| Summary: | Abstract During last decades the research of nanofluid is of great interest all over the World, particularly because of its thermal applications in engineering, and biological sciences. Although nanofluid performance is well appreciate and showed good results in the heat transport phenomena, to further improve conventional base fluids thermal performance an increasing number of researchers have started considering structured nanoparticles suspension in one base fluid. As to make an example, when considering the suspension of three different nanoparticles in a single base fluid we have the so called “ternary hybrid nanofluid”. In the present study three different shaped nanoparticles are uniformly dispersed in blood. In particular, the three different shaped nanoparticles are spherical shaped ferric oxide $$\text{Fe}_{3} \text{O}_{4}$$ Fe 3 O 4 , platelet shaped zinc $$\left( \text{Zn} \right)$$ Zn , and cylindrical shaped gold $$\left( \text{Au} \right)$$ Au , which are considered in blood base fluid because of related advance pharmaceutical applications. Accordingly, we focused our attention on the sharp evaluation of heat transfer for the unsteady couple stress Casson tri-hybrid nanofluid flow in channel. In particular, we formulated the problem via momentum and energy equations in terms of partial differential equations equipped with realistic physical initial and boundary conditions. Moreover, we transformed classical model into their fractional counterparts by applying the Atangana–Baleanu time-fractional operator. Solutions to velocity and temperature equations have been obtained by using both the Laplace and the Fourier transforms, while the effect of physical parameters on velocity and temperature profiles, have been graphically analyzed exploiting MATHCAD. In particular, latter study clearly shows that for higher values of volume fraction $$\phi_{hnf}$$ ϕ hnf of the nanoparticles the fluid velocity declines, while the temperature rises for the higher values of volume fraction $$\phi_{hnf}$$ ϕ hnf of the nanoparticles. Using blood-based ternary hybrid nanofluid enhances the rate of heat transfer up-to 8.05%, spherical shaped $$\text{Fe}_{3} \text{O}_{4}$$ Fe 3 O 4 enhances up-to 4.63%, platelet shaped $$\left( \text{Zn} \right)$$ Zn nanoparticles enhances up-to 8.984% and cylindrical shaped gold $$\left( \text{Au} \right)$$ Au nanoparticles enhances up-to 10.407%.
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