1. Introduction

The relation among pressure and flow is an important phenomena which plays a vital role to understand the circulation of the blood in the human body and its sustainability. The approach of pressure [1] can bring a partial barrier in some areas of the smaller vessels due to the

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

thrilling change of the yield stress. The blood is equally a mixture of two fluids Casson and the other one is Newtonian fluid and studied by Srivastava and Saxena [2]. They focused on the effect of resistance created by the viscosity term and wall shear stresses. Later on, this fluid is studied by many researchers on the stretching surfaces for other industrial and engineering usages [3]. Mahdy [4] have examined the fluid motion over an extending cylinder considering Casson fluid. Hayat et al. [5] have examined the third-order fluid motion over an extending tube within the effect of MHD. Qasim et al. [6] have considered the slip flow of sighted ferrofluid over an extending cylinder. Sheikholeslami [7] has studied the suction idea considering nanofluid over an extended cylinder. Manjunatha et al. [8] have examined the radiation effect in a porous space using dusty fluid and stretching cylinder. Abdulhameed et al. [9] have examined the oscillatory flow phenomena using circular cylinder. Hakeem et al. [10] have studied the flow of Walter's B fluid over an extending sheet. Pandey et al. [11] have studied the Walter's B viscoelastic nanofluid film energetic from below. The interesting and fruitful applications of thin film are the wire and fiber coating, processing of food stuff, extrusion of polymer and metal, drawing of plastic sheets, continuous casting, fluidization of reactor, and chemical processing equipment. On the basis of these applications, researchers did a lot of work on it. Wang [12] was the main researcher who investigated liquid film on an unstable extending surface. Recently Tawade et al. [13] have investigated liquid film flow over an unstable extending surface with thermal radiation, in the existence of continuous magnetic field using numerical method. The liquid film flow considering non-Newtonian fluids proliferates in many life geographies which is used mostly in cylindrical shapes. Several researchers [14–17] investigated power-law fluid with unsteady extending surface using different cases. Megahe [18] and Abolbashari et al. [19] have scrutinized thin film flow of Casson fluid using slip boundary conditions. Recently Qasim et al. [20] have examined the liquid film flow of nanofluid considering Buongiorno's model.

The liquid film spray on a stretching sheet has also an important phenomena to coat the metals and increase their life. The idea of spray on the stretching surface is the study of Wang [21]. Recently Noor et al. [22] considered the thin film spray of nanofluid on a stretching cylinder. They compared their results with the experimental data and found the impact of the physical parameters during flow phenomena. They also discussed the application of their work in detail. Most of the mathematical problems in the field of engineering are composite in their nature, and the exact resolution is very tough or even not conceivable. The solution of these problems is tackled through numerical and analytical methods. Homotopy analysis method is one of the popular techniques for the solution of such complex problems. Liao [22–26] investigates this series solution technique for the solution of nonlinear problems. The other important feature of this method is that its solution contains all the embedded parameters involved in the problem and also the range of the embedded parameters. The high nonlinear problems have been solved by Abbasbandy [27] due to the fast convergence of this method. Alshomrani and Gul [28], Gul [29] have studied the solution of nonlinear differential equations through HAM arises in the field of engineering and industry.
