Examining the thermal dynamics of coffee cups: evaluating the impact of cup material on thermal characteristics via numerical simulations

Emmanuel, Sabastine

Abstract

This work examines the thermal diffusivity properties of four different materials, ceramic, stainless steel, plastic, and glass, using the one-dimensional heat equation's Initial Boundary Value Problem (IBVP) framework. We investigate the transient thermal behaviour of these materials using numerical techniques like the Crank-Nicolson method and the explicit FTCS (Forward-Time Central-Space) method. We perform simulations and analyse heat transfer dynamics and temperature distributions using Python implementations with uniform step sizes. According to our research, there are notable differences in the thermal diffusivity performance of the materials, with stainless steel showing better conductive qualities. Furthermore, a look at the midpoint temperature profiles of the cups provides information on the thermal and temporal dynamics. A comparison of the Crank-Nicolson and FTCS approaches shows how effective the latter is in producing precise and stable solutions. The study contributes to a deeper understanding of material thermal properties and numerical methods' suitability for simulating heat transfer phenomena. Keywords Heat transfer, Thermal performance, Heat equation, Crank-Nicolson method, Thermal conductivity.

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