We examine the thermo-magnetohydrodynamic effects on nanofluid flow in a porous circular annular region bounded by two rotating cylinders in the presence of a constant radial magnetic field but variable thermal conductivity. The nanofluid consists of a sample liquid (water/ engine oil) along with suspended copper nanoparticles. This physical problem is formulated and analytical solutions for the governing equations are obtained by using the homotopy analysis method in the form of the physical variables such as, the pressure, fluid speed, temperature, shear stress, heat transfer, and the concentration of nanoparticles. The obtained results are compared with the existing results for the clear fluid and are found in excellent agreement. The effects of the field parameters on these physical variables are studied. It is found that the fluid speed (pressure) increases (decreases) with the Forchheirmer coefficient, porosity, applied magnetic field intensity, and the angular speed of the outer cylinder, but it decreases with the angular speed of the inner cylinder for both liquids. The reverse flow exists if the inner and outer cylinders are rotating in the opposite directions for both the liquids. Furthermore, the thermal transfer rate in the engine oil is lower than that in water. If the annulus region is squeezed, then the fluid speed decays while the pressure rises. The temperature and the thermal transfer rate decay if we march from the inner cylinder to the outer one. The porosity and the angular speed of the outer cylinder enhance the viscous dissipation and shear stress.
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