Arab J Sci Eng DOI 10.1007/s13369-016-2055-0 RESEARCH ARTICLE - MECHANICAL ENGINEERING Numerical Study of the Hydrodynamic and Thermal Proprieties of Titanium Dioxide Nanofluids Trapped in a Triangular Geometry Seif-Eddine Ouyahia 1 · Youb Khaled Benkahla 1 · Nabila Labsi 1 Received: 1 July 2015 / Accepted: 20 January 2016 © King Fahd University of Petroleum & Minerals 2016 Abstract In the present work, we investigate numerically the fluid flow and heat transfer inside an entrapped cavity, which has an isosceles triangular cross-section and is filled with TiO 2 –water nanofluid. The base wall is maintained at high constant temperature, while the two other sides are kept a lower constant temperature. The length of the cavity is large enough to assume that the flow is two-dimensional. The gov- erning equations are discretized by the finite volume method and solved numerically via the SIMPLER algorithm. In the present work, we investigate the effect of some parameters including the Rayleigh number, the solid volume fraction, the cavity aspect ratio and the inclination angle on both the ther- mal performance and the flow structure. The obtained results show that the thermal performance of the cavity and the flow structure are most sensitive to Rayleigh number and solid vol- ume fraction. On the other hand, the aspect ratio of the cavity and its inclination also affect considerably the heat transfer and fluid flow pattern. We notice the occurrence of a pitch- fork bifurcation phenomenon, which is a function of both Rayleigh number and cavity aspect ratio. Our results pro- vide information that may be useful for design optimization as well as for thermal performance enhancement of energy systems such as solar water heaters. Keywords Triangular cavity · Natural convection · Nanofluid · Finite volume B Seif-Eddine Ouyahia seifeddine.ouyahia@yahoo.fr 1 Laboratory of Transport Phenomena, Faculty of Mechanical and Process Engineering, USTHB, B.P. 32, El-Alia Bab-Ezzouar, 16111 Algiers, Algeria List of symbols A Cavity aspect ratio ( HL −1 ) c p Heat capacity (J kg −1 K −1 ) D Dimensionless distance along the inclined wall g Gravitational acceleration (m s −2 ) H Cavity height (m) k Thermal conductivity (W m −1 K −1 ) L Cavity width (m) Nu Local Nusselt number Nu m Average Nusselt number p Pressure (Pa) P Dimensionless pressure Pr Prandtl number Ra Rayleigh number T Temperature (K) u ,v Velocity components (m s −1 ) U, V Dimensionless velocity components x , y Cartesian coordinates (m) X , Y Dimensionless Cartesian coordinates Greek letters α Thermal diffusivity (m 2 s −1 ) β Thermal expansion coefficient (K −1 ) δ Base angle ( ◦ ) θ Dimensionless temperature λ Apex angle ( ◦ ) μ Dynamic viscosity (kg m −1 s −1 ) ν Kinematic viscosity (m 2 s −1 ) ρ Density (kg m −3 ) φ Volume fraction of nanoparticles ψ max Dimensionless stream function ω Tilt angle ( ◦ ) 123