Axisymmetric mixed convective propulsion of a non-Newtonian fluid through a ciliated tubule

Thousands of chemical reactions occur in the human body when certain biological fluids, such as blood, semen, mucus, and synovial joint materials, move in various organs. These reactions play a vital role in regulating the life sustaining metabolic processes in the body. Analysis of thermal effects on these chemical reactions is relatively a new area in modern clinical medications. The present study investigates a simulation of the combined response due to heat and mass transport mechanisms taking place in the human body during the flow of physiological fluids. In particular, we focus our attention on the human male reproductive system, wherein the semen transports through the ductus efferentes due to metachronal waves of cilia. The constitutive relations of the robust Jeffrey viscoelastic fluid are used to model the human semen. The mathematical model of the present problem constitutes the axisymmetric flow of a Jeffrey fluid inside a vertical tubule under the influence of mixed convective heat and mass transfers. The inner side of the tubule is covered with ciliated structures. The influence of thermal behaviors of various metabolic processes in the human body due to an external heat source or sink is also taken into account. The mathematical formulation consists of using the approach of lubrication theory approximation; the nonlinear momentum, energy, and concentration equations are simplified to get analytical solutions. Explicit expressions for temperature, concentration, velocity, pressure gradient, and volume flow rate of the proposed bodily fluid (i.e., human semen) are formulated. The expression for the volume flow rate is used to estimate the volume flux of the semen under the influence of various parameters. A comparison between the theoretical and experimentally obtained values of the flow rate of the human semen is also made. It is noted that our calculated values are very close to the estimated values. Industrial applications of the present results are obvious in the fabrication of artificial cilia pumping systems for microfluidic flow systems.