Hybrid Nanoparticle-Enhanced MHD Dusty Jeffrey Nanofluid Flow for Microchannel Thermal Management in Engine Oil

Engine oil is used as a lubricant and coolant in engines, compressors and gearboxes, where it also carries wear debris and soot particles. Predicting how dispersed nanoparticles and such dust particles change the transient momentum and heat transport of the oil is therefore of practical interest for the thermal management of lubricated microchannels. This work develops an analytical benchmark for the unsteady free-convection flow of a dusty Jeffrey hybrid nanofluid, graphene oxide (GO) and molybdenum disulphide (MoS2) in engine oil, between two infinite vertical plates under a transverse magnetic field and a ramped wall temperature. The memory of the carrier, the dust phase and the heat conduction is represented by the Caputo–Fabrizio time-fractional derivative. Exact solutions for the temperature and for both phase velocities are obtained with the Laplace and finite sine Fourier transforms, and the velocity transforms are inverted by the residue theorem. The solutions are verified against an independent finite-difference scheme, the classical limit and the exact linearity of the flow in the Grashof number, with relative differences below 0.1%. The Nusselt number, skin friction, entropy generation and Bejan number are evaluated. At t = 1, a 4% GO–MoS2 loading raises the dimensionless wall heat flux by 6.45%, a value between those of the GO (6.03%) and MoS2 (6.86%) nanofluids at the same loading. The results apply to fully developed laminar flow with constant properties and provide reference solutions for numerical solvers of dusty viscoelastic nanofluids.