The current research study is focusing on a mathematical model for free convection boundary flow on a horizontal circular cylinder in a viscoelastic nanofluid has been constructed in this paper with boundary conditions constant heat flux. The Tiwari and Das Nanofluid model have been chosen in this analysis to investigate more nanofluid effects. A dimensionless set of partial differential equations is formed by using suitable non-dimensional variables. The transformed boundary layer equations are solved numerically using a finite difference scheme namely the Keller-box method. The effects of a few chosen factors on flow and heat transmission are investigated. Numerical solutions were obtained for the reduced skin friction coefficient, Nusselt number and Sherwood number as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the viscoelastic parameter and nanoparticles volume fraction were analysed and discussed.

In a cylindrical cavity, the convection and entropy of the hybrid nanofluid were studied. We have introduced a rectangular fin inside the cylinder; the fin temperature is at $T_h$. The right waving wall is cooled to $T_c$. The upper and lower walls are insulated. This study contains the induction of a constant magnetic field. The Galerkin finite element method (GFEM) is utilized to treat the controlling equations obtained by giving Rayleigh number values between $Ra$ (10³–10⁶) and Hartmann number ratio $Ha$ (0, 25, 50, 100) and Darcy ranging between $Da$ (10⁻²–10⁻⁵) and the porosity ratio is $\epsilon$ (0.2, 0.4, 0.6, 0.8), and the size of the nanoparticles is $\varphi$ (0.02, 0.04, 0.06, 0.08). The range is essential for controlling both fluid flow and the heat transport rate for normal convection. The outcomes show how Da affects entropy and leads to a decline in entropy development. The dynamic and Nusselt mean diverge in a straight line. The domain acts in opposition to the magnetic force while flowing. Highest entropy-forming situations were found in higher amounts of $Ra$, $Da$, and initial values of $Ha$. Parameters like additive nanoparticles ($\varphi$) and porosity ($\epsilon$) exert diagonal dominant trends with their improving values.

This study introduces a mathematical model that addresses the mixed convection stagnation point flow of a non-Newtonian Reiner-Philippoff hybrid nanofluid over a shrinking sheet. Through the application of theoretical assumptions, the governing equations were formulated and subsequently simplified into a set of ordinary differential equations (ODEs). The model facilitates the computation of steady flow solutions utilizing the MATLAB software function bvp4c. The primary objectives of this research include an analysis of the effects of various parameters on flow dynamics and thermal behaviour. These parameters encompass the mixed convection parameter, the solid volume fraction of nanoparticles, and the mass flux parameter, all of which significantly influence flow characteristics. Numerical results have been obtained for critical metrics, including the skin friction coefficient, local Nusselt number, and the velocity and temperature profiles. The findings contribute to a deeper understanding of hybrid nanofluid behaviour in thermal management applications, offering valuable insights for future research endeavours in the domains of fluid dynamics and heat transfer.

This study introduces a mathematical model that addresses the mixed convection stagnation point flow of a non-Newtonian Reiner-Philippoff hybrid nanofluid over a shrinking sheet. Through the application of theoretical assumptions, the governing equations were formulated and subsequently simplified into a set of ordinary differential equations (ODEs). The model facilitates the computation of steady flow solutions utilizing the MATLAB software function bvp4c. The primary objectives of this research include an analysis of the effects of various parameters on flow dynamics and thermal behaviour. These parameters encompass the mixed convection parameter, the solid volume fraction of nanoparticles, and the mass flux parameter, all of which significantly influence flow characteristics. Numerical results have been obtained for critical metrics, including the skin friction coefficient, local Nusselt number, and the velocity and temperature profiles. The findings contribute to a deeper understanding of hybrid nanofluid behaviour in thermal management applications, offering valuable insights for future research endeavours in the domains of fluid dynamics and heat transfer.