Turbulent Heat and Mass Transfer about a Cylinder through LRN k-ε Model

The present paper makes an effort to study the silent feature of transient free-convective turbulent heat and mass transfer along a vertical cylinder using the low Reynolds number k-ε model. Reynolds averaged fluid flow equations like continuity, momentum, energy, and concentration are considered along with additional transport equations such as turbulent kinetic energy and its dissipation rate through which the local value of turbulent kinematic viscosity is calculated in a two-dimensional cylindrical coordinate system. Produced turbulent nonlinear coupled dimensionless equations governing the boundary layer flow are solved by using the Crank–Nicolson scheme of finite difference method. Thomas’s algorithm is employed to simplify the discretized tridiagonal system of algebraic equations. The simulated findings such as average velocity, energy, species diffusion, kinetic energy, dissipation rate, and friction parameters of turbulent flow are discussed via tables and graphs. The parametric behavior of turbulent flow is studied in terms of the turbulent buoyancy ratio parameter, Prandtl, Grashof, Reynolds, and Schmidt numbers. It is noticed that the average velocity field diminished with increasing Reynolds and Schmidt parameters. Also, the temperature profile enhanced with Reynolds number and decays with the Prandtl parameter in the turbulent regime. Furthermore, due to the lack of literature on the numerical solution of turbulent flow, authors attempted to demonstrate the turbulent heat and mass transfer about a vertical cylinder through the LRN k-ε turbulence model using the Crank–Nicolson scheme with Boussinesq approximations. A comparison with former in the literature results is performed to show the accuracy and correctness of the current turbulent results, the agreement is excellent.