Numerical prediction of fluid flow and heat transfer in a wavy pipe

Hydrodynamic and thermal characteristics in a pipe with sinusoidal wavy surface for steady laminar flow are investigated numerically in the present study. The integral forms of governing equations are discretized using control volume based Finite Volume method with collocated variable arrangement. SIMPLE algorithm is used and TDMA solver is applied for solution of system of equations. A pipe of length equal to 4λ is considered. Effect of surface waviness, determined by wavelength-amplitude ratio λ/a (=L*), on flow and thermal field is presented. The simulation work has been carried out for L*=11.0−30.0 for a Reynolds number range 50 to 2000. Results are presented in the form of streamfunction, isothermal lines, velocity and vorticity profiles, change of mean friction factor, variation in skin friction, local and average Nusselt number with Reynolds number, wave number (n) and L*. For a particular geometry, length of circulation zone increases with Reynolds number and approaches a limiting value for higher Reynolds number. Wall shear stress in the bulge part of the channel shows smaller values that affect largely the rate of heat transfer and Nusselt number shows minimum values in this region. This circulation zone drastically increases with the increase of surface waviness showing high mean friction factor per wavelength. Mean friction factor inversely varies with Reynolds number. A correlation is proposed for calculating friction factor in the form f=C/(Re)m, where ‘C’ and ‘m’ represents two polynomials of degree 4 and 2 respectively and are function of L*. Higher waviness of the surface shows the higher heat transfer rate than lower waviness. Heat transfer rate falls almost exponentially along the axial direction with the increase of wave number.