The impact of impinging TiO2 nanoparticles in Prandtl nanofluid along with endoscopic and variable magnetic field effects on peristaltic blood flow

Purpose The purpose of this paper is to study the variable magnetic field and endoscope effects on peristaltic blood flow of nanofluid containing TiO2 nanoparticles (NPs) through a porous annulus. The Prandtl fluid model is taken into account for the present flow. The mathematical modelling comprises the temperature, continuity, NP concentration, and equations of motion which are further simplified by taking a long peristaltic wave and creeping flow regime. Design/methodology/approach After using the long wavelength approximation, the obtained highly non-linear partial differential equations are solved using the homotopy perturbation scheme. The inclusion of the pertinent parameters is discussed mathematically and graphically for the pressure rise, friction forces, temperature profile, and concentration profile. The trapping phenomenon is also investigated with the help of contours. Findings Results show that the maximum velocity distribution exists near the centre of the annulus, whereas the average time flow boosts the velocity profile. It has also been shown that flow can pass readily without enormous pressure gradient imposed on the endoscope tube unlike the case of the slim section of the problem. Practical implications The nanofluids containing titanium NPs are increasingly utilised since such type of NPs is used by several manufacturers in sunscreen blockers and different types of endoscopy. In endoscopy, the variable magnetic field is used at the tip in order to detect or treat diseases. The NPs are used since they acquire specific thermal properties as compared with base fluids. The present study provides qualitative results showing the effect of inner tube of annulus on the fluid flow, the effect of variable magnetic field, and the change in the temperature profile on the flow field. Originality/value A new model is introduced that shows the utmost pressure that works against the positive peristaltic pump. It studies the blood flow that results in extremely non-linear partial differential equations that are solved by the homotopy perturbation method. The titanium NPs are being used in blocking the rays that penetrate the epidermis causing skin burns and short ultraviolet ageing rays that cause visible wrinkles, and thus are used in the manufacturing of sunscreens that are partially absorbed through the skin.