Unsteady MHD flow and heat transfer of hybrid diesel B0 nanofluid and micropolar dusty fluid in a horizontal channel

Abstract Hybrid nanoparticle additives have been widely recognized for enhancing the thermal transport capability of low-conductivity fuels; however, their interaction with particle-laden microstructure fluids under electromagnetic effects remains insufficiently understood. In this study, an unsteady, immiscible flow of a $$CuO - TiO_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>u</mml:mi> <mml:mi>O</mml:mi> <mml:mo>-</mml:mo> <mml:mi>T</mml:mi> <mml:mi>i</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> /Diesel B0 hybrid nanofluid and a micropolar dusty fluid are investigated within a horizontal channel subjected to a transverse magnetic field. The hybrid nanofluid layer enhances effective thermal conductivity, while the micropolar dusty fluid accounts for micro-rotational motion and particle fluid interactions commonly encountered in practical multiphase environments. The model incorporates Hall and ion-slip currents, viscous dissipation, Joule heating, and interfacial continuity of momentum and heat flux. The resulting nonlinear governing equations are solved numerically using the Modified Cubic B-Spline Differential Quadrature Method, which ensures high accuracy and smooth resolution of the coupled interfacial dynamics. The results reveal that magnetic damping significantly suppresses velocity, whereas Hall and ion-slip effects effectively weaken Lorentz resistance and enhance flow and heat transfer. The unsteady formulation further highlights the temporal development of velocity, temperature, and microrotation fields, offering insight into transient MHD control of layered multiphase systems. The findings are relevant to magnetically assisted thermal management and fuel-based energy transport applications involving hybrid nanofluids and particulate-laden media.