A Signed-Lorentz-Force Reduced Model for Reversed Electromagnetic Forcing in Stratified Nanofluids

Abstract This study investigates a \emph{signed-Lorentz-force reduced model} for magnetohydrodynamic (MHD) forcing, $\mathbf{F}_L=-s_M\sigma_fB_0^2(\mathbf{v}-\mathbf{V})$ with $s_M=\pm1$ and $M=s_M\sigma_fB_0^2/(\rho_fa)$, applied to stratified Casson nanofluid boundary layers in Blasius-type and Sakiadis-type configurations. The case $s_M=+1$ ($M>0$) is the conventional Lorentz-retarding force obtained from the quasi-static MHD equations, whereas $s_M=-1$ ($M<0$) is a postulated sign-reversed force with the same relative-velocity structure; it does not follow from reversing the electric field in the full vector Ohm's law. The electrical conductivity remains positive in both cases. The governing equations, based on the Buongiorno nanofluid model with heat generation/absorption and Darcy--Forchheimer drag, are reduced by similarity transformation and solved numerically with an adaptive RK45--Newton--Raphson shooting scheme. The current-reversed regime produces distinctive flow modifications: velocity profiles exhibit reversed trends between Blasius-type and Sakiadis-type configurations, while thermal and solutal stratification ($St$, $Ss$) consistently suppress near-wall temperature and concentration. Within the parameter range studied, the displacement thickness decreases monotonically with the Casson parameter $\beta$ for Blasius-type flow (both signs of $M$) and Sakiadis-type flow with $M>0$, confirming boundary-layer thinning. An entropy generation analysis further shows that, for the parameter ranges investigated, the current-reversed regime generates higher total entropy than the current-aligned regime in both flow configurations. These findings position current-reversed MHD as a candidate mechanism for nanofluid flow manipulation, with possible relevance to electromagnetic microreactors and stratified-flow energy systems.