Two-dimensional steady laminar natural convection of a viscoelastic fluid represented by generalized second-grade fluid model in a square enclosure is studied. The cavity is submitted at its vertical sides to a uniform density of heat flux while the horizontal walls are insulated, without slipping conditions at all the solid boundaries. The governing conservation and constitutive equations with the corresponding boundary conditions are solved by finite volume method in a collocated grid system. The contributions of shear rate dependent and elastic characteristics of the viscoelastic fluid are investigated on momentum and heat transport. The effects of elastic number (E) in the range 0 - 1 on heat transfer and fluid motion are interpreted for a power-law index (n) in the range 1.4 - 0.6 and nominal values of Rayleigh number (Ra) range of 103 to 105.
The current study explores numerically mixed convection of thermo-dependent power-law fluids in a square lid-driven enclosure, including the thermal radiation effect. The vertical sidewalls are sustained at both hot and cold temperatures. On the other hand, the cavity is insulated from the horizontal walls. The upper wall is moving along the x-axis. The main governing equations that the Boussinesq approximation is used for are solved using the finite difference method. The simulations focus on the effects of multiple pertinent parameters, including the Richardson number. (Ri = 0.1, 1, 10 and 100), thermal radiation parameter (Rd = 0 and 10), power-law index (0.6 ≤ n ≤ 1.4) and the Pearson number (0 ≤ m ≤ 6). The findings reveal that improving the Richardson number reduces heat transfer. Then, increasing Rd results in a domination of heat conduction for a fluid having a higher thermal conductivity. Also, the growth in the power law-index reduces heat transfer while improving convective flow. Finally, increasing the Pearson number improves the convective flow rate and also the average Nusselt number.
In this paper, numerical study on natural convection heat transfer for confined thermo-dependent power-law fluids is conducted. The geometry of interest is a fluid-filled square enclosure where a uniform flux heating element embedded on its lower wall is cooled from the vertical walls while the remaining parts of the cavity are insulated, without slipping conditions at all the solid boundaries. The governing partial differential equations written in terms of non-dimensional velocities, pressure and temperature formulation with the corresponding boundary conditions are discretized using a finite volume method in a staggered grid system. Coupled equations of conservation are solved through iterative Semi Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The effects of pertinent parameters, which are Rayleigh number (103 ≤ Ra ≤ 106), power-law index (0.6 ≤ n ≤ 1.4), Pearson number (0 ≤ m ≤ 20) and length of the heat source (0.2 ≤ W ≤ 0.8) on the cooling performance are investigated. The results indicate that the cooling performance of the enclosure is improved with increasing Pearson and Rayleigh numbers as well as with decreasing power-law index and heat source length.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.