Turbulent cylindrical heat flow visualization in free convection regime

The present article aims to disclose the silent features of Bejan’s heat flow visualization in turbulent boundary layer flow about a vertical cylinder under the effect of low Reynolds number (LRN) k-ε model. The two-dimensional, incompressible, time-dependent average fluid flow and thermal transport equations are derived based on the considered geometry and the used boundary conditions. Turbulent kinetic energy and turbulent kinetic energy's dissipation rate equations are included to determine the eddy viscosity in the flow regime. Further, the turbulent heat function is constructed and is utilized to describe the concept of Bejan’s thermal flow visualization to explore the advanced flow and heat transport features including isotherms, streamlines along with heatlines in a two-dimensional free convection regime. However, the analytical methods are inadequate to solve the produced coupled nonlinear Navier–Stokes equations. Hence, a numerically efficient finite difference scheme namely the Crank–Nicolson scheme has been employed to solve the present problem. Further, the resultant discretized tridiagonal algebraic equations are solved by using the Thomas algorithm. Computational results are analysed to differentiate the laminar and turbulent flows in view of velocity, energy, heatlines, and streamlines for different parametric values. Due to the industrial applications, the skin-friction coefficient and heat transfer rate are also evaluated. From the current analysis, it is noticed that the momentum transport decreased with rising turbulent Prandtl number. Increasing turbulent Reynolds number suppressed the skin-friction coefficient at the surface of the cylinder.