COMPARATIVE STUDY OF DIFFERENT EIGENFUNCTION BASED APPROACHES FOR 1D MULTILAYER HEAT CONDUCTION PROBLEM WITH TIME DEPENDENT BOUNDARY CONDITIONS

2018 ◽  
Author(s):  
Pranay Biswas ◽  
Suneet Singh
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Comparative Study ◽  
Heat Conduction Problem ◽  
Time Dependent

Orthogonal Eigenfunction Expansion Method for One-Dimensional Dual-Phase Lag Heat Conduction Problem With Time-Dependent Boundary Conditions

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Pranay Biswas ◽  
Suneet Singh
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Heat Conduction Problem ◽  
Separation Of Variables ◽  
Auxiliary Function ◽  
Time Dependent ◽  
Computational Time ◽  
Phase Lag ◽  
Dual Phase

The separation of variables (SOV) can be used for all Fourier, single-phase lag (SPL), and dual-phase lag (DPL) heat conduction problems with time-independent source and/or boundary conditions (BCs). The Laplace transform (LT) can be used for problems with time-dependent BCs and sources but requires large computational time for inverse LT. In this work, the orthogonal eigenfunction expansion (OEEM) has been proposed as an alternate method for non-Fourier (SPL and DPL) heat conduction problem. However, the OEEM is applicable only for cases where BCs are homogeneous. Therefore, BCs of the original problem are homogenized by subtracting an auxiliary function from the temperature to get a modified problem in terms of a modified temperature. It is shown that the auxiliary function has to satisfy a set of conditions. However, these conditions do not lead to a unique auxiliary function. Therefore, an additional condition, which simplifies the modified problem, is proposed to evaluate the auxiliary function. The methodology is verified with SOV for time-independent BCs. The implementation of the methodology is demonstrated with illustrative example, which shows that this approach leads to an accurate solution with reasonable number of terms in the expansion.

Multiquadric Collocation Method for Time-Dependent Heat Conduction Problems With Temperature-Dependent Thermal Properties

2006 ◽  
Vol 129 (2) ◽  
pp. 109-113 ◽  
Author(s):  
Somchart Chantasiriwan
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Collocation Method ◽  
Heat Conduction Problem ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Time Dependent ◽  
Piecewise Linear Functions ◽  
Temperature Dependent ◽  
Kirchhoff Transformation

Abstract The multiquadric collocation method is a meshless method that uses multiquadrics as its basis function. Problems of nonlinear time-dependent heat conduction in materials having temperature-dependent thermal properties are solved by using this method and the Kirchhoff transformation. Variable transformation is simplified by assuming that thermal properties are piecewise linear functions of temperature. The resulting nonlinear equation is solved by an iterative scheme. The multiquadric collocation method is tested by a heat conduction problem for which the exact solution is known. Results indicate satisfactory performance of the method.

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