scholarly journals Discussion: “Numerical Solutions to an Inverse Problem of Heat Conduction for Simple Shapes” (Stolz, Jr., G., 1960, ASME J. Heat Transfer, 82, pp. 20–25)

1960 ◽  
Vol 82 (1) ◽  
pp. 25-25 ◽  
Author(s):  
T. J. Mirsepassi
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Numerical Solutions

Estimation of the Transient Surface Temperature and Heat Transfer Coefficient of Convective Cooling for Large Slab and Long Cylinder by Using an Inverse Heat Conduction Method

2013 ◽  
Author(s):  
Ramin Soujoudi ◽  
Antonio Campo
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Surface Temperature ◽  
Series Solution ◽  
Initial Temperature ◽  
Numerical Solutions ◽  
Thermal Boundary Condition ◽  
Heat Equations ◽  
Inverse Heat Conduction ◽  
Long Cylinder

Inverse heat conduction method is a technique to determine heat flux and surface temperature on an inaccessible surface of wall by measuring the temperature on an accessible boundary. The objective of this paper is to develop a method by which stable prediction of heat transfer on an inaccessible boundary could be obtained without altering the thermal boundary condition that would have existed were sensor not present. In this work, three points backward finite difference applied to the 1-D heat equation for large slab and long cylinder with constant thermophysical properties and uniform initial temperature. The numerical solutions of the heat equations are performed with symbolic Maple software. It is demonstrated that approximate temperature distributions for the three bodies are equivalent to analytical solution using first term series solution. It is also shown that the series solution converge rapidly for long times, and for Fo > 0.2, ony the first term of the series nned to be retained for 2% accuracy.

scholarly journals Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. A. Castro ◽  
F. Rodríguez ◽  
J. Escolano ◽  
J. A. Martín
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat Conduction ◽  
Exact Solutions ◽  
Heat And Mass Transfer ◽  
Numerical Solutions ◽  
Fourier Transforms ◽  
Infinite Medium ◽  
Infinite Domain ◽  
Numerical Computations

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

Numerical Solutions to an Inverse Problem of Heat Conduction for Simple Shapes

1960 ◽  
Vol 82 (1) ◽  
pp. 20-25 ◽  
Author(s):  
G. Stolz
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Numerical Methods ◽  
Surface Heat Flux ◽  
Direct Problem ◽  
Numerical Solutions ◽  
Superposition Principle ◽  
Surface Heat ◽  
Numerical Inversion

Numerical methods are presented for solving an inverse problem of heat conduction: Given an interior temperature versus time, find the surface heat flux versus time. The analysis is developed specifically for spheres; it applies to other simple shapes. The system is treated as linear, permitting use of the superposition principle. The essence of the method is the numerical inversion of a suitable direct problem: Given a surface heat flux versus time, find an interior temperature versus time. Care is required in selecting a time spacing for, if it is chosen too small in relation to the conditions, undesirable oscillation results. Simplifying suggestions are presented, and the use of the methods are illustrated by examples.

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