Analysis of unsteady stagnation point flow

Abstract

he study of stagnation point flow has attracted the attention of many researchers due to its wide applications in engineering and scientific interest (Ishak et al. [1], Lok et al. [2], Hayat et al. [3], Ayub et al. [4]). Stagnation point flows can be viscous or inviscid, steady or unsteady, two dimensional or three dimensional, normal or oblique and forward or reverse. Stagnation point flow basically describes the fluid motion near the stagnation region of a solid surface exist in the case of fixed as well as moving body in a fluid. Stagnation point flow with various physical effects has greater physical importance, for example in the prediction of skin-friction as well as heat/mass transfer near stagnation regions of bodies in high speed flows, design of thrust bearings and radial diffusers, drag reduction, transpiration cooling and thermal oil recovery. Similarity solutions for the three-dimensional flow and heat transfer of a power-law fluid near a stagnation point of an isothermal surface were presented by Subba et al. [5]. Hiemenz [6] and Homann and Angew [7] discussed the study of two-dimensional and axisymmetric three-dimensional stagnation point flow, respectively. Lok et al. [8] and Mahapatra and Gupta [9] discussed mixed convection flow near a nonorthogonal stagnation point toward a stretching vertical plate and considered magnetohydrodynamic stagnation point flow toward a stretching sheet. Wang [10] discussed the stagnation flow toward an off-centered rotating disc. In another study, Wang [11] discussed the stagnation flow toward a shrinking sheet. Nadeem et al. [12] has analyzed the series solutions of boundary layer flow of a micropolar fluid near a stagnation point toward a shrinking sheet. A number of researchers have also studied unsteady stagnation point flow. Mention may be made to the works of Labropulu and Chinichian [13] Nazar et al. [14], Labropulu et al. [15] Matunobu [16-17] and Kawaguti and Hamano [18]. A nanoparticle is a microscopic particle with at least one dimension less than 100 nm. Nanoparticle research is currently an area of intense scientific interest due to a wide variety of potential applications in biomedical, optical and electronic fields. The Nano fluid model was first developed by Choi [36]. After Choi this useful area has been recently highlighted by Buongiorno [20], Khanafer et al. [21], Das et al. [22], Kuznetsov et al. [23], Akbar and Nadeem [24], Nadeem et al. [25], Pop et al. [26] in their research work. Recently Sheikholeslami [27] investigated the MHD nanofluid and heat transfer by means of two phase model with radiation effect. There are few other studies which deal various aspects of nanofluids. Mention may be made to the works of [19-26] Motivated from the above useful studies, the aim of the present dissertation is to highlight the unsteady oscillatory stagnation point flow of Newtonian nanofluid. The present dissertation therefore is arranged as follows: Chapter one contains useful definitions and laws. Chapter two includes unsteady oscillatory stagnation point flow of a Jeffrey fluid. Series solutions of the governing problem are obtained analytically. Results are illustrated with the help of graphs and tables. Chapter three addresses unsteady oscillatory stagnation point flow of a viscous nanofluid. The oscillatory stagnation point flow have been discussed in fixed frame and moving frame of references. A detail parametric study is performed graphically to access the impact of various emerging physical parameter. Both two phase and Buongiorno model are used to explore the present study. A comparison data is also