Transfinite element methodology for non‐liner/linear transient thermal modelling/analysis: Progress and recent advances

Recent progress and advances in the development and applicability of a novel ‘transfinite element’ computational methodology is presented for general non‐linear/linear transient thermal problems. The proposed methodology and concepts are new and unique, and demonstrate the applicability to general transient non‐linear/linear thermal analysis situations by combining classical Galerkin schemes and transform approaches with contemporary finite element methods to preserve the modelling versatility and numerical features–thereby, a hybrid computational methodology is proposed. Characteristic features and pertinent details of the approach are described for non‐linear/linear transient thermal problems, wherein non‐linearities due temperature dependence of thermophysical properties and/or general non‐linear bound ary conditions to include radiation, effects due to phase change, etc., are considered. In addition, the use of high‐continuity formulations in conjuction with the proposed methodology to furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom is also demonstrated. Numerical test cases are presented for a variety of problems to demonstrate the fundamental features and applicability of the proposed formulations. The proposed hybrid transfinite element methodology and concepts offer significant potential for extension to several areas of mathematical physics and engineering and to interdisciplinary research areas.