DESCRIPTION: This project involves theoretical and experimental analysis of gas separation systems using surface adsorption and desorption.

We have developed an advanced theoretical methodology which combines the continuous fluid flow, heat and mass transfer models of the process with the statistical mechanical model for adsorption equilibrium within a unified computational framework. Both slip and no-slip flows have been considered depending upon the dimensions of the system. Our analysis has demonstrated the vital importance of appropriate modeling of non-linear near-wall interactions between heat/mass transport and adsorption/desorption for correct predictions of the overall system dynamics. The fundamental scaling relations for characteristic time constants for the system transient response have been also obtained and verified by detailed parametric simulations.

RELEVANT PUBLICATIONS:

- Fedorov, A. and Viskanta, R., 1999, "Heat and Mass Transfer
Dynamics in the Microchannel Adsorption Reactor",
, Vol. 3, No. 2, pp. 111-140.*Microscale Thermophysical Engineering* - Fedorov, A. and Viskanta, R., 1999, "Scale Analysis and Parametric
Study of Transient Heat/Mass Transfer in the Presence of Adsorption",
, Vol. 171, pp. 231-257.*Chemical Engineering Communications: International Journal* - Fedorov, A. and Viskanta, R., 1999, "Analysis of Transient
Heat/Mass Transfer and Adsorption/Desorption Interactions",
, Vol.42, No.5, pp.803-820.*International Journal of Heat and Mass Transfer* - Fedorov, A. and Viskanta, R., 1998, "Heat/Mass Transfer and
Adsorption Dynamics in a Honeycomb Adsorbent: Application of the Simplified
Local Density Model",
, Vol.6, No.1, pp.1-10.*Thermal Science and Engineering* - Fedorov, A. and Viskanta, R., 1997, "Heat and Mass Transfer
Aspects of Gas Separation by Adsorption",
, Vol.36, No.140, pp.4-11.*Thermal Science and Engineering* - Rabovitser, J., Chudnovsky, Ya., Matsui, K., Viskanta, R., and
Fedorov, A., 1998, "Development of a Compact High Efficiency and Low Emission
Surface Combustor-Boiler",
, San Diego, California, USA.*International Gas Research Conference*

DESCRIPTION: In many practical applications ranging from drying of paper and thermal finishing of coating to chemical vapor deposition and thermal processing of silicon wafers for microelectronics to thermal management of hospital neonatal care units the objects are either stationary or moving continuously inside the reaction chamber while being heated. As an example, an infrared radiant oven for materials processing typically consists of the array of heaters/burners placed on the top, bottom and sometimes on the sides of the enclosure. Electrical resistance or gas-fired heaters are used to heat the material to a desired temperature. The heaters/burners provide a steady supply of the thermal radiation to the load as it moves inside the oven. Another example would selective laser heating of the substrate for highly controlled deposition of thin film coatings in the Laser CVD process.

The problem considered here is concerned with an inverse design of the reaction chamber capable of providing the optimal conditions for thermal treatment of the load. The technical issue is one to determine the design and operating parameters of the oven (e.g., temperatures of each heater/burner, size of the heaters, power of the laser, etc.) which satisfies the optimal performance criteria prescribed by the user (e.g., specific temperature distribution on the surface of the moving load or heating uniformity, energy efficiency, and others). Precise temperature control, according to an a-priori specified processing schedule, if often critically important to achieve desirable quality and safety of the operation. In addition, the flexibility of changing a processing schedule is also essential. The inverse optimal control algorithms combined with detailed thermal modeling of the system dynamics are paramount to intelligent and inexpensive design and operation of the system.

We have developed a transient, quasi-three-dimensional model of heat transfer in the radiant heating oven and CVD chamber coupled to the load which is moving inside of the oven as the material is thermally treated. The model considers radiation exchange between the heaters and the load, interaction between laser irradiation and heat conduction in the load, and convective heat transfer between a moving load and gaseous oven environment. The thermal model developed is then combined with the Levenberg-Marquardt nonlinear least squares optimization algorithm to find the optimal temperatures of each heater/burner, and other operating parameters which produce the temperature distribution on the surface of a load as prescribed by the process designer/operator.

RELEVANT PUBLICATIONS:

- Fedorov, A., Lee, K. and Viskanta, R., 1998, "Inverse Optimal
Design of the Radiant Heating in Materials Processing and Manufacturing",
, Vol.7, No.6, pp.719-726.*ASM Journal of Materials Engineering and Performance* - Malikov, G. K., Lobanov, D., Malikov, K. Y., Lisienko, V. G.,
Viskanta, R. and Fedorov, A., 1999, "Experimental and Numerical Study of Heat
Transfer in a Flame Jet Impingement System",
, Vol.72, pp.2-10.*Journal of the Institute of Energy* - Malikov, G. K., Lobanov, D. L., Malikov, K. Y., Lisienko, V. G.,
Viskanta, R., and Fedorov, A., 2001, "Direct Flame Impingement Heating
for Rapid Thermal Materials Processing",
, Vol. 44, No 9, pp. 1751-1758.*International Journal of Heat and Mass Transfer* - Fedorov, A. and Viskanta, R., 1997, "Direct Contact Drying of a
Moving Porous Strip",
, Vol.15, No.5, pp.1327-1351.*Drying Technology: An International Journal* - Fedorov, A. and Viskanta, R., 1996, "Heat Transfer Enhancement by
Direct Contact Drying of a Moving Porous Strip",
, Atlanta, Georgia, USA.*A. E. Bergles Symposium "Process, Enhanced and Multiphase Heat Transfer"*

DESCRIPTION: Analysis of heat transfer in cellular foam materials is critical to development modern thermal insulating materials (e.g., aerospace and construction industries), to efficient and safe operation and control of various medical and biological procedures and protocols (e.g., radiation treatment of the lung cancer), to efficiency and quality of the final product in materials processing and manufacturing (e.g., glass melting), and to advancement of monolith chemical reactors with a foam-type coating of the reactor walls by the catalyst.

We have developed theoretical models to analyze radiative heat transfer through a semitransparent (absorbing and scattering) foam blanket with application to glass and batch foams. First, an approach for calculating the effective extinction (absorption and scattering) coefficients and scattering phase function for composite materials, such as glass foams in particular, was formulated based on the bubble size distribution function and the complex indices of refraction of the material components. Then, a Schuster-Schwartzchild two-flux approximation was employed to solve a radiative transfer equation (RTE) which results in the analytical expressions for internal reflectance, transmittance, and absorptance of the plane parallel foam layer. Both cases of collimated and diffuse radiation incidence have been considered. Finally, the analytical expressions for the total apparent reflectance, transmittance, and absorptance of the foam layer have been obtained by accounting for external and internal reflecting boundaries of the layer. The combined radiation and conduction heat transfer in glass foams has also been investigated.

RELEVANT PUBLICATIONS:

- Fedorov, A. and Viskanta, R., 2000, "Radiative Transfer in a
Semitransparent Glass Foam Blanket",
, Vol. 41, No. 3, pp. 127-135.*Physics and Chemistry of Glasses* - Fedorov, A. and Viskanta, R., 2000, "Radiation Characteristics
of Glass Foams",
, Vol. 83, No. 11, pp. 2769-2776.*Journal of the American Ceramic Society* - Pilon, L., Fedorov, A. and Viskanta, R., 2000, "Gas Diffusion
in Closed-Cell Foams",
, Vol. 41, No. 3, pp. 127-135.*Journal of Cellular Plastics* - Pilon, L., Fedorov, A., and Viskanta, R., 2001, "Steady-State
Thickness of Liquid-Gas Foams",
, Vol. 242, No. 2, pp. 425-436.*Journal of Colloid and Interface Science* - Pilon, L., Fedorov, A., and Viskanta, R., 2002, "Analysis of
Transient Thickness of Pneumatic Foams",
, Vol. 57, pp. 977-990.*Chemical Engineering Science* - Fan, T. H. and Fedorov, A. G., 2002, "Radiative Transfer in a
Semitransparent Hemispherical Shell",
, Vol. 73, pp. 285-296.__Journal of Quantitative Spectroscopy and Radiative Transfer__ - Varady, M. and Fedorov, A. G., 2002, "Combined Radiation and
Conduction in Glass Foams",
, Vol. 124, No. 6, pp. 1103-1110.__ASME Journal of Heat Transfer__ - Fan, T. H. and Fedorov, A. G., 2002, "Apparent Radiative Properties and Radiation Scattering by a Semitransparent Hemispherical Shell",
, Vol. 124, No. 6, pp. 1103-1110.__ASME Journal of Heat Transfer__ - Fedorov, A. G. and Pilon, L, 2002, "Glass Foams: Formation,
Transport Properties, and Heat, Mass, and Radiation Transfer",
, Vol. 311, pp. 154-173..*Journal of Non-Crystalline Solids*

DESCRIPTION: Design of the efficient and compact heat dissipation devices is paramount to sustaining a continuous growth at almost a geometric progression rate in performance of the leading-edge microelectronic products. The electronic packages typically operate at very high average heat fluxes (10 W/cm^2 and 25 W/cm^2 for plastic DIP and ceramic PGA, respectively) and, for stable and reliable operation, must be maintained at the temperature below of about 130 degrees Celsius. A number of cooling techniques are currently employed by the semiconductor industry for heat dissipation in everything from the mainframe to portable computers. These include the extended surfaces (fins) with turbulators, the highly parallel air and liquid impingement systems, modular internal conduction enhancement, indirect and direct liquid cooling with water and dielectric coolants, respectively, and, finally, the special cooling systems such as the heat pipes and liquid metal heat sinks.

We have developed and validated theoretical models for heat transfer in two novel electronic cooling systems such as porous and microchannel based heat sinks. The porous heat sink explores an advantage of the very large specific surface area available for heat removal from the electronic package, while microchannel heat sink utilizes a drastic decrease in convective resistance to heat transport (due to reduction in the boundary layer thickness) to enhance cooling rates. From the fundamental point of view, our analysis has revealed very complex flow and heat transfer pattern established in the both heat sinks, and demonstrate an importance of accounting for conjugate effects for correct predicting performance of heat sinks. Extremely large transverse and longitudinal temperature gradients have been predicted within the solid walls in the immediate vicinity of the inlet to the microchannel heat sink inlet. This has a potential for significant thermal stresses and structural failure of the heat sink and, therefore, must be addressed in the heat sink design by performing detailed thermomechanical calculations.

RELEVANT PUBLICATIONS:

- Fedorov, A. and Viskanta, R., 2000, "Three-Dimensional Conjugate
Heat Transfer in the Microchannel Heat Sink for Electronic Packaging",
, Vol. 43, pp. 399-415.*International Journal of Heat and Mass Transfer* - Fedorov, A. and Viskanta, R., 1999, "Analysis of Conjugate Heat
Transfer in a Three-Dimensional Microchannel Heat Sink for Cooling of
Electronic Components",
, Nashville, Tennessee, USA.*Int. Mech. Eng. Congress and Exhibition IMECE'99* - Fedorov, A. and Viskanta, R., 1997, "A Numerical Simulation of
Conjugate Heat Transfer in Electronic Package Formed by Embedded Discrete
Heat Sources in Contact with a Porous Heat Sink",
, Vol.119, pp.8-16.*ASME Journal of Electronic Packaging*

DESCRIPTION: Wet (liquid) foams are frequently encountered in different applications ranging from bioprocessing (e.g., protein purification) to materials processing (e.g., glass melting and casting). They are formed at the liquid-gas interface due to entrapment of gas bubbles rising to the surface after being generated by agitation or by the chemical reactions taking place in the liquid, or simply being injected into solution by others means. In most cases, foams are undesirable for various reasons (e.g., provide resistance to heat transfer in glass melting furnaces), so that understanding of origins and characterisitics of the foam is essential for proper operation and control of underlying technological processes. We have developed a series of experimentally validated models to predict formation, stability, and decay of wet foams as well as their effective transport properties.

RELEVANT PUBLICATIONS:

- Pilon, L., Fedorov, A. and Viskanta, R., 2000, "Gas Diffusion
in Closed-Cell Foams",
, Vol. 41, No. 3, pp. 127-135.*Journal of Cellular Plastics* - Pilon, L., Fedorov, A., and Viskanta, R., 2001, "Steady-State
Thickness of Liquid-Gas Foams",
, Vol. 242, No. 2, pp. 425-436.*Journal of Colloid and Interface Science* - Pilon, L., Fedorov, A., and Viskanta, R., 2001, "Analysis of
Transient Thickness of Pneumatic Foams",
, Vol. 57, pp. 977-990.*Chemical Engineering Science* - Fedorov, A. G., "Heat and Mass Transfer in Glass Foams",
, Calcutta, India, January 2002.__5th ISHMT/ASME Heat and Mass Transfer Conference__ - Fedorov, A. G. and Pilon, L, 2002, "Glass Foams: Formation,
Transport Properties, and Heat, Mass, and Radiation Transfer",
, Vol. 311, pp. 154-173.*Journal of Non-Crystalline Solids*

DESCRIPTION: The cost and quality of nearly all commercial glass products are determined by the performance of the glass melting and delivery systems (furnaces). The processes taking place in the glass melting furnaces are extremely complex and involve turbulent flow, heat and mass transfer, and combustion in the combustion chamber, the buoyancy-driven flow and heat/mass transfer of the molten glass in the glass tank, and fusion and melting of raw materials in the batch. The lack of fundamental understanding of the complex physics and chemistry of the batch fusion/melting processes as well as an absence of thermophysical and rheological properties of the batch raw materials impose severe limitations on the fidelity and feasibility of mathematical models which are based on deterministic representation of the physics. Therefore, it is not surprising that modeling of the batch heating and melting has been largely accomplished by using the empirical or semi-empirical techniques.

We have developed a stochastic (probabilistic) model of the batch transport, fusion and melting using the generalized Brownian diffusion process (due to batch dispersion) with probability jumps (due to batch fusion and melting) and deterministic drift (due to local batch motion). The parameters of the model are determined through an inverse parameter estimation procedure by using the experimental data obtained from the digitized and processed video film depicting the batch dynamics in the actual operating furnace.

RELEVANT PUBLICATIONS:

- Fedorov, A. and Viskanta, R., 2000, "Batch Rheology and
Transport in Glass Melting Furnaces",
, DOE Project "Future of the Glass Industry".*Purdue-ANL Technical Report* - Fedorov, A., Jorgensen, K., and Viskanta, R., 1999, "A
Probabilistic Approach to Modeling of Batch Fusion/Melting Dynamics
in Glass Melting Furnaces",
, DOE Project "Future of the Glass Industry".*Purdue-ANL Technical Report* - Fedorov, A., Jorgensen, K., and Viskanta, R., 1999, "A
Quasi-Three-Dimensional Phenomenological Model of Batch Transport,
Fusion and Melting and Foam Formation in Glass Melting Furnaces",
, DOE Project "Future of the Glass Industry".*Purdue-ANL Technical Report*

DESCRIPTION: The quality of glass products is degraded if the small gas bubbles remain in the molten glass as it is being pulled out of the furnace. In addition, prediction of the bubbling rate at the molten glass/combustion space interface is critical for determining the local thickness of the foam layer which provides significant resistance to radiative heat transfer from the combustion products to the glass tank. Therefore, understanding and modeling of bubble generation and transport in the glass melt are of great practical interest to the glass industry.

We have developed a phenomenological model of the bubble generation and transport in the glass melt that accounts for gas generation in the batch and glass melt due to refining reactions, advection and diffusion of major gas species in the glass melt, heterogeneous bubble nucleation in the batch and in the glass melt, and gas exchange between the bubbles and molten glass. In addition, the changes in size (radius) of bubbles (i.e., the size distribution function), as they grow or shrink while being carried by the glass current through the regions of varying temperatures, species concentrations, and pressures, are predicted using the population balance theory.

RELEVANT PUBLICATIONS:

- Pilon, L., Fedorov, A.G., Ramkrishna, D., and Viskanta, R.,
2002, "Bubble transport in three-dimensional laminar gravity-driven flow -
mathematical formulation",
(in review).*Journal of Non-Crystalline Solids*

DESCRIPTION: Heat transfer augmentation through cooling associated with liquid evaporation in turbulent mixed convection is important in many engineering applications. Notable examples include cooling towers, waste heat disposal in process industry, and passive cooling of the containment of advanced nuclear reactors in the case of severe accidents.

We have developed a theoretical model of combined heat and mass transfer to a turbulent gas stream in countercurrent flow from a thin liquid film falling along a vertical wall of an asymmetricaly heated parallel-plate channel. The natural, mixed and forced convection flow regimes are considered, and the low-Reynolds number k-eps turbulence model is used to simulate turbulent transport. Our analysis has revealed a complex flow structure developed in the channel with the solutal buoyancy force being as important as the thermal one. Also, as it follows from the analysis, the analogy of heat and mass transfer breaks down even at low Reynolds number laminar flow regime due evaporation/condensation induced mass injection/suction at the film/air interface. The fundamental scaling relations between Nu/Sh vs. Gr/Re and Pr/Sc numbers have also been developed to gain fundamental understanding of the process.

RELEVANT PUBLICATIONS:

- Kim, Y. J. and Fedorov, A. G., 2002, "Transient Mixed Radiative
Convection Flow of a Micropolar Fluid Past a Moving, Semi-Infinite Vertical
Porous Plate",
(in press).*International Journal of Heat and Mass Transfer* - Fedorov, A. and Viskanta, R., 1997, "Turbulent Natural Convection
Heat Transfer in an Asymmetrically Heated, Vertical Parallel-Plate Channel",
, Vol.40, No.16, pp.3849-3860.*International Journal of Heat and Mass Transfer* - Fedorov, A., Viskanta, R. and Mohamad, A., 1997, "Turbulent Heat
and Mass Transfer in an Asymmetrically Heated, Vertical Parallel-Plate
Channel",
, Vol.18, No.3, pp.307-315.*International Journal of Heat and Fluid Flow*

DESCRIPTION: Design, construction, and operation of large energy systems (e.g., power plants, industrial furnaces, combustion chambers for different purposes) require considerable capital expenditures, and this makes a purely experimental approach to preliminary design optimization hardly visible. In addition, operation testing of such systems is associated with significant implementation difficulties and costs. Therefore, the fundamental thermoeconomic analysis and mathematical simulations combined with the experimental methods provide valuable alternative to solving the optimal energy management and environmental protection problems.

We have developed a new simplified approach to optimal energy management in industrial fuel-to-energy conversion systems which accounts for economic (due to capital expenditures) and operating (due to fuel consumption) costs associated with the system design, construction, and operation. In addition, our approach takes into account the environmental cost of harmful pollutants. In contrast to more sophisticated and comprehensive thermoeconomic approaches, our model allows one to obtain a closed-form analytical solution and, thus, to estimate quickly the optimal operating conditions during the preliminary design of fuel-to-energy conversion systems.

RELEVANT PUBLICATIONS:

- Lisienko, V. and Fedorov, A., 2000, "A Simplified Approach to
Optimal Energy Management under Capital and Ecological Constraints",
(in review).*Energy Economics* - Lisienko, V., Viskanta, R. and Fedorov, A., 1996, "Fundamental
Formulation of the Prognosis and Control Model for Energy and Ecology in the
Power Technology Units",
, Ekaterinburg, Russia.*International Seminar "Modeling, Advanced Process Technology, Expert and Control Systems in Heat and Mass Transfer"*

DESCRIPTION: Combined heat and mass transfer phenomena in porous media relate to many engineering technologies such as drying, ground water hydrology, materials processing, thermally enhanced oil recovery, nuclear reactor safety, geothermal energy utilization and others. The problem considered here is concerned with enhancement of heat and mass transfer during drying through direct contact between the heat source and a moving porous strip which is fully or partially saturated with water. Direct contact heat transfer and direct contact drying have been long recognized as being efficient heat transfer processes. The technical issues are to determine the effectiveness of such a scheme and to develop the optimal control strategies for heating and drying a continuous, moving strip of material while maintaining good thermal contact between the porous load and the heat source. Surprisingly, knowledge of combined heat and mass transfer and evaporation dynamics in the system described is very limited.

We have developed a transient, quasi-two-dimensional model of conjugate heat and mass transfer between a hot massive externally/internally heated plate and wet porous strip moving along the plate is developed by accounting for evaporation dynamics. The model consists of four conjugate energy conservation equations with proper boundary/interface conditions which describe the heat transfer in four distinct zones (1-electrically or indirectly heated massive metal plate, 2-thin superheated vapor film resulting from vaporization of water in the porous strip that separates hot plate and porous strip, 3-dry region of the porous strip, and 4-wet region of the porous strip). The relevant dimensionless parameters governing the problem have been identified, and parametric calculations have been performed to gain fundamental understanding of the process. In particular, the results indicate that the initial heater temperature, the Stefan number (Ste), the vapor film thermal resistance (R_t), and the Biot number (Bi) are the parameters producing the first order effects on the system drying dynamics.

RELEVANT PUBLICATIONS:

- Fedorov, A. and Viskanta, R., 1997, "Direct Contact Drying of a
Moving Porous Strip",
, Vol.15, No.5, pp.1327-1351.*Drying Technology: An International Journal* - Fedorov, A. and Viskanta, R., 1996, "Heat Transfer Enhancement by
Direct Contact Drying of a Moving Porous Strip",
, Atlanta, Georgia, USA.*A. E. Bergles Symposium "Process, Enhanced and Multiphase Heat Transfer"*

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