Effect of local heater size and position on natural convection in a tilted nanofluid porous cavity using LTNE and Buongiorno's models

Natural convection heat transfer within nanofluid porous cavities with local heaters occurs in different engineering applications. Therefore, analysis of nanofluid flow and heat transfer patterns in such systems has a significant value for development of industry. In the present study, free convection of nanofluid in a tilted porous cavity with a local isothermal heater has been investigated numerically. Governing equations with corresponding initial and boundary conditions formulated using the Darcy-Boussinesq model and local thermal non-equilibrium approach have been solved by the finite difference method under the effects of Brownian diffusion and thermophoresis. Effects of heater location (δ = 0.1-0.3) and dimensionless length (D = 0.2-0.8) as well as cavity inclination angle (γ = 0-π/2) and interphase heat transfer coefficient (H = 10-1000) on nanofluid flow and heat transfer have been studied for the following values of other governing parameters: Rayleigh number (Ra = 105), Prandtl number (Pr = 6.82), Darcy number (Da = 10−3), porosity of porous medium (ε = 0.5), buoyancy ratio parameter (Nr = 1), Brownian diffusion parameter (Nb = 10−6), thermophoresis parameter (Nt = 10−6), Lewis number (Le = 1000), thermal diffusivity ratio (Γ = 649.7) and heat capacitance ratio (ξ = 3.4). It has been found the heat transfer enhancement and convective flow attenuation when the distance between the heater and the cold vertical wall reduces.