The paper treats in one space variable a mixed heat transfer problem of steady conduction and radiation in a wire with internal source. We are led to a Cauchy problem consisting of a second order nonlinear ordinary differential equation. A special integrable case with two not independent left boundary conditions requires a hyperelliptic integral, for which a representation theorem has been established through the Gauss hypergeometric function $_{2}F_{1}$. The relevant steady solution is then found to grow monotonically with the distance from boundary, till to a certain limiting position where it suddenly jumps unbounded.
G. Mingari Scarpello, A. Palestini, D. Ritelli (2005). Exact Integration of a Nonlinear Model of Steady Heat Conduction/Radiation in a Wire with Internal Power. JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, 4, 59-67.
Exact Integration of a Nonlinear Model of Steady Heat Conduction/Radiation in a Wire with Internal Power
RITELLI, DANIELE
2005
Abstract
The paper treats in one space variable a mixed heat transfer problem of steady conduction and radiation in a wire with internal source. We are led to a Cauchy problem consisting of a second order nonlinear ordinary differential equation. A special integrable case with two not independent left boundary conditions requires a hyperelliptic integral, for which a representation theorem has been established through the Gauss hypergeometric function $_{2}F_{1}$. The relevant steady solution is then found to grow monotonically with the distance from boundary, till to a certain limiting position where it suddenly jumps unbounded.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
