# On Squeezed Flow of Jeffrey Nanofluid between Two Parallel Disks
## 1 Introduction  
The homogenous mixture of ultrafine nanometer-sized particles and convectional heat transfer base liquids is termed as nanofluid. Nanomaterials have a key role in the industrial and engineering processes like processing of coolants for the nuclear reactors, transformer coolant and radiation therapy in cancer treatment etc. Furthermore, the magneto-nanofluid is very helpful in various sectors including sterilizing devices, oil recovery from the underground reservoirs, gastric medications, and tumor elimination with hyperthermia. The small sized nanoparticles (which are mostly metallic, nonmetallic, metal-oxides) are good thermal conductors. For this reason, the nanofluid in comparison to the base fluid has greater thermal efficiency. [PERSON] [1] proposed the idea of nanofluid. He argued that the addition of nanoparticles into the base fluid enhances the thermal performance of base fluid. [PERSON] [2] provided expressions including thermophoresis and Brownian motion. Later on, numerous researchers discussed the flows of nanofluid under different geometries. The relevant literature can be seen through the investigations [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20] and several studies therein.  
Squeezing flow between the parallel disks has received the attention of recent researchers due to widespread applications of such flows in various mechanical engineering disciplines. The flow is generated because of two parallel approaching surfaces in relative motion. The parallel approaching surfaces phenomena along with the relative motion is mostly used by the engineers in the modeling of flow of oil in bearings, determination of capacity of load-bearings, compression and injection modeling, etc. (see [21; 22]). [PERSON] [23] reported the squeezing flow for lubrication approximation. [PERSON] and [PERSON] [24] studied magnetohydrodynamic squeezing flow of viscous liquid bounded by parallel disks. [PERSON] et al. [25] examined squeezing flow subject to an applied magnetic field. [PERSON] et al. [26] performed an analysis of hydrodynamic squeezing flow by developing series solutions. Some other investigations on squeezing flow can be seen in the studies [27; 28; 29; 30].  
The prime interest in the present communication is to venture further into the regime of the squeezing flow of non-Newtonian nanofluid. Therefore, the explicit contribution here is as follows: firstly, to formulate the relevant problem for constitutive relations of the Jeffrey fluid model; secondly, to analyze Brownian motion and thermophoresis; thirdly, to consider magnetohydrodynamics of nanofluid; and fourthly, to entertain the idea of permeable characteristics of lower disks. The upper impermeable disk moves towards the lower disk with time-dependent velocity. Problem formulation is made through small magnetic Reynolds number approximation. The homotopy analysis technique (HAM) [31; 32; 33; 34; 35; 36; 37; 38; 39; 40] is applied to obtain the convergent solutions of the governing equations. The present study has been arranged as follows. The next section presents problem development. Section 3 depicts the development convergent series solutions. Analysis for convergence and discussion have been examined in Sections 4 and 5, respectively. Section 6 gives the main outcomes of the present study. Note that the considered Jeffrey fluid, although capturing the salient features of relaxation and retardation time, is not able to predict the shear thinning/shear thickening and normal stress effects.