Examples of Two Scale Experimental Approaches. Data Collection and Reduction for Experiments on Coefficients of Thermal Conductivity in Superlattices and Heat Exchange for Heat Sinks

There was recognition that the experiments and their analysis for homogeneous and heterogeneous media should be modeled differently. The basic studies in the field of heterogeneous scaled energy transport brought the understandings of the theoretical basis for experimental set-ups for heterogeneous hierarchical media. It is well known that the scale of measurements and of the modeling must correspond one to another. This obvious and simple principle is violated when what is clearly a two scale physical problem is described on the upper (measurement) scale with the same kind homogeneous mathematics as is used for the lower scale. Substitution of effective coefficients into models of this type is the primary question that must be dealt with.

Analysis of the known methods of reduction of the experimental results for the heat and momentum transport experiments and development of the VAT based methodology for data reduction in porous media were made. Consistency of the experimental effort and the modeling of the process was emphasized. Common questions of applicability of the experimental data and experimental data reduction was stressed based on the new theoretical basis for modeling of experiments in heterogeneous media. Particularly much of study was done on pressure loss, heat exchange coefficients, and heat conductivity coefficients. Pressure loss and heat transfer experiment analysis procedure developed using VAT as the tool for model formulation and for porous media experimental data reduction -

  • " How Many Internal Heat Transfer Coefficients and the Conductivities Can be Measured?(1020k)"

  • Developed the fundamentals of Two-Scale Heterogeneous Experimental Technique for Parameters Measurements and Design the volumetric convection heat dissipation devices. This technique was used for semiconductor heat sinks evaluation and comparison purposes. Obtained the exact relationships and improvements to the widely used in industry parameters of heat exchange performance and shown their flaws in terms of assessment and comparison with physical laws. In an effort to relate the scaled volume average theory (VAT) description and simulation of heat transfer devices (heat sinks) to experimental measurements, there were developed a process of coupling two scale Detailed Micro-Modeling - Direct Numerical Modeling (DMM-DNM) and their corresponding experimental results for few designs of heat sink. It is a problem to properly relate the available local measurements to VAT closure and to measurements within the volume of the heat exchanger (sink). The measurement methods were specified and used for the local and bulk variables data for simulation of the additional terms in the VAT upper scale governing equations.

  • Described in detail how, and for what reasons, the measured data are to be simulated or measured and represented in a way that allows design goals to be formulated primarily with averaged (or bulk) physical characteristics. Demonstrated why studies of only averaged local integrated variables are not enough. Five sample semiconductor heat sinks of three morphologies were studied by different techniques and models. There were changes in by-pass values, external heat flux and flow rate. Results were depicted using new parameters that better represent the needs of a design process for two-scale devices as well as the usual parameters used in the past. Characteristics reported for the first time are the heat transfer rate in solid phase, relative solid phase effectiveness, and influence of only morphology features among others.

  • "Semiconductor Coolers "

  • The two scale VAT description equations applicable to the problem have four additional descriptive terms in the momentum equation (for the 1D turbulent equation), seven terms in the fluid temperature equation, and five additional terms in the solid phase (reflecting heat transport through ribs, pins) temperature equations. These additional terms provide far more information about the heat sink and its design than the usual homogeneous models. Most of the additional terms in the VAT equations are terms which based on effects of interface phenomena and field fluctuations acting in the phase. There is, however, a lack of experimental results and data reduction procedures particularly developed for the purpose of experimental closure or verification of VAT heat exchanger governing equations. Contrary to a numerical simulation experiment, the physical experiment is usually much more restrictive in terms of the number and location of local experimental points. There were provided the simulation using the commercial software packages along with the custom developed computational subroutines and user interface. The simulation results were in good comparison with experiments.

  • Developed Scaled Concepts to Address the Issues of Nanoscale Multiphysics Heat Conductivity Measurement Techniques in electronic materials. The two methods usually applied toward these tasks are made in terms of hierarchical scaled theory of VAT. It has been reported in a number of publications that measured values of superlattice thermal conductivities, for example, GaAs/AlAs, Si/Ge, InAs/AlSb, etc., do not compare well with expected or modeled values. There are questions about measurement techniques that are used and some improvements have been suggested for simulation of the process. One of the used techniques is the 3(omega) measurement of thermal conductivity of superlattices. Another is the Scanning Laser Thermoelectric Microscope (SLTM) technique used for measurement of thermal conductivity and diffusivity of thin films.

  • "Heat Transfer Experiments in Heterogeneous Media"

  • The full two-scale heat transport and electrodynamics governing equations were used to achieve understanding of the possible mechanisms that play a role in shaping the effective (measured) coefficients of thermal and electrical conductivities in superlattices. It is shown that the issues of simulation or measurement of the effective coefficients at the upper scale are essentially the same as simulation of the complete two-scale problem in its complexity. Some of these concerns have been dealt with and published in our work, some are in this website -

  • Thermal_Physics/Effective_Thermal_Properties

    Now we can state that the path to the physically and mathematically correct procedures, methods of design and Scaled Optimization of Heterogeneous structures as - superlattices, heat exchangers, etc. has been opened.

    The one thing is obvious and should be understood - that the workload, amount of measurement procedures, general design of Heterogeneous Two-scale (at least) Experiments are much larger and quite different than of the One scale Homogeneous ones. That is the cost for more exact scientific language, for future findings, for progress.


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