The influence of the external Rayleigh number, inclination angle, and internal
Rayleigh number on natural convection within an air-filled parallelogrammic enclosure
containing a volumetric source has been investigated numerically. The left
sidewall of the enclosure is subjected to a non-uniformly hot temperature and the right
sidewall experiences a uniform cold temperature while the remaining top and bottom
walls are kept adiabatic. The physical problems are represented mathematically by
various sets of governing equations along with the corresponding boundary conditions.
Buoyancy forces are taken into account during the analysis of the present investigation.
By using the finite volume method, the dimensionless governing equations are
discretized numerically based on a non-uniform collocated grid system. Results are
obtained for a wide range of external Rayleigh numbers varying from 103 to 106 with
internal Rayleigh numbers varying from (0) to (108) while the left sidewall from
vertical is varied as 0, 30, –30, 60, and –60°, respectively. In the present study, the
obtained results are presented in terms of streamlines, isotherms, and average Nusselt
number along the hot and cold sidewalls. Two pairs of rotating vortices are observed
due to the non-uniform heating process while the shape of this rotating vortices is
sensitive to the inclination angle. Furthermore, the flow field circulation and the
average Nusselt number increase remarkably with the increase in the external Rayleigh
number. The results of the present work are compared with other published results and
give excellent agreement.