Mathematical modelling of heat transfer effects on swallowing dynamics of viscoelastic food bolus through the human oesophagus

The present paper describes a mathematical study on peristaltic flow of viscoelastic fluids (with the robust Jeffrey model) through a finite length channel under the influence of heat transfer. The study is motivated by the need to further elucidate the mechanisms inherent in swallowing of diverse food bolus types (bread, fruit jam and almost all edible semi-solids) through the oesophagus, by taking account of the viscous and elastic effects. The expressions for temperature field, axial velocity, transverse velocity, volume flow rate, pressure gradient, local wall shear stress, mechanical efficiency, stream function, and reflux limit are obtained, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. The computational results are presented in graphical form. The influence of thermophysical (heat transfer), relaxation time and retardation time parameters on pressure distribution, local wall shear stress profiles, temperature profiles and velocity profiles are studied in detail. Furthermore we investigate the effects of these parameters on two inherent phenomena (reflux and trapping) characterizing peristaltic flow using streamline plots. The present study emphasizes an important observation, namely that pressure along the entire length of the channel reduces when the magnitude of relaxation time (retardation time is fixed) or Grashof number or indeed thermal conductivity increase, whereas pressure is enhanced by increasing the magnitude of retardation time (relaxation time is fixed).