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Mathematical model of warming up a cold hand by contact with a hot pipe

Siedlecka Urszula

Journal of Applied Mathematics and Computational Mechanics

2025

Vol. 24, nr 2

61--70

In this article, the problem of heating a cold hand squeezing a pipe through which hot water flows is considered. The mathematical model concerns a one-dimensional axisymmetric problem in cylindrical coordinates. The aim of the research is to estimate the probability of different degrees of burns depending on the temperature of the flowing hot water, the pipe material, and the heating time. This probability is estimated using the Arrhenius integral. The considered problem is solved numerically using the finite volume method. Numerical examples of simulations for various pipe materials are presented.