**1. Introduction**

The enhancement of heat transfer utilizing nanofluids, specifically in solar collectors, has been gaining much attention among researchers. The necessity of heat transfer improvement by ordinary fluids, like ethylene glycol, water, kerosene oil, etc., cannot be achieved. The researchers have conducted many experiments in order to develop the thermal transfer rate. Erosion and blockage are the major disadvantages in the drop of higher pressure and heat transfer rates. To reduce such problems, nanofluids are introduced. The suspension of particles of size 1–100 nm in base fluids can improve the thermal conduction in nanofluids. Using nanoparticles suspension, the thermophysical properties of conventional fluids was first proposed by Choi [1]. The applications of nanofluids are energy storage, heat exchangers, chemical industry, refrigeration process, power production, etc. Choi and Eastman [1] introduced the idea of augmenting fluids thermal conductivity. The radiation influence on nanofluid flow was discussed by Farooq et al. [2]. Sajjid et al. [3] investigated the magnetohydrodynamic (MHD) Fe3O4 nanofluid flow with radiation effect. The thermal and mass transmission in a nanofluid flow with chemical reaction and thermal radiation influences was presented by Sreedevi et al. [4]. The flow of silver and copper based nanofluid with radiation impact was determined by Qayyum et al. [5].

Furthermore, the same study with mixed convection and thermal radiation influences was extended by Hayat et al. [6]. The heat transfer analysis in nanofluids multi walled carbon nanotubes was discussed by Goodarzi et al. [7]. The enhancement of thermal transfer in MHD ferrofluid using different geometrical features was investigated by Goshayeshi et al. [8,9]. Other studies are cited in references [10–13]. Different materials have different properties in nature, and those materials are named viscoelastic material. Shampoo, care products, many oils and fuels, ketchup, food stuff are few examples of viscoelastic material. For describing these fluids, Jeffrey, Maxwell, Oldroyd-B, Burgers, generalized Burgers, Williamson, etc., are developed. The joule heating influence on MHD upper convected Maxwell fluid was presented by Zaidi and Mohyud-Din [14]. The MHD Maxwell fluid flow with chemical reaction was investigated by Afify and Elgazery [15]. The MHD flow of Oldroyd-B nanofluid with a heat flux model was analytically proposed by Mustafa [16]. The magnetic field impact on Williamson fluid flow in a channel was discussed by Hayat et al. [17]. The unsteady flow of Williamson fluid with radiation and heat source/sink influences was examined by Khan and Hamid [18].

Furthermore, in 1822, the mechanism of thermal transmission was suggested by Fourier's law [19]. This law leads us to the argument that the medium under consideration is immediately identifying the initial temperature. To resolve this problem, a thermal relaxation time to Fourier's law has been added by Cattaneo [20]. This term explains the required time of the medium to transmit heat to its bordering particles. Further, Christov [21] improved this model. The new model is named the heat flux model of Cattaneo-Christov (C-C). Using the C-C model, Hayat et al. [22] studied the fluid flow with homogeneous-heterogeneous reactions. The thermal transfer in an upper convected Maxwell fluid flow with C-C model was invested by Mustafa [23]. Tibullo et al. [24] presented the C-C model of heat flux, which is applicable to incompressible fluids. Han et al. [25] analyzed the couple flow of viscoelastic fluid with C-C model. Khan et al. [26] investigated the viscoelastic fluid flow over a stretching surface with a C-C model.

The consequence of Hall current on nanofluid flow has not been studied in the above mentioned literature. The modern tendency of research is in the direction of low density and strong magnetic field, due to its frequent applications like nuclear fusion, space flight, refrigeration coils, Hall accelerators, magnetohydrodynamic (MHD) generators, electric transformers, etc. The situation when the magnetic field is very strong with low density leads to conductivity reduction normal to the magnetic field. This refers to an induced current, which is called the Hall current. Under different flow configurations, numerous research works have been found. Raptis and Ram [27] examined the electrically conducting rotatory fluid flow with the Hall current. Unsteady hydrodynamic flow over a porous plate with the Hall current was inspected by Das et al. [28]. The unsteady MHD Couette flow through a rotating system with Hall and ion-slip currents combined influences was probed by Jha and Apere [29]. Aurangzeeb et al. [30] investigated the mixed convection flow with chemical reaction, heat generation and the Hall current. The convective heat transmission flow with Hall and ion-slip currents with slip conditions was determined by Ferdows et al. [31]. The numerical investigation of MHD viscous flow with Hall influence was presented by Beg et al. [32]. The MHD viscoelastic flow of fluid with hall current and convective conditions was analyzed by Kumar and Chand [33].

Entropy is the irreversibility process in a system. The heat transmission is associated with the least possible change of entropy in thermodynamics processes. Entropy generation minimization (EGM) is developed to improve the machines' ability. Spin moment, kinetic energy, vibration and internal-molecular friction are some applications of EGM. Such types of energy loss cannot be recovered deprived of additional work. That is why the measure of irreversibility process through mass and heat transfers is called entropy. The EGM process is used by investigators in many systems, like gas turbines, cooling by evaporation, natural convection, fuel cells, etc. Li and Faghri [34] investigated the EGM on high concentration direct methanol fuel cell. Hayat et al. [35] observed the EGM for peristaltic flow in a rotating frame. Nouri et al. [36] analyzed the EGM in a nanofluid flow inside a channel with a heat source. Dalir et al. [37] presented the EGM in MHD Jeffrey nanofluid over a stretching sheet. Khan et al. [38] investigated the EGM in MHD flow of nanomaterial with binary chemical reaction and Arrhenius activation energy. The EGM in a nanomaterial mixed convective flow with slip condition was presented by Khan et al. [39]. Hayat et al. [40] presented the EGM in a second grade fluid with thermal radiation influence.

Previous studies of fluid flow over stretchable rotating disk utilizing nanofluids have not been able to consider the impacts of Cattaneo-Christov heat flux, Brownian motion and thermophoresis distribution. This paper reports on a study which considers the implications of Hall effect, Brownian motion and thermophoresis distribution on the second grade nanofluid flow with the Cattaneo-Christov heat flux model, with entropy optimization over a stretching disk. The aim of this paper is to explore a relationship between nanofluid heat transfer rate, entropy, Bejan number, Brownian motion, thermophoresis distribution and Hall effect.
