Behaviour of a non-local reactive convective problem modelling Ohmic heating of foods

Lacey, AA; Tzanetis, DE; Vlamos, PM

dc.contributor.author	Lacey, AA	en
dc.contributor.author	Tzanetis, DE	en
dc.contributor.author	Vlamos, PM	en
dc.date.accessioned	2014-03-01T01:14:26Z
dc.date.available	2014-03-01T01:14:26Z
dc.date.issued	1999	en
dc.identifier.issn	0033-5614	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13063
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0033224809&partnerID=40&md5=59b5e0a4b43e0fb1de612dfa44313a9f	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.other	Electric conductivity	en
dc.subject.other	Electric currents	en
dc.subject.other	Electric heating	en
dc.subject.other	Electric potential	en
dc.subject.other	Food processing	en
dc.subject.other	Temperature	en
dc.subject.other	Thermal conductivity	en
dc.subject.other	Electric current flowing	en
dc.subject.other	Nonlocal problem	en
dc.subject.other	Mathematical models	en
dc.title	Behaviour of a non-local reactive convective problem modelling Ohmic heating of foods	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	We consider the non-local problem, u(t) + u(x) = lambda f(u)/(integral(0)(1) f(u)dx)(2), 0 < x < 1, which models the temperature when an electric current flows through a moving material with negligible thermal conductivity. The potential difference across the material is fixed but the electrical resistivity f(u) varies with temperature. It is found that, for f decreasing with integral(0)(infinity) f(s)ds < infinity, blow-up occurs if lambda is too large for a steady state to exist or if the initial condition is too big. If f is increasing with integral(0)(infinity) ds/f(s) < infinity blow-up is also possible. If f is increasing with integral(0)(infinity) ds/f(s) = infinity or decreasing with integral(0)(infinity) f(s)ds = infinity the solution is global. Some special cases with particular forms of f are discussed to illustrate what the solution can do.	en
heal.publisher	Oxford Univ Press, Oxford, United Kingdom	en
heal.journalName	Quarterly Journal of Mechanics and Applied Mathematics	en
dc.identifier.isi	ISI:000083973500009	en
dc.identifier.volume	52	en
dc.identifier.issue	pt 4	en
dc.identifier.spage	623	en
dc.identifier.epage	644	en