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The constitutive expressions of unsteady Newtonian fluid are employed in the mathematical formulation to model the flow between the circular space of porous and contracting discs. The flow behavior is investigated for magnetic field-dependent (MFD) viscosity and heat/mass transfers under the influence of a variable magnetic field. The equation for conservation of mass, modified Navier–Stokes, Maxwell, advection diffusion and transport equations are coupled as a system of ordinary differential equations. The expressions for torques and magnetohydrodynamic pressure gradient equation are derived. The MFD viscosity [Formula: see text], magnetic Reynolds number [Formula: see text], squeezing Reynolds number [Formula: see text], rotational Reynolds number [Formula: see text], magnetic field components [Formula: see text], [Formula: see text], pressure [Formula: see text] and the torques [Formula: see text], [Formula: see text] which the fluid exerts on discs are discussed through numerical results and graphical aids. It is concluded that magnetic Reynolds number causes an increase in magnetic field distributions and decrease in tangential velocity of flow field, also the fluid temperature is decreasing with increase in magnetic Reynolds number. The azimuthal and axial components of magnetic field have opposite behavior with increase in MFD viscosity.

Parametric analysis of magnetic field-dependent viscosity and advection–diffusion between rotating discs