A convergent three-level finite difference scheme for solving a dual-phase-lagging heat transport equation in spherical coordinates

✍ Scribed by Weizhong Dai; Lixin Shen; Raja Nassar

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 126 KB
• Volume: 20
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.10073

✦ Synopsis

Abstract

Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation is different from the traditional heat diffusion equation since a second‐order derivative of temperature with respect to time and a third‐order mixed derivative of temperature with respect to space and time are introduced. In this study, we consider the heat transport equation in spherical coordinates and develop a three‐level finite difference scheme for solving the heat transport equation in a microsphere. It is shown that the scheme is convergent, which implies that the scheme is unconditionally stable. Results show that the numerical solution converges to the exact solution. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 60–71, 2004.