A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier-Stokes equations formulation

• Published in: Numerical heat transfer. Part B, Fundamentals Vol. 76; no. 2; pp. 60 - 87
• Main Authors: Cotta, Renato M., Lisboa, Kleber M., Curi, Marcos F., Balabani, Stavroula, Quaresma, João N. N., Perez-Guerrero, Jesus S., Macêdo, Emanuel N., Amorim, Nelson S.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03-08-2019; Taylor & Francis Ltd
• Subjects: Computational fluid dynamics; Computer simulation; Convection-diffusion equation; Convergence; Eigenvectors; Expansion; Fluid flow; Formulations; Heat transfer; Integral transforms; Mass transfer; Navier-Stokes equations
• ISSN: 1040-7790; 1521-0626
• DOI: 10.1080/10407790.2019.1642715

The Generalized Integral Transform Technique (GITT) is reviewed as a hybrid numerical-analytical approach for fluid flow problems, with or without heat and mass transfer, here with emphasis on the literature related to flow problems formulated through the full Navier-Stokes equations. A brief overview of the integral transform methodology is first provided for a general nonlinear convection-diffusion problem. Then, different alternatives of eigenfunction expansion strategies are discussed in the integral transformation of problems for which the fluid flow model is either based on the primitive variables or the streamfunction-only formulations, as applied to both steady and transient states. Representative test cases are selected to illustrate the different eigenfunction expansion approaches, with convergence being analyzed for each situation. In addition, fully converged integral transform results are critically compared to previously reported simulations obtained from traditional purely discrete methods.