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The current analysis deals with the physiological flow of hybrid nanofluid within an expanding and contracting vertical annulus embedding with a permeable medium. Additionally, in the free convective viscous flow, the impact of thermal radiation on the heat transport phenomenon is vital. The significance of this research lies in the utilization of Hamilton–Crosser thermal conductivity to investigate the behavior of nanoparticles with different shapes. In this study, both oxide nanoparticles like Al2O3 and metal nanoparticles like Ag are incorporated into the blood, which serves as the base fluid. This incorporation aims to enhance the performance of hybrid nanofluids in influencing flow phenomena. The proposed mathematical model designed for the above-mentioned constraints is solved analytically following the transformation into their corresponding non-dimensional form. The statistical behavior of the diversified parameters is presented graphically and the numerical results for the rate coefficients are deployed via table. Further, the important characteristics of the results are depicted as follows: the combined effect of the particle concentration used in hybrid nanofluid favors in reducing the fluid velocity greatly than that of nanofluid and pure fluid. [ABSTRACT FROM AUTHOR]

The proposed flow problem is to analyze the behavior of dissipative heat on the time-dependent stagnation motion of nanofluids through a permeable surface. A novel approach to thermal buoyancy through the permeable medium enriches the flow properties. In the recent industrial applications for the cooling processes of the device, like the physiological application of the blood flow inside the capillary tube-like artery, drug delivery system, etc., the role of nanofluid is crucial. The proposed model equipped with various physical properties is used to design and subsequent transformation into a non-dimensional form is obtained for a set of similarity variables. Proposed models with different physical properties are designed and subsequent dimensionless transformations are obtained for a similar set of variables. In addition, shooting based Runge-Kutta fourth-order numerical technique is used to solve boundary value problems for nonlinear ordinary systems. The characteristics of the diversified quantities are presented graphically as well as numerically on the flow profile and other profiles. Furthermore, statistical approaches such as t-tests for simulated results of rate coefficients are also presented and validated with the obtained results. However, the important outcomes are presented as; the fluid velocity is controlled by the inclusion of the particle concentration as well as the magnetic parameter further the particle concentration and the dissipative heat encountered by the inclusion of Eckert number enhances the fluid temperature. [ABSTRACT FROM AUTHOR]