Numerical study of double diffusive buoyancy forces induced natural convection in a trapezoidal enclosure partially heated from the right sidewall

A study of double-diffusive natural convection in a trapezoidal enclosure with a partial heated active right sidewall has been conducted numerically using the finite difference method. The length of the heated active part is equal to half of the inclined wall. Uniform different temperatures and concentrations are imposed along the active parts of the enclosure. The top and bottom boundaries of the enclosure, as well as inactive part of the right sidewall, are being insulated and impermeable. The species diffusivity of the fluid is considered to be constant, but the density varies linearly with the temperature and concentration. Double-diffusive convection for laminar two-dimensional incompressible flow with negligible radiation is expressed in terms of vorticity, temperature or energy, concentration and stream function. A Partial Differential Equation (PDE) technique is adopted to generate regular grid distribution in the physical space. The numerical results are reported for the effect of different heating cases, thermal Grashof numbers, and inclination angles on the contours of streamline, temperature, and concentration. Also, the relevant results for the average Nusselt and Sherwood numbers are demonstrated for several parameters including thermal Grashof number (103⩽GrT⩽106)103⩽GrT⩽106), Lewis number (0.5⩽Le⩽10)0.5⩽Le⩽10), Prandtl number (0.7⩽Pr⩽10)0.7⩽Pr⩽10) at a fixed aspect ratio Ar=1Ar=1 and buoyancy ratio N=-0.2N=-0.2.