Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates

Heat equation is a partial differential equation used to describe the temperature distribution in a heat-conducting body. The implementation of a numerical solution method for heat equation can vary with the geometry of the body. In this study, a three-dimensional transient heat conduction equation was solved by approximating second-order spatial derivatives by five-point central differences in cylindrical coordinates. The stability condition of the numerical method was discussed. A MATLAB code was developed to implement the numerical method. An example was provided in order to demonstrate the method. The numerical solution by the method was in a good agreement with the exact solution for the example considered. The accuracy of the five-point central difference method was compared with that of the three-point central difference method in solving the heat equation in cylindrical coordinates. The solutions obtained by the numerical method in cylindrical coordinates were displayed in the Cartesian coordinate system graphically. The method requires relatively very small time steps for a given mesh spacing to avoid computational instability. The result of this study can provide insights to use appropriate coordinates and more accurate computational methods in solving physical problems described by partial differential equations.

Bubble dynamics and mechanistic boiling heat transfer prediction on a scored copper surface

In this study, pool boiling heat transfer of de-ionized water was experimentally studied on a scored copper surface at a heat-flux range of 0 - 60 W/cm2. Bubble dynamics in an isolated bubble region were carefully investigated, including bubble departure diameters, bubble departure frequencies, and active nucleation site densities. The bubble dynamics were compared with available models, indicating the suitable models regarding the present experimental results. Then, based on the bubble dynamics, a mechanistic heat transfer model, developed in our previous studies, was employed to predict the present boiling curve. In the mechanistic model, heat fluxes from natural convection, transient heat conduction, and microlayer evaporation were incorporated.