## THERMAL SCIENCE

International Scientific Journal

### DYNAMICS OF UNSTEADY FLUID-FLOW CAUSED BY A SINUSOIDALLY VARYING PRESSURE GRADIENT THROUGH A CAPILLARY TUBE WITH CAPUTO-FABRIZIO DERIVATIVE

**ABSTRACT**

This paper presents a study of the unsteady flow of second grade fluid through a capillary tube, caused by sinusoidally varying pressure gradient, with fractional derivative model. The fractional derivative is taken in Caputo-Fabrizio sense. The analytical solution for the velocity profile has been obtained for non-homogenous boundary conditions by employing the Laplace transform and the finite Hankel transform. The influence of order of Caputo-Fabrizio time-fractional derivative and time parameter on fluid motion is discussed graphically.

**KEYWORDS**

PAPER SUBMITTED: 2022-03-01

PAPER REVISED: 2022-03-14

PAPER ACCEPTED: 2022-04-04

PUBLISHED ONLINE: 2023-04-08

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