Convective Heat Transfer of Unsteady Pulsed Flow in Sinusoidal Constricted Tube

Abstract

In many industrial engineering and other technological processes, it is crucial to characterise heat and mass transfer, for example to avoid thermo mechanical damages. Particularly, in the inlet region of internal pulsed flows, unsteady dynamic and thermal effects can present large amplitudes. These effects are mainly located in the wall region. This suggests the existence of intense unsteady stresses at the wall (shear, friction or thermal stresses). Our studies (Andre et al., 1987; Batina, 1995; Creff et al., 1985) show that there could exist an 'adequacy' of different parameters such as Reynolds or Prandtl numbers, leading to large amplitudes for the unsteady velocity and temperature in the entry zone if compared to those encountered downstream in the fully developed region. Consequently, in order to obtain convective heat transfer enhancement, most of the studies are linked to: Firstly, the search for optimal geometries (undulated or grooved channels, tube with periodic sections, etc.) : among those geometrical studies, one can quote the investigations of Blancher, 1991; Ghaddar et al., 1986, for the wavy or grooved plane geometries, in order to highlight the influence of the forced or natural disturbances on heat transfer. Secondly, the search for particular flow conditions (transient regime, pulsed flow, etc.): for example those linked to the periodicity of the pressure gradient (Batina, 1995; Batina et al. 2009; Chakravarty & Sannigrahi, 1999; Hemida et al., 2002), or those which impose a periodic velocity condition (Lee et al., 1999; Young Kim et al., 1998) or those which carry on time periodic deformable walls. The main objective of this study is to analyse the special case of convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is supposed to be developing dynamically and thermally from the duct inlet. The wall is heated at constant and uniform temperature. One of the originality of this study is the choice of Chebyshev polynomials basis in both axial and radial directions for spectral methods, the use of spectral collocation method and the introduction of a shift operator to satisfy non homogeneous boundary conditions for spectral Galerkin formulation. A comparison of results obtained by the two spectral methods is given. A Crank Nicolson scheme permits the resolution in time.