Natural convection flows in a trapezoidal enclosure with uniform and non-uniform heating of bottom wall

A penalty finite element analysis with bi-quadratic elements is performed to investigate the influence of uniform and non-uniform heating of bottom wall on natural convection flows in a trapezoidal cavity. In the present investigation, bottom wall is uniformly and non-uniformly heated while two vertical walls are maintained at constant cold temperature and the top wall is well insulated. Parametric study for the wide range of Rayleigh number (Ra  ), 103⩽Ra⩽105103⩽Ra⩽105 and Prandtl number (Pr  ), 0.07⩽Pr⩽1000.07⩽Pr⩽100 shows consistent performance of the present numerical approach to obtain the solutions in terms of stream functions and the temperature profiles. For certain values of the parameters studied in the above range, a symmetry is observed while representing the flow patterns in terms of stream functions. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. The power law correlations between average Nusselt number and Rayleigh numbers are presented. The effect of Prandtl number in the variation of local and average Nusselt numbers is more significant for Prandtl numbers in the range 0.07–0.7 than 10–100.