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Use of optimization methods to solve heat convection problems with unknown wall boundary conditions
Author(s) -
Gray Michael,
Smith Russell A.
Publication year - 1971
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620030309
Subject(s) - boundary value problem , mathematics , ordinary differential equation , partial differential equation , heat transfer , initial value problem , mathematical optimization , differential equation , mathematical analysis , computer science , mechanics , physics
In convection heat transfer problems, it is convenient to solve the governing differential equations by using straightforward marching techniques for numerical integration. However, the boundary layer equations in these heat transfer problems are not of the initial value type even though they are parabolic equations. Consequently marching techniques are not successful until correct initial values are known. A means of determining these initial values is presented herein. Selected optimization methods are utilized in conjunction with marching integration techniques to solve third‐ and fourth‐order ordinary differential equations which have three unknown initial boundary conditions. Two optimization methods, one deterministic and the other non‐deterministic in nature, are used both independently and in combination as determined by the particular circumstances. Two applications are used to demonstrate the technique and comparison is made with existing solutions.