Natural convective turbulent heat flow visualization around a vertical plate using low Reynolds number k-ϵ model

Abstract

The authors of this present paper used the low Reynolds number (LRN) k-ϵ model to introduce the notion of turbulent heat function for visualization of average heat flow direction in a natural convective flow in the vicinity of the vertical plate. The explored problem is two-dimensional and incompressible. Governing equations such as continuity, momentum, energy, turbulent kinetic energy (TKE), dissipation rate of TKE, and also turbulent heat and stream functions are generated based on geometry and turbulent flow assumptions. Owing to the lack of analytical methods for solving the highly nonlinear set of partial differential equations, the Crank–Nicolson scheme (CNS) of finite difference approach is employed to find a numerical approximation of the governing turbulent equations. Further, this approach is unconditionally stable, and it helps in the discretization of governing equations, which are kept in the tridiagonal system of algebraic equations and solved using the Thomas algorithm. The obtained numerical results ensure convergence since the stability and compatibility holds good in CNS. The simulated results are examined using tables and graphs to determine how laminar flow differs from that of turbulent flow in terms of velocity, temperature, heat lines, and streamlines with the help of turbulent Prandtl () and Reynolds () numbers. Also, the authors demonstrated the behavior of average momentum and heat transfer rates of laminar and turbulent flows. Additionally, average velocity, kinetic energy, and dissipation rate contours are plotted and discussed including turbulent isotherms, heat lines, and streamlines. It has been noted that the average momentum rate decreased and the heat transfer rate increased with increasing in laminar flow. However, these rates decreased with increasing values in the turbulent flow. Furthermore, streamlines are denser in laminar and turbulent flow conditions at the top and the leading edge of the plate, respectively. Finally, as a particular instance, the outcomes obtained using the LRN k-ϵ model for turbulent flows are compared to the usual laminar flow and noted to be in excellent agreement.