Corrected similarity reduction for MHD nanofluid flow between parallel sheets

A range of recent studies on magnetohydrodynamic (MHD) (hybrid) nanofluid flow between parallel sheets apply a common similarity transformation to reduce the governing partial differential equations to a class of boundary-value problems involving ordinary differential equations. However, careful examination of several recent papers reveals a recurring inconsistency in the reduced momentum equation obtained from this transformation. We show that the class of non-dimensionalized ordinary differential equations frequently appearing in the literature cannot follow from the standard transformation due to mathematical inconsistencies in the nonlinear convective term. Since the non-dimensionalized temperature and concentration equations are dependent on the non-dimensionalized velocity function, the mathematical inconsistency from the literature propagates also to reported thermal/mass-transfer predictions. This short communication provides a rigorous mathematical foundation to produce the corrected forms and, to the best of our knowledge, presents the first identification of this inconsistency in the thermofluids literature. Our derivation and forms will be of benefit to the research community in supporting reliable future modelling and analysis.