Numerical-analytical method of solving the nonlinear heat-conduction problem for a doubly connected variable-thickness plate

1987 ◽  
Vol 53 (4) ◽  
pp. 1209-1213
Author(s):  
A. I. Uzdalev ◽  
E. N. Bryukhanova
Keyword(s):  
Heat Conduction ◽  
Variable Thickness ◽  
Analytical Method ◽  
Heat Conduction Problem ◽  
Nonlinear Heat Conduction ◽  
Numerical Analytical Method

Closed Form Solutions to Nonlinear Heat Conduction Problems

2012 ◽  
Vol 326-328 ◽  
pp. 115-119
Author(s):  
J. Zabadal ◽  
R. Garcia ◽  
V. Ribeiro ◽  
F. Van Der Laan
Keyword(s):  
Heat Conduction ◽  
Partial Differential Equations ◽  
Closed Form ◽  
Control Systems ◽  
Analytical Method ◽  
Linear Models ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Heat Conduction ◽  
Closed Form Solutions ◽  
Standard Techniques

This work presents a new analytical method for solving nonlinear heat conduction problems in arbitrary domains. The method is based on approximate mappings which transforms nonlinear partial differential equations into linear models which can be solved using standard techniques. In order to verify whether the proposed formulation can be employed to conceive new online control systems, numerical results are reported.

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

2009 ◽  
Author(s):  
Hosein Molavi ◽  
Ali Hakkaki-Fard ◽  
Alireza Pourshaghaghy ◽  
Mehdi Molavi ◽  
Ramin K. Rahmani
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Measurement Errors ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Adjoint Problem ◽  
Inverse Heat Conduction Problem ◽  
Transient Temperature ◽  
Nonlinear Heat Conduction ◽  
Mechanical Removal

Estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using the numerical experiments with the simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to conjugate gradient method with adjoint problem and variable metric method with adjoint problem. The obtained results show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

Thermal Design of Pavement Structures in Seasonal Frost Areas

1977 ◽  
Vol 99 (4) ◽  
pp. 533-540 ◽  
Author(s):  
P. E. Frivik ◽  
E. Thorbergsen ◽  
S. Del Giudice ◽  
G. Comini
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Thermal Design ◽  
The Finite Element Method ◽  
Nonlinear Heat Conduction ◽  
Empirical Correlations ◽  
Short Term ◽  
Temperature Variations ◽  
Pavement Structures

In many practical situations, adequate thermal design of pavement structures in seasonal frost areas can be done by utilizing a model based on heat conduction alone. In this paper we present a system of computer programs which allow the solution of practically any nonlinear heat conduction problem in soils, provided that a two-dimensional description, plane or axisymmetric, is possible. The finite element method, together with the empirical correlations for thermal properties and boundary conditions, is used in the simulations. Predictions of the thermal regime in different structures are favorably compared with the results of experimental measurements, both for long-term and short-term temperature variations.

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