This paper is centered on a numerical solution of non-Newtonian Casson magnetonanofluid flow underlying an axisymmetric surface through a non-Darcian porous
medium with heat generation/absorption. Using similarity transformations, the
system of PDEs with the corresponding boundary conditions are reduced to system
of nonlinear ODEs. The Chebyshev pseudospectral (CPS) method is used to get a
numerical solution for the formulated differential system. Comparisons of the present
numerical results with previously published results are made, and fine agreements
for some the considered values of parameters were noted. Two cases of nanofluid
are considered. The first case is Newtonian nanofluid, water with suspended gold
(Au) or alumina (Al2O3) nanoparticles, and representative results are obtained for
β → ∞ and Pr = 6.785 (the Prandtl number of water). The second case is nonNewtonian bio-nanofluid, blood with suspended gold (Au) or alumina (Al2O3)
nanoparticles, and representative results are obtained for β = 0.1 and Pr = 25 (the
Prandtl number of blood). The variation of different physical parameters on nondimensional velocity and temperature fields as well as the skin friction coefficient
and the Nusselt number are discussed. It is demonstrated that the implication of a
nanoparticle into bio-fluid can modify the stream design. Also, the nanoparticles with
high thermal conductivity (gold) have better enhancement on heat transfer
compared to alumina, i.e., the effectiveness of adding gold to the water and blood is
higher than adding alumina. One of the most important applications of
nanotechnology in the field of medicine is the use of nanoparticles (gold molecules)
in chemotherapy to get rid of cancer cells.