Magnetothermal peristaltic transport of a Carreau fluid through porous sinusoidally deforming curved concentric tubes

The present study develops a generalized mathematical framework for the peristaltic motion of an incompressible Carreau fluid confined between two concentrically curved tubes undergoing sinusoidal wall deformation. The model incorporates the effects of a transverse magnetic field and porous-medium resistance described through Darcy drag, while thermal transport is examined in the presence of viscous dissipation and thermal radiation. The governing conservation equations are formulated in a curvilinear coordinate system, transformed into the wave frame, nondimensionalized, and simplified under the long-wavelength and low-Reynolds-number approximations. The resulting coupled nonlinear momentum and energy equations are solved numerically using a finite-difference scheme. The numerical results show that increasing the curvature parameter, corresponding to a larger radius of curvature and hence weaker geometric curvature, redistributes the axial–velocity profile, shifts the velocity maximum toward the outer region of the annulus, and reduces curvature-induced asymmetry rather than producing a uniform velocity enhancement. Increasing the imposed flow rate decreases the wave-frame axial velocity and modifies the axial pressure-gradient distribution. For the investigated parameter range, a larger Weissenberg number enhances the axial velocity owing to the reduction in apparent viscosity associated with the shear-thinning Carreau rheology. Increasing the wave-amplitude ratio intensifies the spatial variation of the pressure gradient and strengthens the pressure-rise response, whereas increasing the magnetic parameter modifies and flattens the pressure-rise–flow-rate relationship through Lorentz-force resistance. Thermally, a larger Brinkman number increases the fluid temperature because of enhanced viscous dissipation, while increasing the radiation and Weissenberg parameters reduces the temperature within the annular region.