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Purpose:: This study investigates the effects of hybrid nanoparticles on thermal performance, focusing on convection, magnetic fields, diffusion, radiation, and chemical reactions in porous media. An H2O-based fractional Carreau hybrid nanofluid is utilized to enhance heat transfer for industrial applications like gas turbines and condensers. Design/Methodology/Approach:: The Caputo definition of fractional derivatives models the fluid flow, integrating integer and non-integer dynamics. The governing equations are dimensionally reduced and solved using the explicit finite difference method (EFD), with stability and convergence criteria ensuring accuracy. Key parameters, including the Sherwood and Nusselt numbers, are examined to understand thermal and mass transfer behavior. Findings:: Results show that fractional exponents and thermophysical properties significantly influence flow behavior. Fluid velocity increases with the fractional exponent (α) due to reduced resistance, while higher porosity parameter (λ4) decreases velocity. The temperature gradient decreases by 20.31% with the fractional exponent (β) and by 22.87% with the Weissenberg number. Skin friction increases by 28.17% with the magnetic parameter, and higher thermal conductivity enhances temperature profiles.

This article presents heat transfer analysis at the walls of a circular heated obstacle under the influence of force and natural convection in a triangular domain. The circular obstacle is fixed at the center of triangular domain. The circular obstacle and the inclined walls differ in temperature (Th>Tc). The flow and heat transfer in the computational domain are caused by lid movement and temperature gradient. The triangular cavity is filled with air. The physical setup is described in terms of a system of differential equations. The dimensionless equations are solved using the Finite Volume Method (FVM). The results are computed for various flow controlling variables and presented in the form of isotherms, contours, tabular values and curves. The finding reveals that larger Reynolds number and Grashof number tend to higher heat transfer at the surfaces of heated obstacle. The average Nusselt number is noted to be maximum at w1 in the third quadrant when compared with the other walls of the heated obstacle. The results are compared with literature results in the limiting case.

Nanofluids garner significant scientific interest due to their exceptional heat-conducting abilities and potential to enhance heat transfer efficiency. This manuscript investigates the behavior of a two-dimensional fractional Carreau fluid model on a stretched sheet over time, incorporating convection, magnetic fields, nanoparticles, diffusion, and thermal radiations. The model elucidates viscoelastic nanofluids’ memory and inheritance properties, employing non-integer Caputo fractional derivatives innovatively. Fundamental equations are transformed into dimensionless form and solved using an explicit finite difference approach. Essential parameters like Skin friction coefficient, Nusselt number, and Sherwood number are accurately determined. Rigorous stability and convergence criteria ensure effective solution convergence. Visual representations demonstrate the significant impact of each parameter on fluid flow. It is noted that temperature gradient increases 49.38% with the increase of fractional exponent α while it decreases 13.39% with the increase of magnetic parameter M. Moreover, concentration gradient increases 66.48% with the increase of thermophoresis parameter Nt and 94.71% with the increase of pedesis parameter Nb.