A mathematical model for swallowing of food bolus through the oesophagus under the influence of heat transfer

Abstract

A mathematical model is constructed to study the influence of heat transfer in swallowing of food bolus (water) through the oesophagus. The food bolus is supposed to be viscous fluid and the geometry of wall surface of oesophagus is considered as peristaltic wave. 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 under the assumptions of long wavelength and low Reynolds number. The effect of heat transfer on two inherent phenomena (reflux and trapping) of peristaltic flow is discussed numerically. The comparative study of integral and non-integral number of wave propagating along the channel is discussed under influence of emerging physical parameters. Revelation is that when the magnitude of Grashof number and thermal conductivity increase the pressure along the entire length of the channel reduces whereas the efficiency of pumping increases. Reflux region is found to be increasing function of the both parameters. It is found that the size of upper trapped bolus contracts while size of lower trapped bolus expands with increasing the effect of heat transfer.