Helical flows of fractional viscoelastic fluid in a circular pipe

Abstract

The exploration of this study is devoted to investigate the helical effects for the flow of fractionalized viscoelastic fluid in helically moved cylinder. The cylinder starts to oscillate and rotate about its axis when = 0 + with velocities. By applying mathematical transforms (Hankel and discrete Laplace transforms) exact solutions are found out for velocities and shear stresses. The general solutions satisfy initial conditions 1 ( , 0) = 2 ( , 0) = 1 ( ,0) = 2 ( ,0) = 0, as well as boundary conditions

Use of Atangana–baleanu Fractional Derivative in Helical Flow of a Circular Pipe

“…Inverting Eqs. (17) and (18) by Hankel transform, we obtain the expression involving the gamma functions of linear expressions as described below:…”

“…They solved the second order homogeneous differential equation and generated the gamma function among the solutions of velocities and shears stresses. Although the studies of circular pipe and different fractional approaches can be continuous yet we end here by citing here few recent attempts, for instance, circular cylinder [17][18][19][20][21] and modern fractional differentiations (Caputo, [22][23][24] Caputo-Fabrizio, [25][26][27][28][29][30] Atangana-Baleanu 31,32,34,35 and comparison of Atangana-Baleanu and Caputo-Fabrizio [36][37][38][39][40][41][42] ). Motivating by above significant contribution, our aim is to incorporate the new comparative analysis based on modern fractional differentiation on infinite helically moving pipe.…”

Analytical and fractional model for power transmission of lossy transmission line

“…This is because old definitions of fractional operators for instance Caputo and Riemann-Liouville differential operators are based on the convolution of a given function with power decay function. Such old definitions always encounter artificial singularity to the mathematical models that results inaccuracy of the memory effects [8][9][10][11]. The burning problem among these both definitions so called artificial singularity have been resolved by modern differential operators termed as Caputo-Fabrizio [12][13] and Atangana-Baleanu [14][15].…”

Role of non-integer and integer order differentiations on the relaxation phenomena of viscoelastic fluid

“…The analysis was focused for heat and mass transfer under sinusoidal effects of plate via discrete Laplace transform. The study of viscoelastic fluid can be continued but we add here few recent attempts on viscoelastic fluids [3,[12][13][14][15][16][17][18]. The theory of non-integer order differentiations provides a promising new approach for the descriptions of memory effect or nonlocal behavior in dynamical real systems; this is because of high level of structural complexity among dynamical real systems is involved.…”