Mixed convective heat transfer analysis for the peristaltic transport of viscoplastic fluid: Perturbation and numerical study

Mixed convective peristaltic flow of incompressible viscoplastic fluid is investigated in a two-dimensional symmetric channel. The rheology of viscoplastic material is characterized by the constitutive equation for Bingham plastic model. The coupling between momentum and energy equations is achieved through Boussinesq approximation. The coupled nonlinear partial differential equations are transformed in wave frame using Galilean transformation and then simplified under realistic assumptions of long wavelength and low Reynolds number. Approximate solution is obtained using regular perturbation method which is restricted to the smaller values of Grashof and Bingham numbers. The validity of approximate solution is established by comparing it with the numerical solution obtained via Matlab built-in routine bvp4c. Based on the numerical solution an extensive analysis is performed in order to analyze the effects of various parameters of interest on flow characteristics, pumping and trapping phenomena. It is found that velocity decreases at the center by increasing Bingham number showing a boundary layer character for large values. However, it increases by increasing Brinkman and Grashof numbers. Moreover, pressure rise per wavelength increases with Bingham number, Brinkman number and Grashof number, in the pumping region. The result further indicate that larger values of Bingham number circumvent bolus growth.