<p>Using the hydrodynamics of flow, a new nonlinear differential equation for the rheology of highly viscous crude oils has been derived, reflecting the dependence of shear stress on relaxation time and shear rate. Various analytical solutions are presented, taking into account boundary conditions, allowing for the assessment of shear stress and the effective viscosity of highly viscous dispersed systems. A practical application of the rheology equation for evaluating the apparent viscosity of heavy crude oils is proposed. Additionally, a recirculation scheme for processing heavy crude oils is suggested, aimed at improving their rheological properties.</p>