Analytical solutions to two-dimensional diffusion type problems in irregular geometries

✍ Scribed by J.B. Aperecido; R.M. Cotta; M.N. Özişik

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 685 KB
• Volume: 326
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(89)90021-5

✦ Synopsis

A methodology, bused on the ideas associated with the generalized integral transform technique, is presented for developing analytical solutions to sufJiently general two-dimensional (i.e. x and t space coordinates) dtflision type problems in arbitrarily shaped singl_v or doubly connected regions when the boundary contour in one of the space coordinates can be e.xpressed in terms of the other. The model is also applicable for determining ,ftdly developed velocity distribution in arbitrarily shaped straight ducts. To illustrate the application, laminar,forcedJEow in a right angle triangle duct is considered and the results are compared to the available exact solutions to assess the accuracy of the method. Nomenclature a, b a(t), b(t) A,,(% B,,(t) A,*,(t), B,:(t) n,, .f f;(x) G(z) dz Re T(x> Y) perpendicular sizes of the right angle triangular duct coefficients in operator Z,, defined by Eqs (6d, e) defined by Eqs (4d, e) hydraulic diameter of right angle triangular duct friction factor prescribed boundary function in Eqs (Id, e) imposed pressure gradient in axial direction ,z