A problem motivated by the investigation of the heat and mass transfer in the unsteady magnetohydrodynamic (MHD) flow of blood through a vessel is solved numerically when the lumen of the vessel has turned into the porous structure.The time-dependent permeability and the oscillatory suction velocity are considered. The computational results are presented graphically for the velocity,the temperature,and the concentration fields for various values of skin friction coefficients,Nusselt numbers,and Sherwood numbers.The study reveals that the flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grnshof number.