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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Grahic Jump Location
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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
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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