ATANGANA – BALEANU FRACTIONAL MODELLING OF OLDROYD–B FLUID FLOW AND HEAT TRANSFER IN A CAPILLARY TUBE

Abstract

In this work, the fluid flow and heat performance of Oldroyd-B fluids, through a capillary tube, were analyzed by means of a fractional model based on the Atangana-Baleanu time-fractional derivative. The fluid motion is generated by an arbitrary pressure gradient of a continuous function of the time. Analytical solutions for the velocity and temperature fields were obtained using the Laplace transform and the finite Hankel transform. In order to obtain the physical behavior regarding the velocity and temperature at the variation of the fractional parameters, material time, pulsation frequency effect and Prandtl number we carried out numerical calculations using MathCAD software and results were graphically presented. Numerical results obtained illustrated distinct behaviors of fractional order solutions when compared with classical model solutions. The fluid velocity and heat transfer performance in capillary tube can be controlled by regulating the fractional derivative parameter, relaxation, retardation time and Prandtl number which are very important in capillary devices. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in capillary fluidic devices used for biological analysis and medical diagnosis