Application of fractional derivative in Buongiorno's model for enhanced fluid flow and heat transfer analysis over a permeable cylinder

In order to analyze fluid flow over a contracting permeable cylinder, this study provides a solution to Buongiorno's model based on fractional derivatives. We attempt to model the complex behavior of heat and mass transfer using fractional calculus, which is not possible with the traditional models based on integer order. Both thermophoresis and Brownian motion contributions are included in the modified Buongiorno model, which enhances the study of fluids containing nanoparticles deposited using over-contracting cylinders. In the following, we formulate and solve the governing equations under appropriate boundary conditions using the conformable fractional derivative. The appropriate transformations are used to convert the governing system of PDEs into ODEs. The Iterative Power Series Technique (IPS) with a simple firing strategy is selected to demonstrate the numerical solution of the problem. The analysis makes use of a number of significant figures, such as the Schmidt number, fractional order, unsteadiness, Brownian motion, and thermophoresis. It's interesting to note that a higher velocity profile with larger fractional parameter values indicates that the fractional derivatives provide more control over flow behavior. Also, Increasing the fractional order parameter causes a drop-in concentration and temperature profiles, which is associated with the effect of fractional derivatives on mass and energy transfer.