Heat Conduction with Krylov Subspace Method Using FEniCSx

The study of heat transfer deals with the determination rate energy from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often fundamental principle behind several engineering systems. Heat analysis necessary while designing any product. most common numerical method used analyze finite element method. This paper uses demonstrate steady transient conduction three-dimensional bracket. goal here was determine distribution flow solid. crucial machine elements as they are subjected various thermal loads during operation also due fluctuations surrounding environmental conditions. significantly affects stress, displacements, volumetric strains. Thus, stresses induced element, it find field first. performed using open-source package FEniCSx on Python. program run preconditioned Krylov subspace for higher-order function spaces. solver drastically reduces computational time. time taken execution each order recorded presented.