Investigation of the unsteady MHD fluid flow and heat transfer through the porous medium asymmetric wavy channel

This paper uses three analytical methods to find the novel results in the two-dimensional time-dependent MHD oscillatory flow and heat transfer in an asymmetric wavy porous channel. The corresponding constitutive equations become complex by considering the pressure gradient as a complex function. This results in the existence of both real and imaginary solutions for fluid velocity and temperature. The changes in parameters like the Hartmann number, wavelength, Grashof number, and porous medium shape factor will affect the real fluid velocity. Still, only radiation parameter changes will affect the real fluid velocity and temperature. Increasing the Hartmann number, porous medium shape factor, and radiation parameter will drastically reduce real fluid velocity. The Reynolds number should theoretically affect the imaginary velocity, but according to the boundary condition definition, the imaginary velocity value becomes zero. Altering the frequency of the wavy walls and the Peclet number will only affect the imaginary temperature component, and increasing these parameters will increase the average imaginary temperature profile. The uniqueness of this study lies in the resolution of complex differential equations in a way that has not been attempted before. The results indicated that each set of three solutions was nearly identical, highlighting the outcomes' precision.