Research Papers

Computational Heat Transfer in Complex Systems: A Review of Needs and Opportunities

[+] Author and Article Information
Jayathi Y. Murthy, Sanjay R. Mathur

School of Mechanical Engineering and Birck Nanotechnology Center,  Purdue University, West Lafayette, IN 47907-1288jmurthy@ecn.purdue.edu

J. Heat Transfer 134(3), 031016 (Jan 18, 2012) (12 pages) doi:10.1115/1.4005153 History: Received September 01, 2010; Revised July 27, 2011; Published January 18, 2012; Online January 18, 2012

During the few decades, computational techniques for simulating heat transfer in complex industrial systems have reached maturity. Combined with increasingly sophisticated modeling of turbulence, chemistry, radiation, phase change, and other physics, powerful computational fluid dynamics (CFD) and computational heat transfer (CHT) solvers have been developed which are beginning to enter the industrial design cycle. In this paper, an overview of emerging simulation needs is first given, and currently-available CFD techniques are evaluated in light of these needs. Emerging computational methods which address some of the failings of current techniques are then reviewed. New research opportunities for computational heat transfer, such as in submicron and multiscale heat transport, are reviewed. As computational techniques and physical models become mature, there is increasing demand for predictive simulation, that is, simulation which is not only verified and validated, but whose uncertainty is also quantified. Current work in the area of sensitivity computation and uncertainty propagation is described.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Evolution of peak floating point performance gap between GPUs and CPUs [12]

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Figure 2

Typical cell (C0) and neighbors for cell-based finite volume scheme [29]

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Figure 3

Immersed boundary method. (a) An arbitrarily-shaped solid is immersed in a background fluid mesh. The markings of cells as “fluid,” “solid,” and “IB cell” are shown. (b) Cell nomenclature near IB face.

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Figure 4

Computational domain for decaying vortex problem

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Figure 5

Order of convergence of IBM for decaying vortex problem for (a) Pe = 1, and (b) Pe = 20

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Figure 6

Low Re flow over a stationary cylinder in a channel. Comparisons of the velocity magnitude are made with FLUENT along three vertical lines in the domain

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Figure 7

Discretization of phonon frequency spectrum for silicon. Dispersion curves in the [100] direction are shown [59].

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Figure 8

Comparison of single-mode relaxation times in Si with MD simulations. The solid lines are computed using Fermi’s Golden Rule [56] and the dashed lines are taken from the MD simulations of Ref. [58].

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Figure 9

Schematic of bulk NPN FET showing source, drain, and channel regions, and phonon generation rates taken from Aksamija and co-workers [62]

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Figure 10

Contours of lattice temperature (K) in NPN FET

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Figure 11

Solution loop for hybrid Fourier-BTE model

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Figure 12

Fractional band-wise heat transfer rates for heat conduction in a silicon domain of size L = 100 nm. Comparison is made between the hybrid model and an all-BTE solution.

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Figure 13

Acceleration factors in CPU time for hybrid solver versus an all-BTE solver for the case of a two-band problem, one solved with the BTE, and one with the MFE. The first row of numbers shows the Knudsen number of the MFE versus the BTE band. The second row of numbers shows the lattice ratio (Cω,p /τω,p ) in the MFE versus the BTE band.

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Figure 14

Discrete tangent computation procedure. (a) The functions to be differentiated are decomposed into elemental operations, and elemental derivatives computed. (b) Inputs x and y are prescribed, and also the input derivatives x′ and y′. If one of the input derivatives is set to unity and the other to zero (x′ = 1, y′ = 0, for example), the corresponding output derivatives are computed.

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Figure 15

Sensitivity to hot gas inlet temperature Ti . (a) Contours of temperature on the domain boundaries and (b) contours of ∂T/∂Ti.

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Figure 16

Gas damping of micro-cantilever. The surface corresponding to a second-order generalized polynomial chaos expansion of damping ratio versus cantilever thickness t and gap height h is shown.

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Figure 17

Damping ratio versus pressure for gas damping of microcantilever. Comparison with the experimental results of Ref. [81] (squares) is shown. Triangles indicate computations at nominal dimensions and circles indicate the mean of the computed damping factor distribution. The error bars indicate one (computed) standard deviation on either side of the computed mean.



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