Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions

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BAĞLAN İ., ASLAN E.

Computation, vol.12, no.1, 2024 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.3390/computation12010011
  • Journal Name: Computation
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Aerospace Database, Communication Abstracts, INSPEC, Metadex, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: finite difference method, generalized Fourier method, periodic boundary condition, quasilinear parabolic equation
  • Open Archive Collection: AVESIS Open Access Collection
  • Kocaeli University Affiliated: Yes

Abstract

A two-dimensional heat diffusion problem with a heat source that is a quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are employed. As the problem is nonlinear, Picard’s successive approximation theorem is utilized. We demonstrate the existence, uniqueness, and constant dependence of the solution on the data using the generalized Fourier method under specific conditions of natural regularity and consistency imposed on the input data. For the numerical solution, an implicit finite difference scheme is used. The results obtained from the analytical and numerical solutions closely match each other.