https://doi.org/10.1051/epjap/2009072
Steady thermal explosion with power-law thermal absorptivity in microannuli: wavy-roughness effect
2/F, 24, Lane 260, First Section, Muzha Road, Taipei, 116 Taiwan, P.R. China
Corresponding author: ustcphysqin@gmail.com
Received:
28
November
2008
Revised:
4
February
2009
Accepted:
7
March
2009
Published online:
22
April
2009
We obtain the approximate solutions for the steady temperature profiles of materials with a temperature-dependent thermal absorptivity inside a microannulus with wavy-rough surfaces considering a quasilinear partial differential equation by the boundary perturbation approach. Our numerical results show that the wave number as well as the small amplitude of the wavy roughness will influence the net temperature significantly especially near the inner wall of a microannulus. Meanwhile we observed that the critical Frank-Kamanestkii parameter depends on the small-amplitude wavy-roughness for specific power-law of thermal absorptivity. Our results could be applied to the relevant fields in MicroElectroMechanical System (MEMS).
PACS: 83.80.Jx – Reacting systems: thermosetting polymers, chemorheology, rheokinetics / 66.30.Xj – Thermal diffusivity / 89.30.-g – Energy resources / 89.20.Dd – Military technology and weapons systems; arms control / 44.05.+e – Analytical and numerical techniques
© EDP Sciences, 2009
