Mathematical Modelling on Pulsative MHD Blood Casson Nanofluid in Slip and Porous Capillaries for Nano-cryosurgery with Caputo-Fabrizio Approach

Nano-cryosurgery is a novel approach to treating tumours that integrates cryosurgery and nanotechnology. Researchers are interested in nano-cryosurgery since it minimises damage to healthy surrounding tissue, bleeding, and post-surgery complications. However, conducting experimental research requires a lot of time and money. Hence, the mathematical model developed for blood flow with nanoparticles is significant for nano-cryosurgical treatments. The present study aims to investigate analytically the fractional derivative approach of blood nanofluid flow in the porous medium of a slip cylinder. The effects of pulsatile pressure gradient, MHD, and free convection flow are being considered. Blood nanofluid is modelled with a Casson fluid model dispersed with gold nanoparticles. The Caputo-Fabrizio fractional derivative approach, known for its dimensional consistency through normalisation, is employed in the momentum and energy equations. Then, dimensionless governing equations are obtained by employing the dimensionless variables. The problem is solved by combining the Laplace and finite Hankel transforms to obtain velocity and temperature expressions. The present study graphically illustrates and discusses the effects of various related parameters on the velocity and temperature profiles. The research findings revealed that the slip velocity significantly impacts the blood nanofluid flow at the cylinder’s wall. The fractional model of blood nanofluid is more sensible and accurate than the classical model. The results are essential for optimising the nano-cryosurgery procedure by controlling the ice formation and orientation, heat transfer mechanism between cryoprobe and cells, cryogenic agent delivery, and freezing and thawing time.