Transportation of nonlinear radiative heat flux in Al2O3–Cu/H2O hybrid nanofluid subject to dissipation energy: Dual solutions analysis

This article examines the flow and transfer of heat created by an exponential shrinking surface containing hybrid nanofluid. Nanoparticles composed of alumina (Al2O3) and copper (Cu) are embedded in water to form Al2O3–Cu/H2O hybrid nanofluid with the mutual impact of magnetohydrodynamics and joule heating. The equations of similarity are obtained from the conducting equation utilizing similarity transformation, and their solutions are obtained through the help of the bvp4c solver using MATLAB software. Outcomes illustrate that there are dual solutions for shrinking strength λ > λc. The critical value λ for the presence of a dual solution decreases for increasing Cu, ∅2, and the Hartman number M. In addition, the skin fraction and the rate of heat transfer increase with increasing ∅2 and M for the first solution. The improvement of the Ecker number, Ec, leads to a decrease in the temperature gradient surface which specifies a reduction in the rate of heat transfer for both solutions when λ < 0 (shrinking sheet).