Turbulent heat and mass lines in finite difference regime

Abstract

Finite difference modelling of turbulent heat and mass flow visualization finds numerous applications in atmospheric flows/oceanic currents, wind turbines, thermal transfer in nuclear reactors, drag in oil pipelines, cooling of industrial machineries, and to investigate the complexity, dynamic and chaotic nature of the physical system. A turbulent phenomenon is effectively implemented in engineering, physics, earth sciences, bio‐engineering and medicine. Hence, motivated by the advantages of turbulence in various engineering fields, in the current article, a finite difference analysis is performed to demonstrate the k‐ε turbulence model‐based heat and mass lines visualization in boundary layer regime under turbulent buoyancy‐driven convective conditions along a cylinder. Turbulent flow characteristics are accurately explored by deploying the classical Newtonian flow model. Further, to accomplish a more sophisticated finite difference simulation, the effects of extra kinetic energy and its dissipation rate equations are considered. The produced Navier‐Stokes equations for time‐dependent turbulent heat and mass transmission are rendered to non‐dimensional by deploying suitable dimensionless numbers. The advanced coupled nonlinear turbulent unsteady buoyancy‐motivated vertical convection problem is then solved with a well‐sophisticated finite difference scheme such as Crank‐Nicolson technique using computational software. Authentication of current results with former solutions over a range of buoyancy number, Schmidt, and Prandtl parameters are presented. An extensive tabular and graphical discussion along with contours, heat and masslines visualization is included to enumerate the hydro‐dynamic, thermal and mass diffusion behaviour for the impact of emerged regulating numbers in the Prandtl regime. It is confirmed that, the accelerating turbulent buoyancy‐ratio number, maximizes the velocity, kinetic energy and dissipation rate at . Further, the numerical values of laminar thermal and mass diffusion rates are monotonically enhanced when compared to the turbulent values. Also, to verify the current findings, the authors compared the LRN k‐ε model turbulent results with the existing solutions and found good agreement. Further, the uniqueness and novelty of the current investigation is the exploration of heat and masslines in unsteady buoyancy‐driven convection regime under the influence of k‐ε turbulence model which extends the former studies and offers a more precise appraisal of the thermal and mass diffusion lines via the Crank‐Nicolson analysis.