Analytical/Numerical Study of Fluid Flow and Heat Transfer Across In-Line Cylinders

Abstract

An integral approach to boundary-layer analysis is employed to investigate the effects of the longitudinal-pitch ratio on fluid flow and heat transfer from a longitudinal row of circular cylinders immersed in an infinite medium. The momentum equation is solved using the modified von Kármán–Pohlhausen method, which employs a fourth-order velocity profile within the hydrodynamic boundary layer. The potential-flow velocity is obtained by complex potential theory outside the boundary layer. A third-order temperature profile is used in the thermal boundary layer to solve the energy integral equation for the isothermal boundary condition. Closed-form solution is obtained for the heat transfer coefficient for a longitudinal row of circular cylinders immersed in an infinite medium. In the second part of this research activity, a numerical model based on computational fluid dynamics is developed to validate the closed-form solution. The proposed numerical model has been successfully implemented for simulating the flowfield over a longitudinal row of circular cylinders. Numerical simulations have been carried out for various values of the freestream Reynolds number and longitudinal-pitch ratio. The results obtained from the analytical and numerical models have been found to be in good agreement. The maximum percentage error in values of the average Nusselt number obtained from the numerical and analytical solutions is less than 9% and reduces further to a value of less than 4% with an increase in values of the freestream Reynolds number.