International Scientific Journal

Thermal Science - Online First

online first only

The math modeling research of constant temperature bath

This paper studies how the temperature in the bathroom keeps changing when people bathe in the bathtub. The shape, capacity, behavior and body posture of people in the bathroom are considered. In fluid mechanics point of view, we consider the impact of the flow of heat transfer, by the energy differential equations and boundary layer momentum to establish a set of partial differential equations, and use Laplace operator rewrite it. We use finite difference method (FDM), with Taylor series expansion. We use the function value of grid nodes of difference quotient instead of control equation of derivative, and discretize it, and solve the heat conduction equation.
PAPER REVISED: 2019-02-15
PAPER ACCEPTED: 2019-02-25
  1. Zhang, Y., Heat Transfer, Southeast University Press, Nanjing, China, 2004
  2. Zhao, Z., Enthalpy Difference for Calculating Heat Dissipation on Water Surface and Its Use, Journal of Hydraulic Engineering, 130(2004), 2, pp.34-37
  3. Bozsoki, I., et al., Component Level Modelling of Heat Transfer During Vapour Phase Soldering with Finite Difference ADI Approach, International Journal of Heat and Mass Transfer, 128(2019),1,pp.562-569
  4. Shi, C., Heat Conduction Equation Finite Difference Method to Achieve the Matlab, Journal of Xianyang Normal University, 24(2009), 4, pp.27-29
  5. Zhu, Q., Hen, X., Application of PDE Toolbox and Least Square Method in Heat Conduction of Metal, Process Automation Instrumentation, 32(2011), 6, pp. 26-31
  6. Zhang, C., Application of Matlab in analysis of steady state and unsteady state heat conduction, Computers and Applied Chemistry,23(2006),10,pp.986-990