This paper examines unsteady magnetohydrodynamic (MHD) convective fluid flow described by the Oldroyd-B model using ramped wall temperature and velocity simultaneously. The fluid flow is closed to an infinite vertical flat plate immersed through a porous medium. Laplace transformation is used to find solutions of momentum and energy equations. Afterwards, the Nusselt number and skin friction coefficient are obtained. A parametric study is performed to investigate the effects of ramped velocity and temperature (at wall) on the considered fluid flow model.

This study shows the effects of magnetic field and copper nanoparticles on the flow of tangent hyperbolic fluid (blood) through a ciliated tube (fallopian tube). The present study will be very helpful for those patients who are facing blood clotting in fallopian tube that may cause for infertility or cancer. The nanoparticles and magnetic field are very helpful to break the clots in blood flowing in fallopian tube. Since blood flows in fallopian tube due to ciliary movement, therefore medicines containing copper nanoparticles and magnetic field with radiation therapy help to improve the patient. Ciliary movement has a particular pattern of motion i.e., metachronal wavy motion which helps to fluid flow. For the forced convective MHD flow of tangent hyperbolic nano-fluid, momentum and energy equations are solved by the small Reynolds' number approximation and Adomian decomposition method by constructing the recursive relation of ADM and solved by software "MATHEMATICA". The effects of parameters such as nanoparticle volume fraction, Hartmann number, entropy generation and Bejan's number have been discussed through graphs plotted in software "MATHEMATICA". It is found that blood flow is accelerated and heat transfer enhancement is maximum in the presence of nano particles, also magnetic effects accelerates the blood flow and help to enhance the heat transfer whereas the presence of porous medium increases the fluid's velocity and reduce the transfer of heat through fluid flow.