MODELLING AND SIMULATION OF MAXWELL NON-NEWTONIAN FLUID FLOW AND HEAT TRANSFER IN A CAPILLARY TUBE USING THE ATANGANA-BALEANU FRACTIONAL TIME-FRACTIONAL APPROACH

Abstract

This paper explores the fluid flow and heat transfer characteristics of non-Newtonian fluids within a capillary tube, employing a generalized fractional modeling framework. The analysis utilizes the Maxwell fluid model combined with the Atangana-Baleanu fractional time-fractional derivative. Analytical solutions for velocity and temperature distributions were derived using the finite Hankel and Laplace transform techniques. Key insights reveal that fractional-order models demonstrate notable differences from classical solutions, providing enhanced accuracy in accounting for memory effects and time-dependent dynamics. The fractional fluid velocity shows significant influence at smaller time scales, whereas temperature distribution predominantly varies at larger time intervals.