NUMERICAL SIMULATION OF HEAT TRANSFER DYNAMICS IN SMART RESIDENTIAL ENVIRONMENTS USING FINITE DIFFERENCE METHODS
Kalit so‘zlar:
heat diffusion equation, finite difference method, Forward Euler scheme, Dirichlet boundary conditions, 2D Laplacian, Canvas API, smart home thermal modeling, thermal diffusivity, stochastic perturbation, temperature field visualizationAnnotatsiya
This article investigates the numerical simulation of two-dimensional heat transfer processes within a room modeled after a smart home environment. The governing equation is the classical parabolic heat diffusion partial differential equation , discretized over a 30×50 spatial grid using the Forward Euler finite difference scheme. Dirichlet boundary conditions represent three physically distinct zones: a radiator as the primary heat source, a window as the principal heat sink, and a door modeling ambient ventilation exchange. The computational model is implemented using HTML5 Canvas, CSS3, and JavaScript, enabling real-time interactive visualization. The influence of the thermal diffusivity coefficient on solution stability is analyzed, and the role of stochastic perturbations in achieving physical realism is discussed. Results confirm that the discrete model reproduces the expected steady-state thermal profile consistent with theoretical predictions.
