**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30840

##### Simulation of Fluid Flow and Heat Transfer in the Inclined Enclosure

**Authors:**
M. Akbari,
A. Karimipour,
M. Afrand,
M.R. Safaei

**Abstract:**

Mixed convection in two-dimensional shallow rectangular enclosure is considered. The top hot wall moves with constant velocity while the cold bottom wall has no motion. Simulations are performed for Richardson number ranging from Ri = 0.001 to 100 and for Reynolds number keeping fixed at Re = 408.21. Under these conditions cavity encompasses three regimes: dominating forced, mixed and free convection flow. The Prandtl number is set to 6 and the effects of cavity inclination on the flow and heat transfer are studied for different Richardson number. With increasing the inclination angle, interesting behavior of the flow and thermal fields are observed. The streamlines and isotherm plots and the variation of the Nusselt numbers on the hot wall are presented. The average Nusselt number is found to increase with cavity inclination for Ri ³ 1 . Also it is shown that the average Nusselt number changes mildly with the cavity inclination in the dominant forced convection regime but it increases considerably in the regime with dominant natural convection.

**Keywords:**
mixed convection,
Richardson number,
inclined driven cavity

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1083769

**References:**

[1] D. V. Davis, "Numerical Convection of Air In a Square Cavity: A Bench Mark Numerical Solution", Int. J. For Numerical Methods in Fluids, vol. 3, pp. 249-264, 1983.

[2] M. Corcione, "Effect of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above", Int. J. of Thermal Sciences, vol. 42, pp. 199-208, 2003.

[3] V. A. F. Costa, M. S. A. Oliveira, A. C. M. Sousa, "Control of laminar natural convection in differentially heated square enclosures using solid inserts at the corners", Int. J. of Heat and Mass transfer, vol. 46, pp. 3529-3537, 2003.

[4] A. Kumar, A. Dalal, "A numerical study of natural convection around a square horizontal, heated cylinder placed in an enclosure", Int. J. of Heat and Mass Transfer, vol. 49, pp. 4608-4623, 2006.

[5] I. E. Sarris, I. Lekakis, N. S. Vlachos, "Natural convection in a 2D enclosure with sinusoidal upper wall temperature", Numerical heat transfer, vol. 42, pp. 513-530, 2002.

[6] E. Bilgen, R. B. Yedder, "Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side", Int. J. of Heat and Mass Transfer, vol. 50, pp. 139-150, 2007.

[7] L. M. Cruz, E. Ramos, "Mixing with time dependent natural convection", Int. Communications in Heat and Mass Transfer, vol. 33, pp. 191-198, 2006.

[8] C. Sert, A. Beskok, "Numerical Simulation of Reciprocating Flow Forced Convection in 2 Dim channels", J. of Heat Transfer, vol. 125, pp. 403-412, 2003.

[9] H. F. Oztop, I. Dagtekin, "Mixed convection in two-sided lid-driven differentially heated square cavity", Int. J. of heat and mass transfer, vol. 47, pp. 1761-1769, 2004.

[10] A. M. Amiri, K. M. Khanafer, I. Pop, "Numerical simulation of combined thermal and mass transport in a square lid-driven cavity", Int. J. of Thermal Sciences, vol. 46, pp. 662-671, 2007.

[11] A. Zekeriya, O. Kurtul, "Natural convection in tilted rectangular enclosures with a vertically situated hot plate inside", Applied Thermal Engineering, vol. 27, pp. 1832-1840, 2007.