Research Article Analysis of Heating Effects and Different Wave Forms on Peristaltic Flow of Carreau Fluid in Rectangular Duct Safia Akram 1 and Najma Saleem 2 1 MCS, National University of Sciences and Technology, Islamabad, Pakistan 2 College of Sciences & Human Studies, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia Correspondence should be addressed to Safia Akram; drsafiaakram@gmail.com Received 3 February 2020; Accepted 25 March 2020; Published 20 May 2020 Academic Editor: Ruben Specogna Copyright © 2020 Safia Akram and Najma Saleem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The existing analysis deals with heat transfer occurrence on peristaltic transport of a Carreau fluid in a rectangular duct. Flow is scrutinized in a wave frame of reference moving with velocity c away from a fixed frame. A peristaltic wave propagating on the horizontal side walls of a rectangular duct is discussed under lubrication approximation. In order to carry out the analytical solution of velocity, temperature, and pressure gradient, the homotopy perturbation method is employed. Graphical results are displayed to see the impact of various emerging parameters of the Carreau fluid and power law index. Trapping effects of peristaltic transport is also discussed and observed that number of trapping bolus decreases with an increase in aspect ratio β. 1. Introduction The applications of peristaltic flows in medical and engineer- ing sciences have attracted the attention of a number of researchers. Applications of peristalsis occur in swallowing food through the esophagus, urine transport from the kidney to the bladder through the ureter, transport of the spermato- zoa in the efferent ducts of the male reproductive tract, move- ment of the ovum in the fallopian tube, movement of the chyme in the gastrointestinal tract, the transport of lymph in the lymphatic vessels, and vasomotion in the small blood vessels such as the arterioles, veins, and capillaries. The peristaltic phenomenon was first discussed by Latham [1]. Based on his experimental theory, numerous researchers have inspected the phenomenon of peristaltic transport under many conjectures [2–10]. Another fascinating area in connection with peristaltic motion is the heat transfer which has industrial applications like sanitary fluid transport, blood pumps in the heart-lungs machine and transport of corrosive fluids where the con- tact of fluid with the machinery parts are prohibited. Only a limited attention has been focused to the study of peri- staltic flows with heat transfer [11–15]. An immense amount of literature is presented on two- dimensional peristaltic flow problems. The study of peristal- tic phenomenon in a rectangular channel was first examined by [16]. Based on the theory of [16], several researchers have studied the phenomenon of peristaltic transport in a rectan- gular duct under various approximations [17–23]. In the papers cited above, the phenomena of heat transfer are not taken into account. Keeping in mind the present informa- tion, the heat transfer phenomena on the peristaltic flow of non-Newtonian fluid have not been discussed in a three- dimensional channel. So, the aim of the present problem is to discuss the effects of heat transfer on peristaltic flow of a non-Newtonian fluid in a rectangular duct with different wave forms. The governing equations for the three-dimensional rectangular channel are first modeled for Carreau fluid and then simplified under the long wavelength and low Reynolds number approximation. Homotopy perturbation technique is carried out to calculate the analytical solution of the highly nonlinear partial differential equations. The expressions for Hindawi Advances in Mathematical Physics Volume 2020, Article ID 8294318, 14 pages https://doi.org/10.1155/2020/8294318