This presentation provides an overview of quenching analyses as a specific example of conjugate heat transfer analysis. The presentation was given as part of a webinar on heat transfer analysis using COMSOL Multiphysics. Work conducted on analyzing air and oil quenching appears in this presentation. These quenching analyses include heat transfer mechanisms of conduction, convection, and radiation. Analytical results from both quench methods are compared with experimental data to provide an understanding of the accuracy of this methodology.