Analytical Study of Drag and Mass Transfer in Creeping Power Law Flow across Tube Banks

The Happel and Kuwabara cell models are combined with the Stokes flow approximation (creeping flow) and the Levich thin boundary layer assumption to investigate theoretically the creeping flow and convective mass transfer of power law fluids across banks of cylinders. A well-known perturbation technique involving the use of the Newtonian flow field as a first approximation is employed to determine the closed-form stream function for power law fluids. Analytical expressions are derived for the drag coefficient and Sherwood (or Nusselt) number and applied over a wide range of power law indices (0.6 ≤ n ≤ 1) and voidages (0.4 ≤ ε ≤ ∼1). The behavior of these expressions in the Newtonian limit, i.e., n = 1, is also investigated. The analytical results reported herein for the drag coefficient are validated for the power law index and voidage ranges specified above using the numerical results available in the literature. Unfortunately, outside the Newtonian limit, there are only limited numerical results available for heat transfer to test the validity of the analytical expressions derived in the present study.