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Research Papers

Use of Scaled Sensitivity Coefficient Relations for Intrinsic Verification of Numerical Codes and Parameter Estimation for Heat Conduction

[+] Author and Article Information
Dharmendra K. Mishra

Department of Food Science,
Purdue University,
Philip E. Nelson Hall of Food Science,
745 Agriculture Mall Drive,
West Lafayette, IN 47907-200
e-mail: mishra67@purdue.edu

Kirk D. Dolan

Department of Food Science and
Human Nutrition,
Michigan State University,
East Lansing, MI 48824
e-mail: dolank@msu.edu

James V. Beck

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: jamesverebeck@gmail.com

Ferhan Ozadali

Mead Johnson Nutrition,
2400 W Lloyd Expy,
Evansville, IN 47712
e-mail: fozadali@gmail.com

Manuscript received June 23, 2016; final manuscript received November 14, 2017; published online November 29, 2017. Editor: Ashley F. Emery.

J. Verif. Valid. Uncert 2(3), 031005 (Nov 29, 2017) (7 pages) Paper No: VVUQ-16-1018; doi: 10.1115/1.4038494 History: Received June 23, 2016; Revised November 14, 2017

Numerical codes are important in providing solutions to partial differential equations in many areas, such as the heat transfer problem. However, verification of these codes is critical. A methodology is presented in this work as an intrinsic verification method (IVM) to the solution to the partial differential equation. Derivation of the dimensionless form of scaled sensitivity coefficients is presented, and the sum of scaled sensitivity coefficients is used in the dimensionless form to provide a method for verification. Intrinsic verification methodology is demonstrated using examples of heat transfer problems in Cartesian and cylindrical coordinate. The IVM presented here is applicable to analytical as well as numerical solutions to partial differential equations.

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References

Salari, K. , and Knupp, P. , 2000, “Code Verification by the Method of Manufactured Solutions,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2000-1444.
Roy, C. J. , 2005, “ Review of Code and Solution Verification Procedures for Computational Simulation,” J. Comput. Phys., 205(1), pp. 131–156. [CrossRef]
ASME, 2009, “ Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer,” American Society of Mechanical Engineers, New York, Standard No. V&V 20-2009.
Beck, J. V. , McMasters, R. , Dowding, K. J. , and Amos, D. E. , 2006, “ Intrinsic Verification Methods in Linear Heat Conduction,” Int. J. Heat Mass Transfer, 49(17–18), pp. 2984–2994. [CrossRef]
Beck, J. V. , 1970, “ Nonlinear Estimation Applied to the Nonlinear Inverse Heat Conduction Problem,” Int. J. Heat Mass Transfer, 13(4), pp. 703–716. [CrossRef]
Beck, J. V. , and Arnold, K. J. , 1977, Parameter Estimation in Engineering and Science, Wiley, New York.
Blackwell, B. F. , Dowding, K. J. , and Cochran, R. J. , 1999, “ Development and Implementation of Sensitivity Coefficient Equation for Heat Conduction Problems,” Numer. Heat Transfer, Part B: Fundam., 36(1), pp. 15–32. [CrossRef]
Sun, N. , Sun, N. Z. , Elimelech, M. , and Ryan, J. N. , 2001, “ Sensitivity Analysis and Parameter Identifiability for Colloid Transport in Geochemically Heterogeneous Porous Media,” Water Resour. Res., 37(2), pp. 209–222. [CrossRef]
Chen, B. , and Tong, L. , 2004, “ Sensitivity Analysis of Heat Conduction for Functionally Graded Materials,” Mater. Des., 25(8), pp. 663–672. [CrossRef]
Beck, J. V. , 1967, “ Transient Sensitivity Coefficients for the Thermal Contact Conductance,” Int. J. Heat Mass Transfer, 10(11), pp. 1615–1617. [CrossRef]
Dowding, K. J. , Blackwell, B. F. , and Cochran, R. J. , 1999, “ Application Sensitivity Coefficients Heat Conduction Problems,” Numer. Heat Transfer, Part B: Fundam., 36(1), pp. 33–55. [CrossRef]
Beck, J. V. , 1969, “ Determination of Optimum, Transient Experiments for Thermal Contact Conductance,” Int. J. Heat Mass Transfer, 12(5), pp. 621–633. [CrossRef]
Beck, J. V. , and Woodbury, K. A. , 1998, “ Inverse Problems and Parameter Estimation: Integration of Measurements and Analysis,” Meas. Sci. Technol., 9(6), p. 839. [CrossRef]
Dolan, K. , Valdramidis, V. , and Mishra, D. , 2012, “ Parameter Estimation for Dynamic Microbial Inactivation; Which Model, Which Precision?,” Food Control, 29(2), pp. 401–408. [CrossRef]
Koda, M. , Dogru, A. H. , and Seinfeld, J. H. , 1979, “ Sensitivity Analysis of Partial Differential Equations With Application to Reaction and Diffusion Processes,” J. Comput. Phys., 30(2), pp. 259–282. [CrossRef]
Beck, J. V. , and Litkouhi, B. , 1988, “ Heat Conduction Numbering System for Basic Geometries,” Int. J. Heat Mass Transfer, 31(3), pp. 505–515. [CrossRef]
Dunker, A. M. , 1984, “ The Decoupled Direct Method for Calculating Sensitivity Coefficients in Chemical Kinetics,” J. Chem. Phys., 81(5), pp. 2385–2393. [CrossRef]
Martins, J. , Kroo, I. M. , and Alonso, J. J. , 2000, “An Automated Method for Sensitivity Analysis Using Complex Variables,” AIAA Paper No. 2000-0689.

Figures

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Fig. 1

Dimensionless scaled sensitivity coefficient for k and C in case 1: for k = 0.5, C = 0.35 × 10−7, delta = 0.0001, x/L =0, Δx/L = 0.02

Grahic Jump Location
Fig. 2

Plot of IS in case 1: using second-order finite difference

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Fig. 3

Plot of IS in case 1: with refined and unrefined finite element code

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Fig. 4

Scaled sensitivity coefficients for k and C in case 2

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Fig. 5

Plot of IS in case 2: with refined and unrefined finite element code

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