Jayathi Y. Murthy

Handbook of numerical heat transfer

A comprehensive presentation is given of virtually all numerical methods that are suitable for the analysis of the various heat transverse and fluid flow problems that occur in research, practice, and university instruction. After reviewing basic methodologies, the following topics are covered: finite difference and finite element methods for parabolic, elliptic, and hyperbolic systems; a comparative appraisal of finite difference versus finite element methods; integral and integrodifferential systems; perturbation methods; Monte Carlo methods; finite analytic methods; moving boundary problems; inverse problems; graphical display methods; grid generation methods; and programing methods for supercomputers.

A PRESSURE-BASED METHOD FOR UNSTRUCTURED MESHES

Abstract This article presents a finite-volume scheme for multidimensional incompressible flows. Unstructured, solution-adaptive meshes composed of arbitrary convex palyhedra are used. A cell-centered equal-order formulation is developed. Gradients required for the evaluation of diffusion fluxes and for second-order-accurate convective operators are found by linear reconstruction. An additive-correction multigrid scheme is used to solve the resulting discrete equations. Pressure and velocity are stored at cell centers; momentum interpolation is used to prevent pressure checkerboarding. The SIMPLE algorithm is used for pressure-velocity coupling. Schemes for hanging-node and conformed adaption are implemented. The scheme is applied to benchmark problems using a variety of quadrilateral/hexahedral, triangular/tetrahedral, and hybrid meshes, and is shown to perform satisfactorily.

Thermal Challenges in Next-Generation Electronic Systems

Thermal challenges in next-generation electronic systems, as identified through panel presentations and ensuing discussions at the workshop, Thermal Challenges in Next Generation Electronic Systems, held in Santa Fe, NM, January 7-10, 2007, are summarized in this paper. Diverse topics are covered, including electrothermal and multiphysics codesign of electronics, new and nanostructured materials, high heat flux thermal management, site-specific thermal management, thermal design of next-generation data centers, thermal challenges for military, automotive, and harsh environment electronic systems, progress and challenges in software tools, and advances in measurement and characterization. Barriers to further progress in each area that require the attention of the research community are identified.

Submicron Heat Transport Model in Silicon Accounting for Phonon Dispersion and Polarization

In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the submicron scale. However, most published studies make a gray assumption and do not account for either dispersion or polarization. In this study, we propose a model based on the BTE, accounting for transverse acoustic and longitudinal acoustic phonons as well as optical phonons. This model incorporates realistic phonon dispersion curves for silicon. The interactions among the different phonon branches and different phonon frequencies are considered, and the proposed model satisfies energy conservation. Frequency-dependent relaxation times, obtained from perturbation theory, and accounting for phonon interaction rules, are used. In the present study, the BTE is numerically solved using a structured finite volume approach. For a problem involving a film with two boundaries at different temperatures, the numerical results match the analogous exact solutions from radiative transport literature for various acoustic thicknesses. For the same problem, the transient thermal response in the acoustically thick limit matches results from the solution to the parabolic Fourier diffusion equation. In the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model. Experimental in-plane thermal conductivity data for silicon thin films over a wide range of temperatures are also matched satisfactorily.

Direct Simulation of Transport in Open-Cell Metal Foam

Flows in porous media may be modeled using two major classes of approaches: (a) a macroscopic approach, where volume-averaged semiempirical equations are used to describe flow characteristics, and (b) a microscopic approach, where small-scale flow details are simulated by considering the specific geometry of the porous medium. In the first approach, small-scale details are ignored and the information so lost is represented in the governing equations using an engineering model. In the second, the intricate geometry of the porous structures is accounted for and the transport through these structures computed. The latter approach is computationally expensive if the entire physical domain were to be simulated. Computational time can be reduced by exploiting periodicity when it exists. In the present work we carry out a direct simulation of the transport in an open-cell metal foam using a periodic unit cell. The foam geometry is created by assuming the pore to be spherical. The spheres are located at the vertices and at the center of the unit cell. The periodic foam geometry is obtained by subtracting the unit cell cube from the spheres. Fluid and heat flow are computed in the periodic unit cell. Our objective in the present study is to obtain the effective thermal conductivity, pressure drop, and local heat transfer coefficient from a consistent direct simulation of the open-cell foam structure. The computed values compare well with the existing experimental measurements and semiempirical models for porosities greater than 94%. The results and the merits of the present approach are discussed.

A two-temperature model for solid-liquid phase change in metal foams

Transient solid-liquid phase change occurring in a phase-change material (PCM) embedded in a metal foam is investigated. Natural convection in the melt is considered. Volume-averaged mass and momentum equations are employed, with the Brinkman-Forchheimer extension to the Darcy law to model the porous resistance. Owing to the difference in the thermal diffusivities between the metal foam and the PCM, local thermal equilibrium between the two is not assured. Assuming equilibrium melting at the pore scale, separate volume-averaged energy equations are written for the solid metal foam and the PCM and are closed using an interstitial heat transfer coefficient. The enthalpy method is employed to account for phase change. The governing equations are solved implicitly using the finite volume method on a fixed grid. The influence of Rayleigh, Stefan, and interstitial Nusselt numbers on the temporal evolution of the melt front location, wall Nusselt number, temperature differentials between the solid and fluid, and the melting rate is documented and discussed. The merits of incorporating metal foam for improving the effective thermal conductivity of thermal storage systems are discussed.

Theory of transfer characteristics of nanotube network transistors

Carbon nanotubes (CNT) nanocomposites used for thin-film transistors (TFTs) provide one of the first technologically-relevant test beds for two-dimensional heterogeneous percolating systems. The characteristics of these TFTs are predicted by considering the physics of heterogeneous finite-sized networks and interfacial traps at the CNT/gate-oxide interface. Close agreement between our numerical results and different experimental observations demonstrates the capability of the model to predict the characteristics of CNT/nanowire-based TFTs. Such predictive models would simplify device optimization and expedite the development of this nascent TFT technology.

Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-Insulator Transistors

The problem of self-heating in microelectronic devices has begun to emerge as a bottleneck to device performance. Published models for phonon transport in microelectronics have used a gray Boltzmann transport equation (BTE) and do not account adequately for phonon dispersion or polarization. In this study, the problem of a hot spot in a submicron silicon-on-insulator transistor is addressed. A model based on the BTE incorporating full phonon dispersion effects is used. A structured finite volume approach is used to solve the BTE. The results from the full phonon dispersion model are compared to those obtained using a Fourier diffusion model. Comparisons are also made to previously published BTE models employing gray and semi-gray approximations. Significant differences are found in the maximum hot spot temperature predicted by the different models. Fourier diffusion underpredicts the hot spot temperature by as much as 350% with respect to predictions from the full phonon dispersion model. For the full phonon dispersion model, the longitudinal acoustic modes are found to carry a majority of the energy flux. The importance of accounting for phonon dispersion and polarization effects is clearly demonstrated.

Effect of percolation on thermal transport in nanotube composites

The effective thermal conductivity of two-dimensional (2D) nanocomposites composed of carbon nanotubes (CNTs) dispersed in a host substrate is simulated to quantify the role of tube percolation on the thermal transport. The model is in excellent agreement with a 2D effective medium theory for low tube densities, but departs significantly from it when tube-tube interaction becomes significant. It is found that percolation effects may play a role for tube-tube and tube-substrate thermal resistance parameters typical of CNT composites. They are quantified in terms of a conductivity exponent for a range of governing parameters.

Analysis of the Wicking and Thin-Film Evaporation Characteristics of Microstructures

The topology and geometry of microstructures play a crucial role in determining their heat transfer performance in passive cooling devices such as heat pipes. It is therefore important to characterize microstructures based on their wicking performance, the thermal conduction resistance of the liquid filling the microstructure, and the thin-film characteristics of the liquid meniscus. In the present study, the free-surface shapes of the static liquid meniscus in common microstructures are modeled using SURFACE EVOLVER for zero Bond number. Four well-defined topologies, viz., surfaces with parallel rectangular ribs, horizontal parallel cylinders, vertically aligned cylinders, and spheres (the latter two in both square and hexagonal packing arrangements), are considered. Nondimensional capillary pressure, average distance of the liquid free-surface from solid walls (a measure of the conduction resistance of the liquid), total exposed area, and thin-film area are computed. These performance parameters are presented as functions of the nondimensional geometrical parameters characterizing the microstructures, the volume of the liquid filling the structure, and the contact angle between the liquid and solid. Based on these performance parameters, hexagonally-packed spheres on a surface are identified to be the most efficient microstructure geometry for wicking and thin-film evaporation. The solid-liquid contact angle and the nondimensional liquid volume that yield the best performance are also identified. The optimum liquid level in the wick pore that yields the highest capillary pressure and heat transfer is obtained by analyzing the variation in capillary pressure and heat transfer with liquid level and using an effective thermal resistance model for the wick. DOI: 10.1115/1.3160538