Mathematical model for a liquid heat loss

This paper studies the cooling of coffee phenomena using a first-order linear ordinary differential equation (ODE). There are two models that we propose to investigate this phenomenon. We solve the models analytically to obtain the evolution of the temperature as a function of time. Some numerical s...

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Bibliographic Details
Published in:AIP conference proceedings 2022-07, Vol.2479 (1)
Main Authors: Noor, D. Michiko M., Haniah, Magdalena, Ikha
Format: Article
Language:English
Subjects:
Coffee
Differential equations
Experimentation
Heat loss
Mathematical models
Numerical methods
Ordinary differential equations
Room temperature
Simulation
Online Access:Get full text
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Summary:This paper studies the cooling of coffee phenomena using a first-order linear ordinary differential equation (ODE). There are two models that we propose to investigate this phenomenon. We solve the models analytically to obtain the evolution of the temperature as a function of time. Some numerical simulations are presented by solving the model numerically using the Euler and Heun methods. Moreover, the numerical simulations will be applied to adjust a constant parameter of proportionality of the model that will be suitable for the primary data collected from self-experimentation. The result from the first model shows that the coffee temperature decreases to 0°C as a stable, steady state. Meanwhile, the second model simulation shows similar behavior towards room temperature, which is also the only equilibrium point. In addition, RMSEs for the Euler and Heun methods are used to examine the accuracy of both techniques, and we conclude that the Heun method gives a better approach than the Euler.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0100178