## THERMAL SCIENCE

International Scientific Journal

### APPLICATION OF HEAT-BALANCE INTEGRAL METHOD TO CONJUGATE THERMAL EXPLOSION

**ABSTRACT**

Conjugate thermal explosion is an extension of the classical theory, proposed and studied recently by the author. The paper reports application of heat-balance integral method for developing phase portraits for systems undergoing conjugate thermal explosion. The heat-balance integral method is used as an averaging method reducing partical differential equation problem to the set of first-order ordinary differential equations. The latter reduced problem allows natural interpretation in appropriately chosen phase space. It is shown that, with the help of heat-balance integral technique, conjugate thermal explosion problem can be described with a good accuracy by the set of non-linear first-order differential equations involving complex error function. Phase trajectories are presented for typical regimes emerging in conjugate thermal explosion. Use of heat-balance integral as a spatial averaging method allows efficient description of system evolution to be developed.

**KEYWORDS**

PAPER SUBMITTED: 2008-01-15

PAPER REVISED: 2008-03-10

PAPER ACCEPTED: 2008-03-10

**THERMAL SCIENCE** YEAR

**2009**, VOLUME

**13**, ISSUE

**2**, PAGES [72 - 80]

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