Research Papers: Forced Convection

Reduced-Order Modeling of Conjugate Heat Transfer Processes

[+] Author and Article Information
Trevor J. Blanc

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84604
e-mail: tjblanc@byu.edu

Matthew R. Jones

Associate Professor
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84604
e-mail: mrjones@byu.edu

Steven E. Gorrell

Associate Professor
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84604
e-mail: sgorrell@byu.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 19, 2014; final manuscript received December 14, 2015; published online February 3, 2016. Assoc. Editor: William P. Klinzing.

J. Heat Transfer 138(5), 051703 (Feb 03, 2016) (8 pages) Paper No: HT-14-1323; doi: 10.1115/1.4032453 History: Received May 19, 2014; Revised December 14, 2015

This paper describes the application of reduced-order modeling techniques in the simulation of conjugate heat transfer processes. In a reduced-order model (ROM), the dominate features of a system are represented using a limited number of orthonormal basis vectors, which are extracted from a database containing descriptions of the system. Interpolating methods are then used to calculate expansion coefficients that allow representation of the system as linear combinations of the basis vectors. Evidence of the accuracy and computational savings achieved using the reduced-order modeling technique is presented in order to demonstrate its benefits in simulating conjugate heat transfer processes.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Cullen, A. C. , and Frey, H. , 1999, Probabilistic Techniques in Exposure Assessment: A Handbook for Dealing With Variability and Uncertainty in Models and Inputs, Plenum Press, New York.
Blanc, T. , 2014, “ Analysis and Compression of Large CFD Data Sets Using Proper Orthogonal Decomposition,” M.S. thesis, Brigham Young University, Provo, UT.
Pearson, K. , 1901, “ On Lines Planes of Closest Fit to System of Points in Space,” London Edinburgh Dublin Philos. Mag. J. Sci., 2(11), pp. 559–572. [CrossRef]
Hoteling, H. , 1933, “ Analysis of Complex Statistical Variables Into Principal Components,” J. Educ. Psychol., 24(6), pp. 417–441. [CrossRef]
Atwell, J. A. , and King, B. B. , 2001, “ Proper Orthogonal Decomposition for Reduced Basis Feedback Controllers for Parabolic Equations,” Math. Comput. Model., 33(1–3), pp. 1–19. [CrossRef]
Berkooz, G. , Holmes, P. , and Lumley, J. L. , 1993, “ The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows,” Annu. Rev. Fluid Mech., 25(1), pp. 539–575. [CrossRef]
Ding, P. , Wu, X.-H. , He, Y.-L. , and Tao, W.-Q. , 2008, “ A Fast and Efficient Method for Predicting Fluid Flow and Heat,” ASME J. Heat Transfer, 130(3), p. 032502. [CrossRef]
Ostrowski, Z. , Bialecki, R. A. , and Kassab, A. J. , 2005, “ Estimation of Constant Thermal Conductivity by Use of Proper Orthogonal Decomposition,” Comput. Mech., 37(1), pp. 52–59. [CrossRef]
Larson, R. S. , and Jones, M. R. , 2008, “ Reduced-Order Modeling of Time-Dependent Reflectance Profiles From Purely Scattering Media,” J. Quant. Spectrosc. Radiat. Transfer, 109(2), pp. 201–209. [CrossRef]
Blanc, T. , Jones, M. , Gorrell, S. , and Duque, E. , 2013, “ Reduced Order Modeling and Compression of Data Produced by Simulations of Transient and Periodic Heat Transfer Processes,” ASME Paper No. HT2013-17064.
Holmes, P. , Lumley, J. L. , Berkooz, G. , and Rowley, C. W. , 2012, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 2nd ed., Cambridge University Press, pp. 68–100.
Sirovich, L. , 1987, “ Turbulence and the Dynamics of Coherent Structures, Parts I–III,” Q. Appl. Math., 45(3), pp. 561–590.
Strang, G. , 2006, Linear Algebra and Its Application, Addison-Wesley, Reading MA, pp. 432–433.


Grahic Jump Location
Fig. 1

Schematic representation of the process of assembling a database

Grahic Jump Location
Fig. 2

Illustration of a transient conjugate heat transfer problem. A cylinder is initially at a uniform temperature, Ti. The dimensions and thermophysical properties of the cylinder are known constants. Each end of the cylinder is connected to heat sinks that are maintained at Ti throughout the process. At time zero, the cylinder is exposed to air in cross flow. The objective of this problem is to determine the time-dependent, axisymmetric temperature profile in the cylinder, T(r,z,t), as the velocity and temperature of the freestream are varied.

Grahic Jump Location
Fig. 3

This is the grid used for all of the cylinder heat transfer simulations; it consisted of a 100,000 cell cylinder region and a 365,000 cell fluid region

Grahic Jump Location
Fig. 4

The computational domain for the cooled turbine blade is separated into three regions: the main turbine passage fluid, the internal blade cooling fluid, and the turbine blade solid

Grahic Jump Location
Fig. 5

The plot shows the parameter space spanned by the database of solutions; therefore, the ROM should only be seen as valid for parameter values that fall within this space

Grahic Jump Location
Fig. 6

Comparison of the CFD and ROM maximum and mean cylinder temperatures for the random parameter set of 470.6 K and 29.5 m/s

Grahic Jump Location
Fig. 7

Temperature contours of the 470.6 K and 29.5 m/s parameter set for the (a) CFD and (b) ROM solutions at t = 2 s along with respective error contours (c). The highest ROM error occurs in the front of the cylinder at the symmetry plane.

Grahic Jump Location
Fig. 8

The variation in maximum and minimum temperatures in the cooled turbine blade for each of the CFD simulations

Grahic Jump Location
Fig. 9

Temperature contours for the outer surface of the cooled turbine blade for the (a) CFD and (b) ROM solutions for set 4. The error contours between the solutions are displayed in (c).



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In