Document Type : Research Article
Department of Mechanical Engineering, University of Lagos, Nigeria
In this study, Galerkin’s method of weighted residual has been applied to present simple approximate analytical solutions to flow and heat transfer in a pipe conveying Johnson-Segalman fluid. The developed approximate analytical solutions are verified with the results in literature and then used to investigate the effects of the pertinent parameters such as relaxation time parameter, viscosity parameter and Brinkman number on the fluid velocity and the temperature distributions of the pipe flow. From the results, it shows that the fluid velocity and temperature increase with the relaxation time parameter and Brinkman number. It is also established that relaxation time parameter increases with increase in the velocity of the fluid but decreases with increase in the fluid temperature. It is found that the effects of relaxation parameters on the velocity distribution are not significant as the viscosity parameter approaches unity and when it is greater than unity.
On the use of Galerkin’ method of weighted residual in providing approximate analytical solutions to nonlinear problems, it is demonstrated in this study that the second degree's trial function converges to result with a good accuracy. This fact had been pointed out earlier studies that additional terms should not be necessary in most instances and further refinement should not be necessary. It is hope that the study will provide more physical insight into the flow phenomena.