Magnetohydrodynamics Mixed Convective Couple Stress Hybrid Nanouid Darcy-Forchheimer Flow through a Rotating Porous Space

In this study, we consider the magnetohydrodynamics mixed convective couple stress hybrid nanofluid Darcy-Forchheimer flow through a rotating porous space with velocity slip condition. The nonlinear thermal stratification and thermal radiation of Magnetohydrodynamics (MHD) are discussed in detail. For relative analysis, we have taken the nanoparticals samples of Aluminum oxides ( 2 3 A l O ) and Titanium dioxide ( 2 T i O ). The rotation in the disk is produces for the generation of the flow in the system.Furthermore, the variable permeability and porosity of porous space is regarded as Darcy-Forchheimer expression. The resulting nonlinear system of ODE’s are solved by Homot opy Analysis Method (HAM). The governing of several sundry parameters i.e. “Couple Stress, coefficient of inertia, radiation parameter, magnetic parameter, Prandtl number, heat source or sink parameter” are presented both graphically as well as in numerical tables. The behavior of the flow predicted that the increase of both mixed convection and couple stress parameters cause increase in the momentum profile. Temperature of the system rises for higher values of radiation parameter and magnetic parameter. The higher local heat transfer rate of Aluminum oxides ( 2 3 Al O ) and Titanium oxide ( 2 TiO ) or water is examined as compared to hybrid nanofluid.


Symbol Description
Symbol Description (  The study of nanofluids has gained a valuable attraction due it vast applications in different fields of industry. In order to increase thermal conductivity of base fluid nanopartical has been introduced. Because the simplest base fluids do not meet the required cooling in the industries. For this purpose the nanoparticles of very small size of (1nm to 100nm) can be included in both Newtonian and non-Newtonian models.  [3] represented his work on the topics concern to the nanofluids flow on stretching surfaces. The analytical solutions of steady laminar nanoliquids flow for suction or injection effects by Nadeem et al. [4]. Mehboob et al. [5] explored numerically the impact of heat transfer on boundary layer flow of nanofluid over nonlinearly elongating sheet. Exponentially flow of the nanofluid with the condition of convective boundary layer stream was explored by Mustafa et al. [6]. It has been observed that the geometry of particles strongly disturbs the nanoparticles thermal conductivity. Das and Tiwari et al. [7], providing numerical solutions of mixed convective flow of nanofluids. The improvement in heat transfer in the past on stretch surface flow of nonfluid has been analyzed by Vajravelu [8]. The stream of nanofluid in 3D under the condition of convective boundary layer over sheet elongating in two direction was explored by Khan [9]. The flow of mixed convective nanofluid composed of 22 SiO H O  past a spinning circular cylinder was explored by Selimfedigil [10]. Hayat and Nadeem et al [11] investigated the heat transfer enhancement in chemically reactive flow of silver and copper oxide ( Ag CuO  /water) hybrid nanofluid. Rashad [12] presented in his work the natural convective stream of 3 Cu AlO  /water hybrid under the impacts of MHD and joule heating. Some developments in the study of hybrid nanofluids are consulate in refs: [13][14][15]. In industries Mixed convection boundary layers flows having the large number of real life uses such as electronic devices, heat exchanger, nuclear reactor, central solar receiver et al. [16]. In light of these numerous applications it is opening a new door for the researchers, to investigate the consequences of mixed convection boundary layer flow analytically as experimentally. Hayat [17] have discussed analytically viscoelastic mixed convective nanofluid through stretched cylinder. The transfer of heat through time dependent convective flow over an elongating belt was discussed by Turkyilmazoglu [18]. The heat transfer through time dependent convective boundary layer over shrinking/stretching surface by the spectral relaxation technique was analyzed by Haroun [19].
Behazadmehr [20] designed and studied convective flow of nanoliqiuds in tube. The heattransfer properties of convective nano-fluids subjected to stretched sheet was investigated by Mahdi [21]. The branch of magnetohydrodynamics shortly known as MHD has incorporates ascending phenomenon when attractive fields is smeared to electrically engaged liquids. The Srinivasacharya and Surender at el. [29]. Sheremet [30] has explored the free convective stream of nanofluid by keeping the impact of thermal stratification inside the cavity with square shape. The Thus the energy equation becomes: The hybrid nanofluid Theoretical model is [13]  In Table 1 thermo-physical properties of nanoparticles and water are discussed and given as: The Nusselt number and Skin friction coefficient for the problem is defined as :

Solution by HAM
The solution of the problem in Equation (13 to 15) was found by using HAM under the boundary conditions in Equation (16).

Results and Discussion:
This    when the values of r p is increased.

Conclusions:
The Darcy-Forchheimer flow of mixed convective couple stress hybrid nanofluid with Magnetohydrodynamics (MHD), nonlinear thermal radiation and thermal stratification is investigated. The major outcomes are listed as follows:  There is a decreasing in    