Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 56, Issue 2 (2019) 195-210 195 Journal of Advanced Research in Fluid Mechanics and Thermal Sciences Journal homepage: www.akademiabaru.com/arfmts.html ISSN: 2289-7879 Influence of Velocity and Thermal Slip on the Peristaltic Transport of a Herschel-Bulkley Fluid Through an Inclined Porous Tube Divya Baliga 1 , Manjunatha Gudekote 1,* , Rajashekhar Choudhari 1 , Hanumesh Vaidya 2 , Kerehalli Vinayaka Prasad 3 1 Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India 2 Department of Mathematics, SSA Government First Grade College (Autonomous), Ballari, Karnataka, India 3 Department of Mathematics, VSK University, Ballari, Karnataka, India ARTICLE INFO ABSTRACT Article history: Received 6 January 2019 Received in revised form 7 February 2019 Accepted 21 March 2019 Available online 13 April 2019 The present paper investigates the impact of velocity slip and thermal slip on the peristaltic transport of a Herschel-Bulkley fluid, flowing through a uniform two- dimensional porous tube under the assumptions of long wavelength and low Reynolds number. The mathematical representations of temperature and velocity fields, pressure gradient, and stream function have been found through the closed-form solutions of the energy and momentum equations. Numerical integration has been employed to compute the frictional force and pressure rise. The influence of relevant parameters in the problem have been discussed and presented graphically. The results reveal the increasing effects of thermal and velocity slip on pressure rise and temperature. Also, trapping phenomena of the Herschel-Bulkley fluid is discussed. The volume of the bolus is observed to increase along with the velocity slip parameter. Keywords: Brinkmann number, Darcy number, inclination, velocity slip Copyright © 2019 PENERBIT AKADEMIA BARU - All rights reserved 1. Introduction Peristalsis is the fluid flow mechanism in which the fluid is transported through a distensible tube by means of progressive waves of expansion and contraction. This mechanism has attracted many researchers, owing to its important applications in the fields of engineering science and medicine. The motion of chyme through the gastro-intestinal tract, the transport of urine to the urinary bladder, the activity of swallowing of food through the esophagus, mixing of the contents in the bile duct, blood pump in dialysis are just a few of the examples which use the principles of peristalsis. Latham [1] carried out the first investigations on peristaltic transport of urine flow through the ureter. Since then, several researchers have carried out numerical, analytical and experimental studies on peristalsis. Burns and Parkes [2] used the low Reynolds number assumptions along with the linearized boundary conditions to carry out studies on the peristaltic motion in a two-dimensional as well as * Corresponding author. E-mail address: manjunatha.g@manipal.edu (Manjunatha Gudekote) Open Access