Research of the Optimal Shape of Bathtub

Abstract

We take heat transfer between water and air and heat dissipation capacity of bathtubs into consideration and discuss the influence of bathtub shapes on temperature. We keep the temperature of bathtub in 39 degrees Celsius.We assume that the bathtub’s capacity is the same and try to find the best shape of the bathtub. After calculating, we discover cylindrical bathtub do better on heat preservation. Introduction There is heat convection between water and bathtub wall. Due to the fact that the bathroom temperature is generally lower than the water temperature in the bathtub. The heat will dissipate through bath wall. The ability of heat dissipation is related with material and shape of the bathtub. We assume that bathtubs’ wall is vertical, the capacity of bathtub is the same and the interface between water and air is the same. Problem analysis There are many factors influence water temperature in the bathtub, mainly including: The liquidity of water: including the heat conduction and diffusion, the geometry of a water, and the location of overflow drain, etc. The heat exchange at the water surface:  Convection: Water and air heat transfer between two different media mainly by convection  Heat conduction: If the air temperature and water temperature is different, energy exchange can occur through heat conduction.  Evaporation: On the border of water and air, when some water molecules have enough energy, they will escape to the air. Water and energy exchange in the bathtub: the heat exchange of bathtub with water is by solid heat conduction. In the bathtub, water temperature is determined by heat exchange between the interior and exterior parts of water. The heat exchange between the water and exterior environment is determined by the temperature brought by inflowing hot water and that taken away by overflow. The heat exchange in the interior of water including:  The water vertical flowing caused heat exchange  The heat exchange caused by water density convection Besides we also need to consider the shape and volume of the tub. Basic Assumption  The initial air temperature and humidity are fixed value in the bathroom.  The bathroom is an independent system.  Per unit time, the addition of hot water is constant.  The temperature of the water flowing into bathtub is 45°C.  Initial water temperature in the bathtub is 39°C.  Hot water is supplied through bath all.  Overfall gap won't be blocked up. 2nd International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2016) © 2016. The authors Published by Atlantis Press 440  At first the bathtub is filled with water The Optimal Shape of Bathtub The changes of water quality throughout the system are present as following: