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.
Issue Section:
Research Papers
References
1.
Li
, S.
, and Liu
, W. K.
, 2002, “Meshfree and Particle Methods and Their Applications
,” Appl. Mech. Rev.
, 55
(1
), pp. 1
–33
.2.
Mittal
, R.
, and Iaccarino
, G.
, 2005, “Immersed Boundary Methods
,” Annu. Rev. Fluid Mech.
, 37
, pp. 239
–261
.3.
Tezduyar
, T. E.
, Sathe
, S.
, and Stein
, K..
, 2006, “Solution Techniques for the Fully Discretized Equations in Computation of Fluid-Structure Interactions With Space-Time Formulations
,” Comput. Methods Appl. Mech. Eng.
, 195
, pp. 5743
–5732
.4.
De
, S. K.
, and Aluru
, N. R.
, 2004, “Full-Lagrangian Schemes for Dynamic Analysis of Electrostatic MEMS
,” J. Microelectromech. Syst.
, 13
(5
), p. 737
–758
.5.
Demirdzic
, I.
, and Muzaferija
, S.
, 1995, “Numerical Method for Coupled Fluid Flow, Heat Transfer and Stress Analysis Using Unstructured Moving Meshes With Cells of Arbitrary Topology
,” Comput. Meth. Appl. Mech. Eng.
, 125
, pp. 235
–255
.6.
Laux
, S. E.
, and Grossman
, B. M.
, 1984, “A Generalized Control-Volume Formulation for Modeling Impact Ionization in Semi-Conductor Transport
,” IEEE Trans. Comput.-Aided Des.
, 4
(4
) pp. 520
–526
.7.
Griewank
, A.
, and Walther
, A.
, 2008, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
2nd ed., SIAM
, Philadelphia
.8.
Ghanem
, R.
, and Spanos
, P. D.
, 1991,and Karniadakis
, G. E.
, 2002, “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations
,” SIAM J. Sci. Comput. (USA)
, 24
(2
), p. 619
–644
.9.
Xiu
, D.
, and Karniadakis
, G. E.
, 2002, “The WienerAskey Polynomial Chaos for Stochastic Differential Equations
,” SIAM J. Sci. Comput. (USA)
, 24
(2
), p. 619
–644
.10.
“Historical Computing Trends,” The New York Times, Nov. 17, 2008.
11.
Owens
, J. D.
, 2007, “A Survey of General-Purpose Computation on Graphics Hardware
,” Comput. Graph. Forum
, 26
, pp. 80
–113
.12.
“NVIDIA CUDA Complete Unified Device Architecture Programming Guide,” Version 2.0.
13.
Senocak
, I.
, Thibault
, J.
, and Caylor
, M.
, 2009, “Rapid-Response Urban CFD Simulations Using a GPU Computing Paradigm on Desktop Supercomputers
,” Eighth Symposium on the Urban Environment
, Phoenix, AZ
, Jan. 10-15.16.
Patankar
, S. V.
, 1980, Numerical Heat Transfer and Fluid Flow
, Hemisphere
, Washington DC
.17.
Vanka
, S. P.
, 1986, “Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables
,” J. Comput. Phys.
, 65
, pp. 138
–158
.18.
Mathur
, S. R.
, and Murthy
, J. Y.
, 1999, “Coupled Ordinate Method for Multi-grid Acceleration of Radiation Calculations
,” J. Thermophys. Heat Transfer
, 13
(4
), pp. 467
–473
.19.
Pope
, S.
, 2000, Turbulent Flows
, 1st ed., Cambridge University Press
, Cambridge, UK.20.
Prosperetti
, A.
, and Tryggvason
, G.
, 2009, Computational Methods for Multiphase Flow
, 1st ed., Cambridge University Press
, Cambridge, UK.21.
Gidaspow
, D.
, 1994, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions
, 1st ed., Academic Press
, San Diego, CA
.23.
Tien
, C. L.
, Majumdar
, A.
, and Gerner
, F.
, 1998, Microscale Energy Transport
, Taylor and Francis
, Washington, D.C.
24.
Cola
, B. A.
, Xu
, X..
, and Fisher
, T.S.
, 2007, “Increased Real Contact Resistance in Thermal Interfaces: A Carbon Nanotube Foil Material
,” Appl. Phys. Lett.
90
, p. 093513
.25.
Dresselhaus
, M.
, Chen
, G.
, Tang
, M. Y.
, Yang
, R.
, Lee
, H.
, Wang
, D.
, Ren
, Z.
, Fluerial
, J.-P.
, and Gogna
, P.
, 2007, “New Directions for Low-Dimensional Thermoelectric Materials
,” Adv. Mater.
, 19
, pp. 1043
–1053
.26.
Seol
, J. H.
, Jo
, I.
, Moore
, A. L.
, Lindsay
, L.
, Aitken
, Z. H.
, Pettes
, M. T.
, Li
, X.
, Yao
, Z.
, Huang
, R.
, Broido
, D.
, Mingo
, N.
, Ruoff
, R. S.
, and Shi
, L.
, 2010, “Two-dimensional Phonon Transport in Supported Graphene
,” Science
, 328
(5975
), pp. 213
–216
.27.
Hadjiconstantinou
, N. G.
, 1999, “Hybrid Atomistic-Continuum Formulations and the Moving Contact-Line Problem
,” J. Comput. Phys.,” J. Comput. Phys
, 154
(2
), pp. 245
–265
.28.
Choi
, J. H.
, Bansal
, A.
, Meterelliyoz
, M.
, Murthy
, J. Y.
, and Roy
, K.
, 2007, “Self-Consistent Approach for Leakage Power and Temperature Estimation to Predict Thermal Runaway in FinFET Circuits
,” IEEE Trans. Comput.-Aided Des.
, 26
(1
), pp. 2059
–2068
.29.
Mathur
, S. R.
, and Murthy
, J. Y.
, 1997, “A Pressure-Based Method for Unstructured Meshes
,” Numer. Heat Transfer
, 31
(2
), pp. 195
–216
.30.
Davidson
, L.
, 1996, “A Pressure-Correction Method for Unstructured Meshes With Arbitrary Control Volumes
,” Int. J. Numer. Methods Fluids
, 22
, pp. 265
–281
.31.
Baliga
, B. R.
, 1997, “Control-Volume Finite Element Methods for Fluid Flow and Heat Transfer
,” Advances in Numerical Heat Transfer
W. J.
Minkowycz
and E. M.
Sparrow
, ed., Taylor & Francis
, New York
, Vol. 1
, Chap. III, pp. 97
–135
.32.
Schneider
, G. E.
, and Raw
, M. J.
, 1986, “Control-Volume Finite Element Method for Heat Transfer and Fluid Flow Using Co-located Variables—I. Computational Procedures
,” Numer. Heat Transfer
, 9
, pp. 253
–276
.33.
Acharya
, S.
, Baliga
, B. R.
, Karki
, K.
, Murthy
, J. Y.
, Prakash
, C.
, and Vanka
, S. P.
, 2007, “Pressure-Based Finite-Volume Methods for Computational Fluid Dynamics
,” ASME J. Heat Transfer
, 129
, pp. 407
–424
.34.
Hutchinson
, B. R.
, and Raithby
, G. D.
, 1986, “A Multigrid Method Based on the Additive Correction Strategy
,” Numer. Heat Transfer
, 9
, pp. 511
–537
.35.
Saad
, Y.
, Iterative Methods for Sparse Linear Systems
, SIAM
, 2003, Philadelphia, PA.36.
Rhie
, C. M.
, and Chow
, W. L.
, 1983, “A Numerical Study of the Turbulent Flow Past an Isolated Airfoil With Trailing Edge Separation
,” AIAA J.
, 21
, pp. 1525
–1532
.37.
Webster
, R.
, 1994, “An Algebraic Multigrid Solver for Navier-Stokes Problems
,” Int. J. Numer. Methods in Fluids
, 18
, pp. 761
–780
.38.
Mavriplis
, D. J.
, 2000, “Viscous Flow Analysis Using a Parallel Unstructured Multigrid Solver
,” AIAA J.
, 38
(11
), pp. 2067
–2076
.39.
Raithby
, G. D.
, and Chui
, E. H.
, 1990, “A Finite-Volume Method for Predicting Radiant Heat Transfer in Enclosures With Participating Media
,” J. Heat Transfer
, 112
, pp. 415
–423
.40.
Murthy
, J. Y.
, and Mathur
, S. R.
, 1998, “Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes
,” J. Thermophys. Heat Transfer
, 12
(3
), pp. 313
–321
.41.
Mathur
, S. R.
, and Murthy
, J. Y.
, 2009, “A Multigrid Method for the Poisson-Nernst-Planck Equations
,” Int. J. Heat Mass Transfer
, 52
, pp. 4031
–4039
.42.
Murthy
, J. Y.
, and Mathur
, S. R.
, 2002, “Computation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method
,” J. Heat Transfer
, 124
(6
), pp. 1176
–1181
.43.
Iaccarino
, G.
, and Verzicco
, R.
, 2003, “Immersed Boundary Technique for Turbulent Flow Simulation
,” Appl. Mech, Rev.
, 50
(3
), pp. 331
–347
.44.
Peskin
, C. S.
, 1981, “The Fluid Dynamics of Heart Valves: Experimental, Theoretical and Computational Methods
,” Annu. Rev. Fluid Mech.
, 14
, pp. 235
–259
.45.
Mohd-Yusof
, J.
, 1997, “Combined Immersed Boundaries/B-Spline Methods for Simulations of Flows in Complex Geometries
,” Annual Research Briefs
, Center for Turbulence Research
, Stanford, CA, pp. 317
–328
.46.
Fadlun
, E. A.
, Verzicco
, R.
, Orlandi
, P.
, and Mohd-Yusof
, J.
, 2000, “Combined Immersed Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Situations
,” J. Comput. Phys.
, 161
, pp. 37
–60
.47.
Gilmanov
, A.
, and Sotiropoulos
, F.
, 2005, “A Hybrid Cartesian/Immersed Boundary Method for Simulating Flows With 3D Geometrically Complex Moving Bodies
,” J. Comput. Phys.
, 207
, pp. 457
–492
.48.
Gilmanov
, A.
, and Acharya
, S.
, 2008, “A Hybrid Immersed Boundary and Material Point Method for Simulating 3D Fluid-Structure Interaction Problems
,” Int. J. Numer. Methods Fluids
, 56
, pp. 2151
–2177
.49.
Kang
, S.
, Iaccarino
, G.
, and Ham
, F.
, 2009, “DNS of Buoyancy-Dominated Turbulent Flows on a Bluff Body Using the Immersed Boundary Method
,” J. Comput. Phys.
, 228
(9
), pp. 3189
–3208
.50.
Sun
, L.
, Mathur
, S. R.
, and Murthy
, J. Y.
, 2009, “An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries
,” ASME Paper No. IMECE2009-12917
.51.
Kang
, S.
, Iaccarino
, G.
, Ham
, F.
, and Moin
, P.
, 2009, “Prediction of Wall-Pressure Fluctuation in Turbulent Flows With an Immersed Boundary Method
,” J. Comput. Phys.
, 228
, pp. 6753
–6772
.52.
Ansys, 2009, “FLUENT 12 User Manual
,” Ansys Inc.
, Canonsburg, PA
.53.
Ashcroft
, N.W.
, and Mermin
, N. D.
, 1976, Solid State Physics,
Harcourt, Inc., Orlando, FL
.54.
Bazant
, M. Z.
, Kaxiras
, E.
, Justo
, J. F.
, 1997, “Environment-Dependent Interatomic Potential for Bulk Silicon
,” Phys. Rev. B
56
, pp. 8542
–8552
.55.
Mingo
, N.
, and Yang
, L.
, 2003, “Predicting the Thermal Conductivity of Si and Ge Nanowires
,” Nano Lett.
, 3
(12
), pp. 1713
–1716
.56.
Pascual-Gutierrez
, J. A.
, Murthy
, J. Y.
, and Viskanta
, R. V.
, 2009, “Thermal Conductivity and Phonon Transport Properties of Silicon Using Perturbation Theory and the Environment-Dependent Interatomic Potential
,” J. Appl. Phys.
, 106
(6
), p. 063532
.57.
Broido
, D.
, Ward
, A.
, and Mingo
, N.
, 2005, “Lattice Thermal Conductivity of Silicon From Empirical Interatomic Potentials
, Phys. Rev. B
, 72
, p. 014308
.58.
Henry
, A. S.
, and Chen
, G.
, 2008, “Spectral Phonon Transport Properties of Silicon Based on Molecular Dynamics Simulations and Lattice Dynamics
,” J. Comput. Theor. Nanosci.
, 5
, pp. 1
–12
.59.
Loy
, J.
, 2010, “An Acceleration Technique for the Solution of the Phonon Boltzmann Transport Equation
,” M.S. thesis
, Purdue University
, West Lafayette, IN
.60.
Loy
, J.
, Singh
, D.
, and Murthy
, J. Y.
, 2009, “Non-Gray Phonon Transport Using a Hybrid BTE-Fourier Solver
,” ASME Paper No. HT2009-88056.
61.
Choi
, J. C.
, Bansal
, A.
, Meterelliyoz
, M.
, Murthy
, J. Y.
, and Roy
, K.
, 2006, “Leakage Power Dependent Temperature Estimation to Predict Thermal Runaway in FinFet Circuits
,” ICCAD
, San Jose, CA
, Nov. 5
–9
.62.
Ni
, C.
, 2009, “Phonon Transport Models for Heat Conduction in Sub-Micron Geometries With Applications to Microelectronics
,” Ph.D thesis
, Purdue University
, West Lafayette
.63.
Rowlette
, J.
, and Goodson
, K. E.
, 2008, “Fully-Coupled Non-equlilbrium Electron-Phonon Transport in Nanometer-Scale Silicon FETS
,” IEEE Trans. Electron Devices
, 55
, pp. 220
–232
.64.
Sinha
, S.
, Pop
, E.
, and Goodson
, K. E.
, 2006, “Non-equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors
,” ASME J. Heat Transfer
, 128
, pp. 638
–647
.65.
Chui
, E. H.
, and Raithby
, G. D.
, 1992, “Implicit Solution Scheme to Improve Convergence Rate in Radiative Transfer Problems
,” Numer. Heat Transfer
, 22
, pp. 251
–272
.66.
Fiveland
, W. A.
, and Jessee
, J. P.
, 1996, “Acceleration Schemes for the Discrete Ordinates Method
,” J. Thermophys. Heat Transfer
, 10
(3
) pp. 445
–451
.67.
Hassanzadeh
, P.
, Raithby
, G. D.
, and Chui
, E. H.
, 2008, “Efficient Calculation of Radiation Heat Transfer in Participating Media
,” J. Thermophys. Heat Transfer
, 22
(2
), pp. 129
–139
.68.
Mathur
, S. R.
, and Murthy
, J. Y.
, 2009, “An Acceleration Technique for the Computation of Participating Radiative Heat Transfer
,” ASME Paper No. IMECE2009-12923
.69.
Andrea Saltelli
, Editor, 2009, “Special Issue on Sensitivity Analysis
,” Reliab. Eng. Syst. Saf.
, 94
(7
), pp. 1133
–1244
.70.
Martins
, J.
, Kroo
, I. M.
, and Alonso
, J. J.
, 2000, “An Automated Method for Sensitivity Analysis Using Complex Variables
,” Paper No. AIAA-2000-0689.71.
Jameson
, A.
, 2003, “Aerodynamic Shape Optimization Using the Adjoint Method
,” Aerodynamic Drag Prediction and Reduction (VKI Lecture Series), von Karman Institute of Fluid Dynamics
, Rhode St Genese
, pp. 3
–7
.72.
Nadarajah
, S. K.
, and Jameson
, A.
, 2005, “A Comparison of the Continuous and Discrete Adjoint Approach to Automatic Aerodynamic Optimization
,” AIAA Paper 2005–324
.73.
Jemcov
, A.
, and Mathur
, S. R.
, 2004, “Algorithmic Differentiation of General Purpose CFD Code: Implementation and Verification
,” ECCOMAS 2004
, Jyvaskyla, Finland.
, 24–28 July.74.
Jemcov
, A.
, and Mathur
, S.
, 2005, ” Sensitivity Analysis and Uncertainty Propagation in Compressible Inviscid Flows
,” 6th World Congress of Structural and Multidisciplinary Optimization
, Rio de Janeiro
, Brazil
, 30 May–03 June.75.
Mathur
, S.
, 2009, Personal Communication.76.
Mathur
, S.
, Murthy
, J. Y.
, and Chai
, J. C.
, 2009, unpublished work.77.
Heidmann
, J. D.
, 2008, “A Numerical Study of Anti-Vortex Film Cooling Designs at High Blowing Ratio
,” ASME Paper No. GT2008-50845
.78.
Dhungel
, S.
, Phillips
, A.
, Ekkad
, S.
, and Heidmann
, J. D.
, 2007, “Experimental Investigations of a Novel Anti-Vortex Design
,” ASME Paper GT2007-27419.79.
ASME, 2009, “Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer,” No. ASME V&V 20, ASME, New York
.80.
Guo
, X.
, and Alexeenko
, A.
, 2009, “Compact Model for Squeeze Film Damping Based on Rarefied Flow Simulations
, J. of Micromech. Microeng.
19
, p. 045026
.81.
Ozdoganlar
, O. B.
, Hansche
, B. D.
, and Carne
, T. G.
, 2005, “Experimental Modal Analysis for Micromechanical Systems
,” Experimental Mechanics
, 45
(6
), pp. 498
–506
.82.
Xiu
, D.
, and Hesthaven
, J.
, 2005, “Higher-Order Collocation Methods for Differential Equations With Random Inputs
,” SIAM J. Sci. Comput.
, 27
(2
), pp. 1118
–1139
.83.
Smolyak
, S.
, 1963, “Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions
,” Soviet Math. Dokl.
v4.
, pp. 240
–243
.84.
Murthy
, J.
, Mathur
, S.
, Pax
, B.
, Chigullapalli
, A.
, Li
, J.
, and Xiu
, D.
, 2009, unpublished results
.85.
Karniadakis
, G.
, Beskok
, A.
, and Aluru
, N. R.
, 2005, Microflows and Nanoflows
, Springer
, New York
.86.
Agarwal
, N.
, and Aluru
, N. R.
, 2009, “A Domain Adaptive Stochastic Collocation Approach for Analysis of MEMS Under Uncertainties
,” J. Comp. Phys.
, 228
(20
), pp. 7662
–7668
.87.
Mathur
, S.
, Chigullapalli
, A.
, and Murthy
, J.Y.
, “A Unified Unintrusive Discrete Approach to Sensitivity Analysis and Uncertainty Propagation in Fluid Flow Simulations
,” ASME Paper No. IMECE2010-37789
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
