Multiple solutions for the modified Fourier and Fick’s theories for Carreau nanofluid

Abstract

The present paper numerically investigated the dual solutions of Carreau nanofluids in the presence of Cattaneo–Christov double diffusion with focus on heat and mass transfer which contains the effects of Brownian motion and thermophoresis parameter. A nonlinearly shrinking sheet has been utilized to create the flow. The thermal and concentration diffusions are considered by introducing Cattaneo–Christov fluxes. This paper provides information about the energy and concentration equations which are constructed with the help of Cattaneo–Christov double-diffusion theory in the existence of Brownian motion parameter and thermophoresis parameter. The study showed the local similarity variables are used to renovate the governing equations into a set of nonlinear ordinary differential equations. The ascending differential system which is a collection of momentum, temperature and concentration equations is preserved through a numerical approach called the Runge–Kutta–Fehlberg integration technique. The study reveals that the multiple solutions occur for the different vital physical parameters, for example, suction parameter s, Weissenberg number We, Prandtl number Pr, velocity slip parameter $$\delta $$ , viscosity ratio parameter $$\beta ^{*}$$ , non-dimensional thermal relaxation time $$\delta _{e}$$ , Brownian motion parameter Nb and thermophoresis parameter Nt. Moreover, higher values of thermal relaxation time $$\delta _{e}$$ decrease the temperature profile.