Heatline visualization of natural convection flows within trapezoidal enclosures

Abstract: Numerical visualization of heat transport for convective heat transfer were studied by two-dimensional heat function formulation within a trapezoidal cavity, differentially heated in the vertical direction, is presented. Penalty finite element method is used to obtain the isotherm lines, streamlines and heatlines to perceive the understanding of heat and fluid flow. Numerical results are presented for Rayleigh numbers, Ra = 103, 106 and Prandtl numbers, Pr = 0.7 and 10. For low Rayleigh number Ra = 103 it is observed from the heatlines that the heat is transported from the hot wall to the cold wall uniformly. For Ra = 106 the heat transfer is more intense at the lower-left and upper-right walls of the cavity. Flow characteristics depends strongly on the Rayleigh number and Prandtl number for various side wall inclination angles φ = 45◦, 30◦ and 0. Maximum value of heatline provides directly the value of the average Nusselt number. The secondary circulations were observed for Ra = 106. Heatlines were observed to predict the energy transfer better than isothermal lines.