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We present a novel theoretical model to investigate the pressure-driven flow of a non-Newtonian Oldroyd-B nanofluid in an expanding channel. The momentum and temperature field equations are developed on the bases of momentum conservation law and Fourier’s principle of heat transfer in conjunction with Buongiorno’s model of nanofluids. Numerical investigations on a viscoelastic Oldroyd-B fluid flowing in horizontal, converging, and diverging channel have been carried out to collect point-by-point stress data i.e., the shear stresses and flow field). The constitutive model of a viscoelastic fluid adopting the Oldroyd-B model is considered to characterize the rheological behavior of the fluid. The flow equations are changed to a non-linear system and solved numerically using the Runge–Kutta Butcher method via MATLAB code. Numerous emerging flow parameters are probed for their effects on flow and heat transfer characteristics using extensive numerical computing. In converging flow, increasing the Reynolds number and channel angle leads to an increase in velocity distribution, indicating that backflow is eliminated. However, the velocity decreases as the retardation parameter increases significantly. Furthermore, the Oldroyd-B nano liquid literature is elevated by the Brownian motion and thermophoresis parameter, while for the concentration of the nanoparticles the behavior is contrary. The velocity field of an Oldroyd-B fluid is compared with the velocity fields for viscous fluids, which are then traced out as limiting instances. In comparison, the results for polymer solutions obtained in this analysis are compared with a Newtonian fluid.

Jeffery-Hamel flow extension and thermal analysis of Oldroyd-B nanofluid in expanding channel