A review is made of certain analytical methods used in heat transfer. Singular perturbation methods, asymptotic methods, and methods associated with the solution of integral equations are considered for the purpose of solving problems in various types of heat transfer.

摘要: In the excellent monographs [1-7], achievements in various fields of heat transfer are considered from physical point view a systematic and unique way. An attempt is made this present review to generalize these mathematical methods. It should be emphasized that some most important methods current literature on still process development examples quoted frequently order show virtue method those branches where it can as potential means obtaining solution. Therefore, considering specific method, desirable cite based considerations. We also try cite, wherever possible, references fundamental works connected with methods, for which author does not make any claims completeness enormous volume existing literature. The criteria selecting how has been applied problems associated types transfer. However, their being generally well known, there will no need refer integral [8] devoted, or description application nonsteady-state [9]. similar way, classical operational calculus, used widely [10-12]. shall consider detail perturbation asymptotic solution equations. 1. Perturbation Methods consist mainly series expansion dependent variables respect powers known value, assumed small. When small quantity parameter, T~parametric perturbation" if coordinate called "coordinate perturbation, rT Assuming equal e, differential equation e ~ 0 zero order. inserted identical equated, we obtain system equations solutions successive orders. obtained convergent sense [96] scheme mentioned above suitable, then regular perturbation. This was number led very useful results. many ratio terms ceases becomes untenable certain region flow field. Thus, impossible valid over whole field by These singular Sometimes situation described arises because presence singularity at line inthe investigation. greater according increases. A procedure solving such proposed [13], variable v(x, e) an independent x expanded low value form: