Natural convection in an inclined parallelogram-shaped enclosurecontaining internal energy source with linearly heated sidewall

Abstract

The main objective of this paper is to study the natural convection flow inside a parallelogram enclosure having uniform internal heat generation. The left inclined wall is linearly heated while the right inclined wallis kept at cold temperature (T_c) and top and bottom walls are thermally insulated. Steady state, two-dimensional numerical study is carried out by using the finite volume technique after the equations are put into dimensionless forms. The governing parameters studied are external Rayleigh number, internal Rayleigh number and inclination angle from horizontal axis which are varied from 10³≤Ra_E≤10⁶, 0≤Ra_I≤10⁸and 0^o≤Φ≤45^o. Air is used as a working fluid with a Prandtl number of 0.71. Efforts are focused on the interaction between the internal Rayleigh number (heat generation) and external Rayleigh number (temperature difference between the sidewalls) for various inclination angles. The accuracy of the numerical method compared with the previous published works shows an excellent agreement. The obtained results show that the maximum heat transfer performance occurs at zero inclination angle and low values of external heating.

Keywords: Natural convection; heat generation; linear heating; parallelogram enclosure; finite volume.