Mathematical Model of Blood Plasma Flow through Pulmonary Capillaries

The transport of blood plasma through pulmonary capillaries plays a
crucial role in the exchange of oxygen and carbon dioxide within the
human respiratory system. Understanding the dynamics of plasma
flow in the presence of external forces is important for studying
physiological processes and biomedical applications. In the present
study, a mathematical model is developed to investigate the unsteady
laminar flow of blood plasma in the lung mechanism under the
influence of an applied magnetic field. Blood plasma is treated as a
viscous, incompressible and electrically conducting fluid flowing
through a permeable medium representing the pulmonary tissue. The
governing equations of continuity, momentum, energy and mass
transfer are formulated using the principles of
magnetohydrodynamics. These equations are converted into
dimensionless form using suitable non-dimensional parameters such as the Grashof number, Hartmann number, Prandtl number and
Schmidt number. An analytical solution is obtained using the
perturbation method. The influence of various physical parameters
on plasma velocity, temperature and oxygen concentration
distributions is analyzed graphically. The results indicate that
magnetic field strength, buoyancy effects and permeability of lung tissue significantly influence plasma transport in pulmonary
circulation. The present model provides a theoretical framework for
understanding blood plasma flow and gas transport in the human
lung.