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MATHEMATICAL THEORY OF THERMAL INERTIA REVISITED 1: IMPROVING OUR UNDERSTANDING OF MARTIAN THERMOPHYSICAL PROPERTIES THROUGH ANALOGOUS EXAMPLES OF PERIODIC DIFFUSIVE INERTIAS

Introduction: In Planetary Science, thermal inertia has been defined the ability of a material to resist a temperature change when applying a periodic forcing function. Thermal inertia is used to answer scientific questions about the Martian surface and is used to constrain engineering requirements. However, one not familiar with its derivation, may inquire the following: 1) Why are the factors of thermal inertia under a radical? 2) What is the significance of an inverse roots second? 3) How does thermal inertia affect the heat flow i.e. what is the applicable equation? 4) Are there any analogous scenarios to improve conceptual understanding? We reproduce the mathematical derivation of thermal inertia from first principles to recall this parameter’s origin and application. Finally we provide a set of analogous equations and propose a new term, periodic diffusive inertia that describes the ability of a potential variable (e.g. temperature) to change within a class of scenarios described by a diffusion equation undergoing a periodic boundary condition. Background: Thermal inertia is a thermophysical property of a material and is defined as the square root of the thermal conductivity, specific heat, and density—with the units of joules per square meter per kelvin per root second.  I ≡ kρc [J ∙m!! ∙ K!! ∙ s!!/! ] Eq. 1