Third-grade non-Newtonian fluid flow and heat transfer in two coaxial pipes with a variable radius ratio with magnetic field

The purpose of this paper is to investigate the hydromagnetic third-grade non-Newtonian fluid flow and heat transfer between two coaxial pipes with a variable radius ratio.

To solve the approximate nonlinear and linear problems with variable coefficients, a trial function was applied. Methods include collocation, least square and Galerkin that can be applied for obtaining these coefficients.

It is revealed that an increase of the non-Newtonian parameter, Hartmann number, and radius ratio leads to an augmentation of the absolute value of the dimensionless velocity, temperature, velocity gradient, and temperature gradient of about 10-60%. Further, the augmentation of Bi₁ reduces the absolute value of the dimensionless temperature profile and dimensionless temperature gradient about three to four times; hence, the dimensionless heat transfer rate reduces. However, the growth of Bi₂ has a contrary impact. Besides, the increase of Pr and Ec leads to an increase in the dimensionless temperature profile and dimensionless temperature gradient; therefore, the dimensionless heat transfer rate increases.

The convection heat transfer on the walls of the pipes is considered, and the nonlinear coupled momentum and energy equations are solved using the least squared method and collocation methods, respectively.