_{1}

This study is devoted to the computational fluid dynamics (CFD) modeling of steady laminar mixed convection flow and heat transfer in lid driven cavity (10 ≤ <i>Re</i> ≤ 1000). The ratio of the height to the width of the cavity is ranged over <i>H/L</i> = 0.5 to 1.5. The governing equations are solved using commercial finite volume package FLUENT to visualize the nature of the flow and estimate the heat transfer inside the cavity for different aspect ratio. The simulation results are presented in terms of average Nusselt number of the hot wall, velocity profile, and temperature contours. It was found that the average Nusselt number inside the cavity is strongly governed by the aspect ratio as well as the Reynolds number. A parametric study is conducted to demonstrate the effect of aspect ratio on the flow and heat transfer characteristics. It is found that heat transfer enhancement was obtained by decreasing the aspect ratio and/or increasing the Reynolds number.

One of the major problems in the thermos-fluids is the free and forced convection flow and heat transfer in different aspect of cavity. The lid-driven cavity flow is the motion of a fluid inside a rectangular cavity created by a constant translational velocity of one side while the other sides remain at rest. Fluid and heat flow behaviors inside lid driven cavities have been the subject of extensive computational and experimental studies over the past years. It has many applications in engineering, material processing, dynamics of lakes, metal casting and galvanizing.

The influence of a lid movement on the fluid flow and thermal structures in a lid-driven cavity was conducted by [

The cubic interpolated pseudo particle method and verified their results with the shear driven flow in square cavities were considered by [

Gau and Sharif [

Wang et al. [

Many researchers, investigate the mixed convection heat transfer characteristics of a square cavity over the years, however, there seems to be lack studies relates the numerical investigation covered the effect of aspect ratio. Therefore, the main objective of this study is to study the effect of aspect ratio (0.5 ≤ AR ≤ 1.5) on fluid and heat transfer characteristic for laminar, steady and mixed convection using commercial finite volume package FLUENT. Also, the present study focuses on flow visualizations on moderate Reynolds number range varying the aspect ratio of driven cavity.

The fluid flow and heat transfer in open lid driven cavity can be simulated by a set of mass, momentum and energy conservation equations. The flow is assumed to be two-dimensional, laminar, incompressible, Newtonian and neglecting the viscous effect. The dimensionless governing non-linear partial differential equations can be written as follows:

The dimensional variables are as follows:

The L is the reference length dimension (width of the cavity along lower lid), while U_{∞} is the reference velocity dimension. The fluid property ν, refers to the kinematic viscosity. The Reynold’s number, Re, is the ratio of inertial to viscous forces, which influences the fluid flow features within the cavity. No-slip velocity boundary condition (u = v = 0) is applied on all the walls, except the top lid. On the top lid (U = 1 and V = 0) is applied. The bottom boundary of the domain is modeled as wall .The boundary conditions which describing the current simulated computational domain as well as the surface boundary layer is depicted in

A finite volume method is employed using commercial software FLUENT 6.2 to solve the governing equations together with the specified boundary conditions. The velocities and pressure are coupled by the SIMPLE algorithm. More cells are constructed near the surface of the cavity to compensate the high velocity gradient in the boundary layer region of the viscous flow. A commercial software GAMBIT is used for grid generation. A second order upwind scheme is used for the convection. Here in this study, following [

Simulation results for laminar mixed convection in square cavity (AR = 1) are compared to experimental data to verify the validity of the CFD simulation solution. Then, the code is employed to investigate the mixed convection fluid flow and heat transfer inside the different aspect ratio of cavity.

aspect ratio decreases for Re = 100. Decreasing the aspect ratio means that the cold lid would be close to the hot wall and sense the heat significantly. Therefore, the heat transfer enhanced near the cold lid.

The contours of static temperature that has the same temperature difference and various aspect ratio are shown in

patterns, the isotherm contours plots from the computational data for different aspect ratio are at Reynolds number = 100 is shown in

respect to right wall cavity. Further, an energy rate increases due to circulation movements of fluid molecules which enhance the thermal dispersion especially for smaller cavity aspect ratio.

Reyad Omari, (2016) Numerical Investigation of a Mixed Convection Flow in a Lid-Driven Cavity. American Journal of Computational Mathematics,06,251-258. doi: 10.4236/ajcm.2016.63026