Analysis of a self-propelling sheet with heat transfer through non-isothermal fluid in an inclined human cervical canal.

The present theoretical analysis deals with biomechanics of the self-propulsion of a swimming sheet with heat transfer through non-isothermal fluid filling an inclined human cervical canal. Partial differential equations arising from the mathematical modeling of the proposed model are solved analytically. Flow variables like pressure gradient, propulsive velocity, fluid velocity, time mean flow rate, fluid temperature, and heat-transfer coefficients are analyzed for the pertinent parameters. Striking features of the pumping characteristics are explored. Propulsive velocity of the swimming sheet becomes faster for lower Froude number, higher Reynolds number, and for a vertical channel. Temperature and peak value of the heat-transfer coefficients below the swimming sheet showed an increase by the increment of Brinkmann number, inclination, pressure difference over wavelength, and Reynolds number whereas these quantities decrease with increasing Froude number. Aforesaid parameters have shown opposite effects on the peak value of the heat-transfer coefficients below and above the swimming sheet. Relevance of the current results to the spermatozoa transport with heat transfer through non-isothermal cervical mucus filling an inclined human cervical canal is also explored.

Mathematical assessment of the spermatozoa transport through couple stress fluid in an asymmetric human cervical canal.

Swimming of spermatozoa through couple stress fluid in an asymmetric human cervical canal is investigated in the present theoretical analysis. A couple of fourth-order partial differential equations arising from the mathematical modelling of the proposed model is solved analytically. Flow variables like pressure gradient, propulsive velocity, mucus velocity and time mean flow rate are analysed for the pertinent parameters. Conspicuous features of the pumping characteristics are explored. It is found that pressure rise facilitates the motion of spermatozoa to fertilize an ovum in the female reproductive tract, whereas pressure drop by inverting the direction of spermatozoa controls the probability of pregnancy. Maximal propulsive velocity of the spermatozoa is reported in the absence of travelling waves along the cervical walls. Minute impact of phase difference on propulsive velocity is evident. An analogy of the current analysis with the existing literature is also made.