Jeffery–hamel flow of a second-grade blood-based ternary nanofluid in a porous medium with slip and temperature jump effects

Abstract

Ternary hybrid nanofluids (TNFs) have gained growing interest in recent years because of their potential to enhance heat transfer and fluid flow behavior in a wide range of engineering and biomedical applications. In particular, blood-based TNFs with biocompatible nanoparticles (Al2O3, TiO2, and Ag) can be tailored for drug delivery, cancer hyperthermia, and anti-microbial therapy. This study discusses steady, incompressible blood flow with a ternary nanoparticle suspension with the second-grade non-Newtonian model in converging/diverging channels. The second-grade non-Newtonian model has been employed because it is applicable in both small and large vessels. The channels are embedded in a non-Darcy porous medium and are further exposed to a transverse magnetic field. Velocity slip and temperature jump effects at the walls are also considered since such boundary conditions apply to flow in microchannels, biological tissues, or low-friction engineered surfaces. The overall objective of this research is to investigate how the combined impacts of porosity, magnetism, slip-velocity, temperature jump, and the existence of TNFs alter velocity and temperature profiles, as well as significant engineering parameters like skin friction coefficient and Nusselt number. The research aims to contribute to the design of improved biomedical fluid therapies and engineered channels for optimized heat and momentum transfer. Two rigid plates are symmetrically inclined about a centerline, which creates a channel of half-opening angle (α) that can either be converging or diverging. The channels are placed in the porous medium in this study. The base fluid, blood, which is a second-grade non-Newtonian fluid, is used to examine the viscoelastic behavior of the fluid. The blood is blended with Al2O3, TiO2, and Ag nanoparticles to form a TNF with superior thermophysical properties. An external magnetic field is implemented crosswise to the direction of flow, creating MHD conditions for effective control of the flow and accurate placement of the nanoparticles. Also, the different dimensionless parameters such as the Reynolds number (Re), Hartmann number (Ha), the Darcy (Dr1) parameter, Forchheimer (Dr2) parameter, and the Deborah number (De) represent the influence of inertial, magnetic, porous, and elastic effects, as well as the mechanisms governing the flow regime under varying operating conditions. Slip-velocity is included through a coefficient Sv, enabling partial fluid slip on walls. Temperature jump is regulated through a coefficient JT, enabling discontinuity in near-wall temperature gradients, particularly useful in applications involving engineered surfaces. Heat radiation is included through the Rosseland approximation, which is applicable for high-temperature or radiative situations, where targeted cell killing is facilitated by local heating. Governing equations include continuity, momentum, and energy equations. Momentum equations include second-grade fluid elasticity (via α1), Darcy–Forchheimer coefficients, and a magnetic term for MHD. Energy transport accounts for viscous dissipation, radiative heat transfer, and magnetic media, with the thermal conductivity accounting for nanoparticles' shape factors. Dynamic viscosity is greater than in clean blood because there are nanoparticles and second-grade elasticity. Further, particle shape factors ranging from spherical to blade can greatly affect gross heat transfer performance by changing conductivity routes. A similarity transformation reduces the obtained partial differential equations to coupled ordinary differential equations in dimensionless form, with boundary conditions handling both centerline and channel walls (slip/jump conditions). MATLAB's bvp4c solver, which uses a finite difference collocation scheme, is used to obtain velocity and temperature profiles. Initial guesses are based on limited scenarios, and convergence tests ensure that mesh refinement does not alter the results. Validation comparisons with popular established Jeffrey–Hamel flow and porous-flow benchmarks confirm the accuracy and reliability of the numerical process, allowing for extensive parametric studies for possible applications in optimized drug delivery, cancer hyperthermia, or enhanced thermal management in miniature fluidic devices. Our parametric study revealed that at very low Reynolds numbers (Re = 1), diverging and converging channels exhibit nearly identical velocity profiles with slight acceleration when the channel half-angle is raised. Diverging channels exhibit a more detailed velocity profile as Re is raised to 50 for large Darcy and Forchheimer values, whereas converging channels have reduced flow due to the increased porous-medium drag. Non-Newtonian flow caused by the Deborah number creates small but noticeable changes in both temperature and velocity, especially for high Re. Temperature profiles also rely quite strongly on Re, with low-Re flows creating much larger thermal values and hiding geometrical differences between converging and diverging shapes. Larger Darcy or Forchheimer parameters in diverging channels raise temperatures due to increased dissipation, but the influence is the reverse in converging channels. Increased slip coefficients decrease wall shear but can increase or decrease peak temperatures depending on Re, and a high-temperature jump coefficient creates more rapidly rising thermal gradients, which enhance heat transfer. The nanoparticle shape factor has little effect on velocity but a considerable effect on temperature, with increased shape factors contributing greater thermal conductivity. Simultaneously, radiation parameters reduce overall temperatures through losses, and the Brinkman number rises due to increased dissipation-related heating. Simultaneously, increased magnetic fields and nanoparticle volume fractions increase wall shear and heat transfer, which indicates a potential method of flow and thermal control in convergent/divergent channels. Our computational study shows that Forchheimer and Darcy parameters do not greatly change velocity and temperature fields in converging and diverging channels: higher values improve the flow rate and raise the temperature in diverging channels, but induce an opposite trend in converging channels. Relatively small second-grade (non-Newtonian) effects provide several percent divergence from velocity profiles for low to high Reynolds numbers, therefore demonstrating fluid elasticity effects for both geometries. Slip-velocity boundary conditions reduce skin friction significantly, whereas wall temperature jumps enhance heat transfer significantly by improving the local thermal gradient. The particle geometry has a major influence on temperature but not on velocity; the thermal conductivity increases with increasing shape factors. The rise in the magnetic field increases wall friction and heat transfer, providing a basic method of controlling fluid flow and temperature profiles. These results highlight globally the need to consider, at the same time, porous media properties, elasticity of non-Newtonian fluid, slip/jump boundaries, and nanoparticle properties to maximize thermal and hydrodynamic performance in convergent/divergent channels.