Solution of the two-dimensional heat equation for a square in terms of elliptic functions

Kurt, Nurcan

doi:10.1016/j.jfranklin.2007.09.003

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…For example Nurcan Kurt solved two-dimensional heat equation in a square region in terms of elliptic functions [31] but this paper, due to the existence of the coordinate varying coefficient in the beam equation of motion, uses a Galerkin based reduced order model to solve coupled thermoelastic equations. Based on Galerkin based reduced order model the dynamic deflection and temperature changes of the system can be approximated in terms of linear combinations of finite number of suitable shape functions with time dependent coefficients:…”

Section: Thermoelastic Coupled Equationsmentioning

confidence: 99%

Effects of axial and residual stresses on thermoelastic damping in capacitive micro-beam resonators

Vahdat

Rezazadeh

2011

Journal of the Franklin Institute

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Section: Thermoelastic Coupled Equationsmentioning

confidence: 99%

Effects of axial and residual stresses on thermoelastic damping in capacitive micro-beam resonators

Vahdat

Rezazadeh

2011

Journal of the Franklin Institute

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“…Solution of the two-dimensional heat equation in a square region was given by Kurt [11]. Analytic solution was given two-dimensional heat equation for some regions by Baykuş Savaşaneril et al [2,3,5,7].…”

Section: Introductionmentioning

confidence: 99%

Bernstein Series Solution of the Heat Equation in 2-D

Savaşaneril¹

2017

ntmsci

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A broad class of steady-state physical problems can be reduced to finding the harmonic functions that satisfy certain boundary conditions. The Dirichlet problem for the Laplace equation is one of the above mentioned problems. In this paper, a numerical matrix method is developed for numerically solving the Heat equation in 2-D. The method converts the heat equation in 2-D to a matrix equation, which corresponds to a system of linear algebraic equations. Error analysis is included to demonstrate the validity and applicability of the technique. Finally, the effectiveness of the method is illustrated in the heat equation for a cut ring region.

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“…The Green function of the Dirichlet problem for the Laplace differential equation in a triangle region was expressed in terms of elliptic functions and the solution of problem was based on the Green function, and therefore on elliptic functions by Kurt and Sezer [13]. Green function of the two-dimensional heat equation in a square region was expressed in terms of elliptic functions and the solution of the problem was based on the Green function and therefore on elliptic functions by Kurt [14]. Least Square Method (LSM), Collocation Method (CM) and a new approach which is called Akbari-Ganji's Method (AGM) are applied to solve the nonlinear heat transfer equation of fin with power-law temperature-dependent both thermal conductivity and heat transfer coefficient by Ledari et al [15].…”

Section: Introductionmentioning

confidence: 99%