Finite analytic numerical solutions of laminar and turbulent convective heat transfer for pipe flow past a cavity

Convective heat transfer for laminar and turbulent flow in a pipe through a cylindrical chamber with a sudden expansion and contraction is solved by the finite analytic numeric method. The chamber wall temperature is isothermal and lower than the uniform temperature at the pipe inlet. To predict the turbulent flow and heat transfer, the analysis employs a turbulence model with two differential turbulent transport equations for the turbulent kinetic energy, K, and the rate of turbulent dissipation epsilon. The finite analytic method differs from other numerical methods in that it utilizes a local analytic solution in an element to obtain algebraic representations of the governing partial differential equations. The finite analytic method is shown to provide accurate numerical solutions for Navier-Stokes and energy equations from low to high Reynolds number flow without using the upwind technique.