One dimensional nonlinear nonsteady state heat conduction I: general solution by perturbation theory

1990 ◽  
Vol 68 (2) ◽  
pp. 198-205 ◽  
Author(s):  
Heinrich Hoff
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Perturbation Theory ◽  
Heat Waves ◽  
Nonlinear Partial Differential Equation ◽  
Homogeneous System ◽  
Nonlinear Field ◽  
One Dimensional ◽  
Future Paper ◽  
Nonsteady State

Taking into account the dependence of the heat capacity and heat conductivity on temperature, one obtains a nonlinear field equation of temperature. This nonlinear partial differential equation is resolved by perturbation theory for the particular case of a homogeneous system. The solution is checked by some criteria of control derived from thermostatics, from steady state transport, and from spatial symmetry. It forms the theoretical framework of nonlinear heat waves to be discussed in a future paper.

scholarly journals A Numerical Well-Balanced Scheme for One-Dimensional Heat Transfer in Longitudinal Triangular Fins

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
I. Rusagara ◽  
C. Harley
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Transfer Coefficients ◽  
Partial Differential ◽  
One Dimensional ◽  
Heat Transfer Coefficients ◽  
Highly Nonlinear ◽  
Triangular Fin

The temperature profile for fins with temperature-dependent thermal conductivity and heat transfer coefficients will be considered. Assuming such forms for these coefficients leads to a highly nonlinear partial differential equation (PDE) which cannot easily be solved analytically. We establish a numerical balance rule which can assist in getting a well-balanced numerical scheme. When coupled with the zero-flux condition, this scheme can be used to solve this nonlinear partial differential equation (PDE) modelling the temperature distribution in a one-dimensional longitudinal triangular fin without requiring any additional assumptions or simplifications of the fin profile.

Unsteady Flow of Gas Through a Semi-Infinite Porous Medium

1957 ◽  
Vol 24 (3) ◽  
pp. 329-332
Author(s):  
R. E. Kidder
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Gas Flow ◽  
Transient Flow ◽  
Order Term ◽  
Nonlinear Partial Differential Equation ◽  
Flow In Porous Media ◽  
Partial Differential ◽  
One Dimensional

Abstract This paper presents an analytic solution to a problem of the transient flow of gas within a one-dimensional semi-infinite porous medium. A perturbation method, carried out to include terms of the second order, is employed to obtain a solution of the nonlinear partial differential equation describing the flow of gas. The zero-order term of the solution represents the solution of the linearized partial differential equation of gas flow in porous media given by Green and Wilts (1).

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems

2013 ◽  
Vol 5 (04) ◽  
pp. 407-422 ◽  
Author(s):  
Matthew A. Beauregard ◽  
Qin Sheng
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Spatial Adaptation ◽  
Monitor Function ◽  
Monitoring Strategies ◽  
Highly Nonlinear ◽  
Equidistribution Principle

AbstractFinite difference computations that involve spatial adaptation commonly employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This straightforward concept has proven to be extremely effective and practical. However, selections of core monitoring functions are often challenging and crucial to the computational success. This paper concerns six different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy singularities. While the first four monitoring strategies are within the so-calledprimitiveregime, the rest belong to a later category of themodifiedtype, which requires the priori knowledge of certain important quenching solution characteristics. Simulated examples are given to illustrate our study and conclusions.

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