<p>Nanoscale materials have the potential to release energy efficiently, which has major benefits for applications involving temperature control and energy storage. In channel flow, the driving pressure gradient controls temperature and velocity distributions, but it is sometimes imprecise because of flow uncertainty and particle interactions. This study investigates the flow dynamics of immiscible Saffman dusty fluid and <i>Al</i>₂<i>O</i>₃ Ethylene glycol–water nanofluid mixture induced by trapezoidal fuzzy pressure gradient in a horizontal channel. The novelty of the work lies in the incorporation of uncertain pressure gradients, modeled through fuzzy differential equations, to realistically capture variations that occur under practical operating conditions. To obtain accurate solutions for the transformed fuzzy dimensionless boundary value problem, the radial basis function pseudospectral (RBF-PS) method is employed. The analysis considers the effect of magnetic fields, ion slip, and Hall parameters on the coupled momentum and energy transport in immiscible fluids. The results reveal that although <i>Al</i>₂<i>O</i>₃ nanoparticles are confined to the nanofluid region, their presence significantly influences both velocity and temperature distributions across the entire duct. The fuzzy framework shows that velocity decreases slightly with increasing Reynolds number due to trapezoidal scaling of the pressure gradient, while higher nanoparticle concentrations enhance temperature and momentum profiles. The fuzzy framework further shows that pressure gradient uncertainty significantly alters the transient development of flow and thermal fields, thereby providing a more reliable prediction of system performance. The findings, presented through grayscale fuzzy profiles of velocity and temperature for fluid and particle phases, offer important information for the design and optimization of nanofluid-based thermal applications operating under variable external conditions.</p>