On exact and perturbation solutions to nonlinear equations for heat transfer models

TL;DR

This paper critically examines various exact and approximate solutions to nonlinear heat transfer equations, highlighting issues in recent Lie algebra-based methods and evaluating alternative analytical and perturbation approaches.

Contribution

It provides a critical analysis of existing methods, disproves some recent Lie algebra-based solutions, and explores alternative analytical and perturbation techniques for nonlinear heat transfer equations.

Findings

Recent Lie algebra methods are either trivial or incorrect.

A simple hypervirial theorem-based expression is tested.

Earlier perturbation results are discussed and evaluated.

Abstract

We analyze some exact and approximate solutions to nonlinear equations for heat transfer models. We prove that recent results derived from a method based on Lie algebras are either trivial or wrong. We test a simple analytical expression based on the hypervirial theorem and also discuss earlier perturbation results.