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

Creative Commons License

BAĞLAN İ., ASLAN E.

Computation, cilt.12, sa.1, 2024 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/computation12010011
  • Dergi Adı: Computation
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Aerospace Database, Communication Abstracts, INSPEC, Metadex, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: finite difference method, generalized Fourier method, periodic boundary condition, quasilinear parabolic equation
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.