Transient natural convection in parallelogrammic enclosures with isothermal hot wall. Experimental and numerical study applied to on-board electronics

Abstract This work treats 2D transient natural convection in closed cavities of parallelogrammic section. Such cavities are formed by two vertical, active walls maintained at different temperatures, connected by a closing channel that can be inclined at an angle α with respect to the horizontal. The channel is adiabatic, the angle of tilt α being defined by the inclination of the upper and lower walls while the fitting lateral ones denote the parallelogram-shape section of the cavity. We present the temperature fields and the flow lines at some representative instants of the transient state for all angles treated. The temporal evolution of the maximum Nusselt number and maximum velocity near the hot wall are determined for all the angles and compared to those of the square cavity. The evolution of the local Nusselt number on the active hot wall is also presented for the transient and steady states, what constitutes the main original contribution of the present work. Numerical results are complemented by experimental thermal measurements at steady state. The small deviation found between measurements and calculations serve to validate the model used and to properly size real devices. This study is done for several Rayleigh numbers Ra whose high values, varying between 105 and 109, are representative of engineering assemblies, as it is the case of on-board electronics.