Mixed convection in a lid driven square cavity using lattice Boltzmann method: Effects of thermal gradient direction and moving lid length

Abstract

This numerical study investigates the effect of thermal boundary conditions and moving lid length on the mixed convective heat transfer and flow regime dynamics in a square top-lid driven cavity. The numerical simulations are performed using an in-house developed thermal lattice Boltzmann solver. Here, the two cavity walls are defined using the opposite pairs of hot and cold isothermal walls. The rest walls are set as adiabatic with zero thermal flux conditions such that a thermal gradient is established either in the vertical or horizontal direction. Additionally, we have varied the size of the moving top-lid to couple the inertia effect with the thermal gradient and investigated how the mixed convective heat transfer and flow regime are affected in the square lid-driven cavity. Here, the Richardson number () is varied as 0.1, 1.0, and 10.0 to cover a wide range of mixed convective flow situations in the lid-driven cavity. is fixed at 106 in all the cases. Qualitative results of the flow regime and heat transfer characteristics are presented as isotherms and streamline patterns. The quantitative information is analyzed by the conduction-convection characteristics along the cavity centerlines and on the boundary walls. It is intuitive to say that the rate of heat transfer or Nusselt number will be higher for larger moving lid lengths, but this is achieved at the cost of higher driving force estimated by the line integral of the shear stress at the moving wall. Additionally, we have defined an efficiency parameter that can relate the heat transfer rate (Nuhot ) with the fluid friction (Cf ). Furthermore, η helps identify the effective and energy-efficient way to achieve the optimized heat transfer in the lid-driven cavity in the considered parametric range.