A Mathematical Method to Keep The Temperature In The Bathtub

DOI

10.2991/wartia-16.2016.120How to use a DOI?

Keywords

Lumped Parameter Model Runge-Kutta Method Hot Bath

Abstract

In this paper, we do the best to extend the time of bathing without wasting too much water. In the Lumped Parameter model[1], we predict the change of temperature by the use of Runge-Kutta method. We also consider the heat dissipation between the water and the bathtub wall as well as the air. And we discuss the change of temperature under different height of water surface. In our opinion, when a person is sitting in the tub, he just gets heat energy from water. We add a new equation of conservation of energy. Compared with the heat dissipation on the water, the body has less influence on the temperature of water. A person is in motion instead of stationary when bathing. In other to correct the evaporative coefficient of water, we introduce a correction coefficient (we call it ). Under the depth of 0.43 meters, we can determine to reach the value of the correction coefficient ( ) of 38 within 15 minutes, where =1.15. After researching the relationship between different rate of drainage and temperature, we use to predict the time arriving at 38 for the second time. Compared with the longest suitable bathing time, it is longer than 30 minutes in general. It can be proved that our strategy is able to keep the temperature throughout the bathtub and as close as possible to the initial temperature without wasting too much water.

Copyright

© 2016, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - CONF
AU  - Huinian Li
AU  - Shuting Li
AU  - Jiong Zhang
PY  - 2016/05
DA  - 2016/05
TI  - A Mathematical Method to Keep The Temperature In The Bathtub
BT  - Proceedings of the 2016 2nd Workshop on Advanced Research and Technology in Industry Applications
PB  - Atlantis Press
SP  - 585
EP  - 588
SN  - 2352-5401
UR  - https://doi.org/10.2991/wartia-16.2016.120
DO  - 10.2991/wartia-16.2016.120
ID  - Li2016/05
ER  -