Approximate analytical solutions for the flow of a third-grade fluid in a pipe

The flow of a third-grade fluid in a pipe with heat transfer is considered. Constant viscosity. Reynold's model viscosity and Vogel's model viscosity cases are treated separately. Approximate analytical solutions are presented for each case using perturbations. The criteria for which the solutions are valid are determined for the dimensionless parameters involved. The analytical solutions are contrasted with the finite difference solutions given in Massoudi and Christie (Int, J. Non-Linear Mech. 30 (1995) 687-699) and within admissible parameter range, a close match is achieved. (C) 2001 Elsevier Science Ltd. All rights reserved.