Electro-thermal coupled MHD Jeffrey fluid modeling of cervical mucus: implications for thermal-sensitive drug delivery and sperm motility diagnostics

Purpose This study aims to develop an electro-thermal magnetohydrodynamic (ET-MHD) model of sperm transport in the cervical canal, treating cervical mucus as a Jeffrey fluid to capture memory and relaxation effects. It also examines the influence of thermal effects, magnetic and electric fields and wall waviness on sperm motion, heat transfer, trapping and pumping in fertile and infertile mucus. Design/methodology/approach The cervical canal is modeled as a two-dimensional wavy channel, and the swimming sperm as a deforming sheet. The mucus is considered an electrically conducting Jeffrey fluid. Under creeping-flow conditions, closed-form solutions are derived for velocity, temperature, pressure gradient, pressure rise, propulsive velocity and work done. Parametric effects of Hartmann number, Brinkman number, electric field, fluid relaxation and wave amplitude are studied for fertile and infertile mucus. Findings Magnetic field and fluid memory reduce sperm-induced flow, propulsion and bolus trapping, with stronger suppression in infertile mucus. Fertile mucus shows higher flow and propulsion, especially without magnetic effects. Temperature increases due to Joule heating and viscous dissipation, while elasticity lowers it. Magnetic forces reduce trapped bolus size, electric field has little effect on trapping and stronger electromagnetic fields increase pressure demand. Pumping improves in the retrograde region but declines with increasing fluid elasticity. Originality/value To the best of the authors’ knowledge, this study presents the first analytical ET-MHD Jeffrey fluid model for sperm transport in the cervical canal, offering useful insights for fertility assessment and thermally sensitive drug-delivery applications.