Transient laminar forced convection to power-law fluids inside ducts resulting from a sudden change in wall temperature

The transient laminar forced convection to power-law fluids in thermally developing, hydrodynamically developed flow inside parallel-plate ducts and circular tubes resulting from a sudden change in wall temperature is studied. The generalized integral transform and the Laplace transform techniques are employed to develop approximate analytic solutions. The local Nusselt number and average fluid temperature are presented over the range of the dimensionless axial coordinate Z varying from 10^?4 to 10^?1 for several dimensionless times. Three different values of the power-law index are considered in the study includedn=1/3,n=1 andn=3 corresponding to, respectively, the pseudoplastic, Newtonian and dilatant fluids.