On the Darcy–Brinkman–Boussinesq Flow in a Thin Channel with Irregularities
In this paper, we investigate the effects of a small boundary perturbation on the non-isothermal fluid flow through a thin channel filled with porous medium. Starting from the Darcy–Brinkman–Boussinesq system and employing asymptotic analysis, we derive a higher-order effective model given by the explicit formulae. To observe the effects of the boundary irregularities, we numerically visualize the asymptotic approximation for the temperature, whereas the justification and the order of accuracy of the model is provided by the theoretical error analysis.
KeywordsBoundary perturbation Thin domain Darcy–Brinkman–Boussinesq flow Asymptotic solution Error analysis
The authors of this work have been supported by the Croatian Science Foundation (Scientific Project 2735: Asymptotic analysis of boundary value problems in continuum mechanics—AsAn). The authors would like to thank the referee for his/her helpful comments and suggestions that helped to improve our paper.
- Boussinesq, J.: Théorie Analytique de la Chaleur, vol. 2. Gauthier-Villars, Paris (1903)Google Scholar
- Brinkman, H.: A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1, 27–34 (1947)Google Scholar
- Darcy, H.: Les Fontaines Publiques de la ville de Dijon. Victor Darmon, Paris (1856)Google Scholar
- Galdi, G.P.: An Introduction to the Mathematical Theory of the Navier–Stokes Equations, vol. I. Springer, Berlin (1994)Google Scholar
- Marušić-Paloka, E., Pažanin, I., Marušić, S.: Comparison between Darcy and Brinkman laws in a fracture. Appl. Math. Comput. 218, 7538–7545 (2012)Google Scholar