**The Solutions of Non-Integer Order Burgers' Fluid Flowing through a Round Channel with Semi Analytical Technique**

#### **M. Imran 1, D. L.C. Ching 2, Rabia Safdar 1, Ilyas Khan 3,\*, M. A. Imran 4 and K. S. Nisar 5**


Received: 4 April 2019; Accepted: 6 May 2019; Published: 1 August 2019

**Abstract:** The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel's equation for the rotational flow of Burgers' fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = 0 and afterward fluid flow is because of the circular motion of the around channel with velocity Ω*Rtp* with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by "Stehfest's algorithm" and "MATHCAD" numerically. The numerically obtained solutions in the terms of the Modified Bessel's equations of first and second kind, are satisfying all the imposed conditions of given mathematical model. The impact of the various physical and fractional parameters are also indeed and so presented by graphical demonstrations.

**Keywords:** Burgers' fluid; velocity field; shear stress; Laplace transform; modified Bessel function; Stehfest's algorithm; MATHCAD
