S. Wortmann, M. T. Vilhena, H.F. de Campos Velho, C. F. Segatto (2004): An Improved Generalized Integral Transform Technique Solution for the Diffusion-advection Fluid Flow, (IMSE-2004), 02-05 August, Dept. of Mathematics and College of Engineering, Orlando, Florida, USA.

Abstract: A new version of the Generalized Integral Transform Techique (GITT) is report to solve fluid flow problems. The main feature of the GITT approach consists in construction of an appropriate Sturm-Loiuville problem, which after solved, allow us to expand the problem solution in a trucated series in term of the calculated eigenfunctions. After taking moments we come out with a set of ordinary differential equations which is traditionally solved by numerical subroutines [1, 2]. In this work, we step forward by solving this set of equations by the Laplace transform technique [3]. This methodology is applied in two problems [4]. The first one refers to simulation of pollutant dispertion by solving diffusion-adivective equation assuming variable coefficients. The second one consists in the solution of the laminar fluid flow between two parallel plates problem either for the developped velocity field and energy. Bearing in mind the nonlinearity of the second problem, the formulation for the linear problem (the first problem) is applied iterativelly in the solution of the nonlinear problem. Numerical simulations and comparisons are reported for the two problems [5].

References

[1] R. M. Cotta; ”Integral Transforms in Conputational Heat and Fluid Flow”; CRC Press, Boca Raton, Florida (1993).

[2] R. M. Cotta, M. D. Mikhailov; ”Heat Conduction - Lumped Analysis, Integral Transforms, Symbolyc Computation”, John Wiley & Sons, Chichester (1997).

[3] C. F. Segatto, M. T. Vilhena. The state of art of the LTSn method, Proceedings of Mathematics and Computational Reactor Physics and Enviromental Analysis in Nuclear Applications, Madrid, pp. 1618-1631 (1999).

[4] Wortmann, S.; "Formula\c{c}\~ao Semi-Analitica para a Equa\c{c}\~ao Transformada Resultante da Aplica\c{c}\~ao da GITT em Problemas Difusivos-Advectivos", D.Sc. thesis, Graduate Program on Mechanical Engineering, UFRGS, Porto Alegre, RS, Brazil (2003).

[5] R. K. Shah, A. L. London; "Laminar Flow Forced Convection in Ducts", Adv. Heat Transfer; Academic Press (1978).