**1. Introduction**

The word nanofluid denotes a mixture of nanoparticles and base fluids. Usually nanoparticles contain metals such as silver, copper, aluminum, nitrides like silicon nitride, carbides such as silicon carbides, oxides e.g., aluminum oxide and nonmetals such as graphite. The usual liquids are water, oil, and ethylene glycol. The combination of nanoparticles with a base liquid greatly helps to develop

the thermal qualities of the vile liquid. Choi et al. [1] introduced the term nanofluid and heat transfer features of vile fluids and studied the thermal conductivity enhancement. Wang et al. [2] investigated convective physiognomies of vile fluid and they found that these fluids are enriched by adding metal and non-metal atoms to them. Heat transfer enhancement and thermal conductivity variation of fluids by the addition of copper nanoparticles were studied by Eastman et al. [3,4]. Murshed et al. [5] found the thermal conductivity of vile liquid increases by adding sphere-shaped nanoparticles. Maïga et al. [6], scrutinized nanofluid flow in a uniformly heated tube with heat transfer. Bianco et al. [7] studied the implication between nanoparticles and liquid matrix in two-phase flow; further, nanofluids involuntary convection in circular tubes was deliberated. Buongiorno [8] introduced the two-phase model for convective transport in nanofluids. The single-phase model was studied by Tiwari et al. [9]. After these two models, several investigators considered nanofluids thermal attraction to investigate the actual fluid characteristics discussed in references [10–12]. Thin film Darcy–Forchheimer nanofluid flow with Joule dissipation and MHD effect were scrutinized by Jawad et al. [13]. Rotating flow in the existence of aqueous suspensions with the effect of non-linear thermal radiation was investigated by Jawad et al. [14]. Bhatti et al. [15] scrutinized Jeffrey nanofluid with immediate effects of variable magnetic field. MHD non-Newtonian nanofluid flow over a pipe with heat reliant viscosity was scrutinized by Ellahi et al. [16]. A Cu-water nanofluid applying porous media with a micro-channel heat sink was investigated by Hatami et al. [17]. Laminar nanofluid flow with heat transfer between rotating disks was studied by Hatami et al. [18]. Recently, Shah et al. [19–22] considered Hall current and thermal radiations of the nanofluid flow through a rotating system. Non-Newtonian fluids are complex in nature and various models have beenconstituted and developed for the purpose of defining the strain rate in these fluids. Recently, Ullah et al. [23] analyzed the Reiner–Philippoff fluid model analytically over a stretching surface. They studied the thermophoresis and Brownian motion impacts over the thin film. The heat transfer enhancement not only depends on the nanoparticles added, but also depends on the nature of the fluid. The couple stress impacts with joule heating and viscous dissipation have been studied and analyzed by different researchers over different surfaces [24–26]. Heat transfer enhancement and its detailed study with engineering applications can be found in the references [27–31].

Various techniques have been used to analyze the problem constituted and modeled in the literature. Soleimani et al. [32] used the finite element method for natural convective nanofluid flow with transfer of heat, in a semi-annular object. They described the turning angle effect on the isotherms, streamlines, and local Nusselt number. Rudraiah et al. [33] studied numerically the natural convection inside a rectangular obstacle subject to magnetic field. They found that the heat transfer reduces with a magnetic field. For the simulation of magnetic drug targeting and ferrofluid flow, Sheikholeslami and Ellahi and Kandelousi [34] considered the lattice Boltzmann method (LBM). They found that both the magnetic parameter and the Reynolds number decrease the coefficient of skin friction. Ramzan et al. [24] found a series solution by using HAM for the flow of 3D nanofluid couple stress with joule heating. Recently, with the impacts of convective condition couple stress 3D MHD nanofluid flow in the presence of Cattaneo–Christov heat flux was explored by Hayat et al. [35,36]. Maxwell boundary layer flow of nanofluid was investigated by Hayat et al. [37]. Malik et al. [38] considered MHD flow through a stretching surface of Erying Powell nanofluid. Nadeem et al. [39] considered a vertical stretching surface and analyzed the flow of Maxwell's liquid with nanoparticles. Raju et al. [40] investigated an MHD nanoliquid flow with free convective heat transfer through a cone. The impact of Lorentz forces and entropy generation for different nanofluids were numerically investigated by Sheikholeslami et al. [41–43]. They also used the control volume finite element method (CVFEM) and some new modified techniques for the analysis of the nanofluid flow through a square cavity by considering shape factors. More detailed studies on nanofluid investigation by considering different models can be found in the references [44–49].

Keeping in view the applications of nanofluid and its role in heat transfer enhancement various analyses have been made by researchers. Shah et al. [50] analyzed the Titanium nanofluid flow over a rotating surface analytically. In their work, they studied the impacts of the Hall current and the magnetic parameter. Considering a similar approach for the problem geometry, in this work an inclined rotating surface is considered and is extended to the couple stress nanofluid MHD flow with convective heat transfer by ignoring the mass flux. Furthermore, the impacts of viscous dissipation and Joule heating are also considered in investigating the overall effects of the fluid parameters. The basic equations for the physical problem are constituted from the geometry of the problem and the assumptions made. The set of PDEs obtained from the fundamental equations of fluid dynamics and further assimilated from the boundary layer theory are transformed to a non-linear ODEs system, by using similarity transformations. The analytical Homotopy Analysis Method [51–54] is applied to solve the set of ODEs.
