of streamwise component are consistent with data which are obtained in previous researches. The secondary flow is also measured on each measurement plane. Reynolds stresses, v＇v＇ and w＇ w＇, are analyzed from the fluctuation of the secondary flow. The law of similarity is observed in the dimensionless distributions of mean velocity and fluctuation. However, the distributions in nearer field （i.e., in the measurement plane at X/D = 100） tend to disobey the similarity law, especially in the cases of fluctuation. It seems that jet-blast is not fully developed by reaching X/D = 100. The experimental results are compared with computational results which are obtained by CFD （computational fluid dynamics） with SST （shear-stress transport） turbulence model. And it is shown that the results by the simulation with SST turbulence model do not follow the similarity law. The present database of the Reynolds stresses is critically important for development of a new turbulence model of RANS （reynolds-averaged navier-atokes） simulations on wall-jet.     

Hysteretic Phenomenon of Shock Wave in a Supersonic Nozzle

In recent years, hysteretic phenomena in fluid flow systems drew attention for their great variety of industrial and engineering applications. When the high-pressure gas is exhausted to atmosphere from the nozzle exit, the expanded supersonic jet with the Mach disk is formed at a specific condition. In two-dimensional expanded supersonic jet, the hysteresis phenomenon for the reflection type of shock wave is occurred under the quasi-steady flow and the transitional pressure ratio between the regular reflection and Mach reflection is affected by this phe- nomenon. However, so far, there are very few researches for the hysteretic phenomenon of shock wave in a supersonic internal flow and the phenomenon has not been investigated satisfactorily. The present study was concemed with the experimental and numerical investigations of hysteretic phenomena of shock wave in a supersonic nozzle, and discussed the relationship between hysteresis phenomenon and rate of the change of pressure ratio with time.     

From California to the New York Island： Is this land made for you and me？

A fundamental aspect of America＇s identity is built upon the narrative that the overwhelming majority were immigrants. Everybody, at some point, whether their background is from Europe, Africa, Asia or Latin America, went through the imanigrant＇s experience, coming to America＇s shores or borders in search of freedom, opportunity, and a better life. Essentially, that is what America is all about. Beating that in mind, the importance of the bill intending to put millions of illegal immigrants on the path to citizenship represents a milestone for the American people. The reform previously thought as something impossible to pass through Congress and become law now has tremendous momentum and unprecedented levels of bipartisan support. The only challenge remaining facing this bill is a handful of Republicans in the House of Representatives, viewing it as an unjustified amnesty to people who willingly broke the law, and thus deeming it a mistake. While this represents an obstacle, so far it is unlikely the bill will be derail as seemingly the majority of Republicans, especially those who want to attract more Hispanic into their lines.     

An Extraction of the Dominant Rotor-Stator Interaction Modes by the Use of Proper Orthogonal Decomposition （POD）

The Proper Orthogonal Decomposition method is applied to the instantaneous velocity field within the rotor-stator inter-row region of a high-speed high-pressure centrifugal compressor. The processed data come from experiments and numerical simulations. In comparison with a Fourier transform, the POD gives the best modal approximation for both initial fields, in terms of the energy expressed on any given number of modes to be taken into account: to reach 98% of the total energy of the velocity field, the required number of POD modes is around nine times smaller than the number of Fourier harmonics. The individual POD modes are given and show that the unsteady rotor-stator interaction is already present in the very first modes.     

Developing a knock predictive criterion in spark ignition engines fuelled with gaseous fuels

Consideration of the chemical reaction activity of the end gas in a spark ignition and operating conditions are combined to predict the onset of knock and associated performance in an engine fuelled with methane.A two-zone predictive combustion model was developed based on an estimate of the effective duration of the combustion period and the mass burning rate for any set of operating conditions.The unburned end gas preignition chemical reaction activity is described by a detailed chemical reaction kinetic scheme for methane and air,The variation with time of the value of a formulated dimensionless knock parameter(k)is calcuated.It is shown that whenever knocking is encounteren.the value of “k” builds up to a sufficiently high value that exceeds a critical value.Under normal operating conditions,the value of “k” remains throughout the whole combustion period at comparatively very low levels.It is shown that the model and the use of this knock criterion“k” produce results that are in good agreement with experiment.     

Modeling Abrasion Forces in a Pneumatically Powered Grinding Tool Using Compressible Large Eddy Simulation

This paper describes the design of a new kind of miniature abrading sphere, which is magnetically mounted inside a spherical gap and set in rotation pneumatically with air. Large eddy simulation is performed in conjunction with the compressible Smagorinsky model. Minimal temperature variation allows for the assumption of adiabatic walls. Fluid-solid interaction is modeled using the law of the wall for compressible turbulent flow. A parametric study is done to determine optimal geometric layout while taking physical restrictions into account. The resulting optimal configuration is then examined in detail in order to determine demands to be met by the computerized control of the magnetic bearing as well as to quantify the force available to the abrasion process. Finally, a mathematical relation is given that determines available abrasion force depending on standard volumetric flow rate and rotation frequency. The findings presented here provide a basis for further development of smaller versions of the tool.     

A new numerical method to simulate the non-Fourier heat conduction in a single-phase medium

Many non-equilibrium heat conduction processes can be described by the macroscopic dual-phase lag model (DPL model). In this paper, a numerical method, which combines the dual reciprocity boundary element method (DRBEM) with Laplace transforms, is constructed to solve such mathematical equation. It is used to simulate the non-Fourier phenomenon of heat conduction in a single-phase medium, then numerically predict the differences between the thermal diffusion, the thermal wave and the non-Fourier heat conduction under different boundary conditions including pulse for one- and two-dimensional problems. In order to check this numerical method's reliability, the numerical solutions are still compared with two known analytical solutions.     

Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance

The non-Fourier transient heat conduction in a finite medium under arbitrary periodic surface thermal disturbance is investigated analytically. In order to obtain the desired temperature field from the known solution for non-Fourier heat conduction under a harmonic disturbance, the principle of superposition along with the Fourier series representation of an arbitrary periodic function is employed. The developed method can be applied for more realistic periodic boundary conditions occurred in nature and technology.     

3-Omega Method for Thin Films with the Non-Fourier Boundary Condition

The effect of non-Fourier boundary condition on the 3-omega method for measuring the thermal conductivity of microscale thin films using the hyperbolic heat conduction equation and the Fourier equation is examined. Non-Fourier boundary condition with the Fourier equation leads to 80% error in the temperature oscillations and increases the error to 85% in the case of non-Fourier boundary condition with the hyperbolic heat conduction equation. The solution of the non-Fourier boundary condition with the hyperbolic heat conduction equation gives the most accurate thermal conductivity expression. The analysis also provides a method for determining the relaxation time of thin films.     

Lattice Boltzmann Method Applied to the Solution of Energy Equation of a Radiation and Non-Fourier Heat Conduction Problem

This article concerns the application of the lattice Boltzmann method (LBM) to solve the energy equation of a combined radiation and non-Fourier conduction heat transfer problem. The finite propagation speed of the thermal wave front is accounted by non-Fourier heat conduction equation. The governing energy equation is solved using the LBM. The finite-volume method (FVM) is used to compute the radiative information. The formulation is validated by taking test cases in 1-D planar absorbing, emitting, and scattering medium whose west boundary experiences a sudden rise in temperature, or, with adiabatic boundaries, the medium is subjected to a sudden localized energy source. Results are analyzed for the various values of parameters like the extinction coefficient, the scattering albedo, the conduction-radiation parameter, etc., on temperature distributions in the medium. Radiation has been found to help in facilitating faster distribution of energy in the medium. Unlike Fourier conduction, wave fronts have been found to reflect from the boundaries. The LBM-FVM combination has been found to provide accurate results.     

Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux

Presented is the analysis of non-Fourier effect in a hollow sphere exposed to a periodic boundary heat flux. The problem is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at outer and inner surfaces of the sphere are evaluated for various thermal relaxation times. By comparing the results of non-Fourier model with those obtained from Fourier heat conduction equation, the transition process from parabolic model to hyperbolic one is shown. The phase difference and amplitude ratio of boundary surfaces are calculated as functions of the thermal relaxation time and the results are depicted graphically.     

Fourier and non-Fourier heat conduction analysis in the absorber plates of a flat-plate solar collector

This paper presents an analytical analysis of both Fourier and non-Fourier heat conduction in the absorber plates of a flat-plate solar collector. Separation of variables was employed to develop the model. For the analysis, a repetitive heat transfer module was used for the solution of parabolic and hyperbolic equations. From the practical point of view, two types of boundary conditions were separately chosen. A numerical technique based on the finite difference method was employed to determine the temperature for validation purposes. A comparative investigation was carried out to understand the requirements for use of the non-Fourier heat conduction model easily. A significant difference in the temperatures obtained from the Fourier and non-Fourier models was observed for lower values of the Fourier number and higher values of the Vernotte number. Finally, the effect of the boundary conditions on the Fourier and non-Fourier heat transfer was demonstrated.     

Analysis of Non-Fourier Conduction-Radiation Heat Transfer in a Cylindrical Enclosure

This article deals with the analysis of non-Fourier conduction and radiation heat transfer in a participating medium contained between 1-D concentric cylinders. The conducting-radiating medium is radiatively absorbing, emitting, and scattering. The non-Fourier effect is analyzed by suddenly perturbing the temperatures of the concentric cylinders. With radiative information computed using the finite volume method, the finite difference method is used to solve the hyperbolic energy equation. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the emissivity and the radius ratio are studied on the temporal evolution of temperature field in the medium. These parameters have been found to significantly influence the temporal temperature field, and non-Fourier effects are captured well. For non-Fourier conduction and Fourier conduction–radiation cases, results have been benchmarked against those available in the literature. A good comparison has been observed. In case of non-Fourier conduction-radiation, for some sample cases, the steady-state temperature distributions have been compared against those available in the literature. Results have been found to agree well.     

An axisymmetric bioheat transfer analysis through a unified model

A unified model is developed for the analysis of heat transfer (radiation and non-Fourier conduction) in an axisymmetric participating medium. The proposed model includes three different variants of hyperbolic–parabolic heat conduction models, that is, the single phase lag model, dual phase lag model, and the Fourier (no phase lag) model. The radiating-conducting medium is radiatively absorbing, emitting, and isotropically scattering. Significance of all the above mentioned models on the heat transfer characteristics is investigated in a two-dimensional axisymmetric geometry. The equation of transfer and the coupled non-Fourier conduction-radiation equation are solved via finite volume method. A fully implicit scheme is used to resolve the transient terms in the energy equation. For spatial resolution of radiation information, the STEP scheme is applied. Tri-diagonal-matrix-algorithm is used to solve the resulting set of linear discrete equations. Effects of two important influencing parameters: the scattering albedo and the radiation- conduction parameter are studied on the temporal evolution of temperature field in the radiatively participating medium. The non-Fourier effect of heat transport captured well with the proposed unified model. A good agreement can be found between the proposed model predictions and those available in the literature. It is also found that when the phase lag of the temperature gradient and the heat flux are the same, it reduces to conventional Fourier conduction-radiation and the wave behavior diminishes. However, the reduction to this Fourier model fails in the presence of constant blood perfusion and metabolic heat generation.     

NON-FOURIER HEAT CONDUCTION PHENOMENA IN POROUS MATERIAL HEATED BY MICROSECOND LASER PULSE

Experiments on porous material heated by a microsecond laser pulse and the corresponding theoretical analysis are carried out. Some non-Fourier heat conduction phenomena are observed in the experimental sample. The experimental results indicate that only if the thermal disturbance is strong enough (i.e., the pulse duration is short enough and the pulse heat flux is great enough) is it possible to observe apparent non-Fourier heat conduction phenomenon in the sample, and evident non-Fourier heat conduction phenomenon can only exist in a very limited region around the thermal disturbance position. The hyperbolic heat conduction (HHC) equation and the dual-phase lag (DPL) model are employed, respectively, to describe the non-Fourier heat condution process happening in the experimental sample, and the finite-difference method (FDM) is used to solve them numerically. The numerical solutions show that both the HHC equation and the DPL model can predict the non-Fourier heat conduction phenomenon emerging in the experimental sample qualitatively. Moreover, if τ_q and τ_T are assumed to have suitable values, the theoretical result of the DPL model is more agreeable to the experimental result.     

Identification of boundary conditions for non-Fourier heat conduction problems by differential transformation DRBEM and improved cuckoo search algorithm

Abstract

The differential transformation method is combined with the dual reciprocity boundary element method to solve the non-Fourier heat conduction problems in functionally gradient materials. The cuckoo search algorithm is improved by the Broyden–Fletcher–Goldfarb–Shanno algorithm to identify the boundary conditions for the heat conduction problems. The polynomial function related to coordinate and time is proposed to approximate the unknown boundary conditions. Numerical examples discuss the influences of measurement point numbers and measurement errors on inverse solutions. Numerical results demonstrate the effectiveness and accuracy of the proposed method.