Numerical Study of Natural Convection Flow in Rectangular Cavity with Viscous Dissipation and Internal Heat Generation for Different Aspect Ratios

Numerical simulations have been performed to investigate the influence of constant volumetric heat generation and viscous dissipation on the unsteady natural convection flow of an incompressible Newtonian fluid contained in a rectangular cavity. The left vertical wall of the cavity is cooled, while the right vertical wall is heated, and the bottom and top walls are adiabatic. A numerical technique based on the implicit finite difference method (IFDM), along with an upwind finite difference scheme and an iterative successive over relaxation (SOR) technique, is employed to solve the governing equations numerically. The effect of physical parameters, namely the modified Rayleigh number ( 10 3 ≤ R a ≤ 10 7 ), aspect ratio ( 1 ≤ A ≤ 4 ), Prandtl number ( P r = 0.7 , 1.0 , 6.2 , 15), volumetric internal heat generation parameter ( Q λ = 0 , 1), and Eckert number ( 0 ≤ E c ≤ 10 − 6 ), on the streamlines and isotherms are discussed graphically. Variations of maximum stream function, as well as average and local Nusselt number, are also discussed. The results show that the increase in Eckert number from 0 to 10 − 4 causes the average heat transfer to decrease, while P r = 0.71 , R a = 10 4 , and Q λ = 0 . Additionally, the average heat transfer decreases as the cavity width increases from 1 to 4, while P r = 0.71 , R a = 5 × 10 4 , E c = 10 − 6 and Q λ = 1 . The results of the numerical model used here are in excellent accord with earlier findings.