The primary determination of this study is a numerical investigation of the entropy generation (EG) in the steady two-region flow of viscous fluid and hybrid nanofluid (NF) in a long-infinite vertical annulus having a clear region as well as porous media. Stoke’s and single-phase NF models are used to study the viscous fluid and hybrid nanofluid (HNF) heat transfer developments

respectively. Two types of nanoparticles are taken

such as copper (Cu) and silver (Ag) within base fluid water to make it a HNF. Darcy-Brinkman law is also used to examine the flow through the porous zone in the annulus. Necessary quantities have been used in the system of equations to transfer them into non-dimensional forms. For momentum and energy transport

the numerical results are evaluated for various model parameters and are examined via the shooting method in MATHEMATICA. It is noted that the momentum and energy transport are more significant when two immiscible fluids in a clear vertical annulus are taken. The findings also indicate that two-phase momentum and heat flow are greater when a NF is used in Region-II and lower when a HNF is used. The temperature (in Region-II) falls with a high nanomaterials volume fraction (see Figure 4) while it is increased when the Hartman number is increased. Moreover

velocity declines with increment in nanomaterials volume fraction. Thus

higher thermal conductivity can be accomplished by using a magnetic field.