**1. Introduction**

Fluids can be divided into two types i.e., Newtonian and non-Newtonian fluid. The Newtonian fluids are simple and ideal. In real life there is no exitance of Newtonian fluids but water and air consider as Newtonian fluid. However, the non-Newtonian fluids are complicated and cannot be solved easily. The fluid motion within a cylinder has a wide application in the field of physics, engineering and specially in the food industry. In (1923), Taylor presented the results of stability of fluid in rotating cylinders [1]. Stephen Childress, in 2009 talked about the lift and drag in ideal fluids in two-dimensional, Stoke's flow and gas dynamics [2]. Waters and King [3] discussed the Oldroyd-B fluid in a circular tube by taking Poiseuille flow into account. The investigation of basic unsteady pipe flow and viscoelastic upper-convected Maxwell fluid in uniform circular cross section, is available in [4]. They used the Fourier Bessel series to obtain the closed form solutions. The exact solutions of different fluids in circular cylinders (may be finite and infinite) can be obtained by applying the Laplace transformation on the system. There has been published a number of papers on this idea.

The action of circular cylinder and pressure gradient for both translational and rotational flows for viscoelastic fluids discussed in [5]. Fox and Macdonald [6] focussed on differential analysis of one dimensional and steady state flow of incompressible and non viscous fluid. He also discussed the flow of fluid through pipes and channels. Fetecau [7] worked on unidirectional unsteady flow through an infinite pipe for Oldroyd-B fluids. For analytical solutions, an expansion theorem of Steklov is used with a no slip condition. The viscoelastic fluids have many exertions in various fields of industry, also in bio engineering. Ting [8] and Srivastava [9] find out the analytical solutions of non-Newtonian fluids for second grade and Maxwell fluids respectively. Sherief et al. [10] considered an infinitely magnetic insulating circular cylinder for the steady one-dimensional flow of an incompressible MHD fluid. The slip boundary conditions are applied on velocity and they calculated the results for the micro rotation, ratio of flow and skin coefficients.

The Helical flow is the composition of translation and rotational motion, is applicable in vascular hydrodynamics and biomedical engineering. Many papers have been published on this type of flow. The general solutions of some helical flow corresponding to the second grade fluid are seems in [11]. The analytic solutions of same fluid for unsteady flow has been derived by Hayat et al. [12]. In rotating circular cylinder, Fetecau [13] obtained the analytical solutions for the helical flow of Oldroyd-B fluid. In the same domain, the solutions of Maxwell and second grade fluids are available in [14,15].

Fractional calculus plays a very important rule in the field of fluid mechanics. Podlubny [16] discussed the differential equations of fractional model. The elements of fractional model defines viscoelastic fluids of special kind. Now a days, such models frequently [17,18] commonly encounter in our daily lives. The analytical solutions of generalized second grade fluids are available in [19]. Exact solutions of generalized Burgers' fluid in annulus of circular cylinders and helical flow of Burgers' fluid, in terms of fractional derivatives, are found in [20,21] respectively. Whereas the analysis of velocity and stress field, vortex sheet of same fluid by considering the fractional anomalous diffusion by Xu et al. [22]. Song and Jiang [23] studied the five parametric constitutive equations with fractional derivatives of linear viscoelastic Jeffreys model. For the applications, they consider the Sesbania gel and Xanthan gum and ge<sup>t</sup> the satisfactory results. Tan et al. [24] and Xu et al. [25] applied a fractional derivative model to Maxwell and generalized second grade fluids between two parallel plates. Abdullah et al. [26] considered the fractional Maxwell fluid in a boundless circular pipe with velocity *f t*. To obtained the solutions for velocity and shear stress they applied the Laplace transformation and modified Bessel equation. To find out numerically inverse Laplace transformation MATLAB is used by them.

In this article, the solutions for Burgers' fluid in rotating pipe like domain are determined. Here, a Laplace transformation technique was used to study fluid motion in a circular domain. The variable of time is removed with the help of a Laplace transform and modified Bessel functions to convert the complex equations into simple algebraic equations. The derived results are complicated so that inverse Laplace transformation were difficult to apply. So "Stehfest's algorithm" [27] and "MATHCAD" software was used to find the numerical solutions for the Burgers' fluid in circular domain. Graphs were drawn to elaborate the influences of fluids on velocity against different parameters. The results and discussions of all parameters are given at the end that shows the consistency in obtained results.
