**1. Introduction**

Nanofluids consist of solid particles called nanoparticles with higher thermal characteristics suspended in some base fluid. Moreover, convective heat transfer through nanoparticles has motivated many researchers for its industrial applications, pharmaceutical processes, domestic refrigerators, chillers, heat exchangers, electronic cooling system, and radiators, etc., [1]. Nanofluids are considered as the finest coolants for its various industrial applications. Nanofluids exhibit promising thermos-physical properties e.g., they have small viscosity and density and large thermal conductivity and specific heat [2]. As far as transportation of energy is concerned, the ideal features of nanofluids are the high thermal conduction and low viscosity [3]. Choi and Eastman [4] primarily examined the upsurge in thermal

conductivity by submerging nanoparticles into the ordinary fluid. Because of these thermos-physical characteristics, nanofluids are considered as the finest coolants that can work at various temperature ranges [5]. Sheikholeslami et al. [6] found a numerical solution ferrofluid flow under the influence of applied magnetic field in a hot elliptic cylinder. It is examined by them that strong Lorentz force is a source in declining the temperature of the fluid. The water-based nanofluid flow with numerous magnetite nanoparticles amid two stretchable rotating disks is numerically studied by Haq et al. [7]. Khan et al. [8] numerically addressed the water and ethylene glycol based nanofluid flow containing copper nanoparticles with suction/injection effect between parallel rotating stretchable disks. Saidi and Tamim [9] examined the pressure drop and heat transfer properties of nanofluid flow induce amid parallel stretchable disks in rotation by considering thermophoresis effects. Hayat et al. [10] also found a series solution of Jeffrey nanofluid flow between two coaxial rotating stretchable disks having convective boundary condition. Pourmehran et al. [11] numerically simulated the nanofluid flow between coaxial stretchable rotating disks.

Molecules of carbon atoms arranged in a cylindrical shape to form a structure called carbon nanotubes (CNTs). This arrangement of the molecule may be by rolling up of single sheet or by multiple sheets of graphene [12]. The novel properties of CNTs are light weight and high thermal conductivity, which make them potentially useful. CNTs are not dangerous to the environment as they are composed of carbon atoms [13]. The CNTs are the most desirous materials of the twenty-first century. Modern applications of CNTs are in microfabrication technique, pancreatic cancer test, and tissue engineering, etc., [14]. The flow of nanofluid containing both types CNTs with thermal radiation and convective boundary condition effects is examined analytically by Imtiaz et al. [15]. The water-based nanofluid flow containing CNTs of both categories under the impact of magneto-hydrodynamics (MHD) amid two parallel disks is studied by Haq et al. [16]. Mosayebidorcheh et al. [17] did heat transfer analysis with thermal radiation impacts of CNTs-based nanofluid squeezing flow between two parallel disks numerically via the least square method. Effects of thermal radiation in a magnetic field comprising both types of CNTs aqueous based nanofluid flow by two rotating stretchable disks are debated by Jyothi et al. [18]. Transparent carbon nanotubes coating to obtain conductive transparent coating is analyzed by Kaempgen [19]. Keefer et al. [20] studied carbon nanotube-coated electrodes to improve the current electrophysiological techniques. Enzyme-coated carbon nanotube as a single molecule biosensor was reported by Besteman et al. [21]. Some recent investigations featuring Carbon nanotubes amalgamated fluid flow may be found in [22–30] and many therein.

Thermal energy transformation possesses significant importance in engineering applications such as fuel cell efficiency, biomedical applications including cooling of electronic devices, heat conduction in tissues, energy production, heat exchangers, and cooling towers etc., [31]. Classical Fourier law of heat conduction was employed to describe the mechanism of heat transfer. But this model gives parabolic energy equation that is medium encountered initial disturbance instantly which is called "heat conduction paradox." Cattaneo [32] tackled this enigma by introducing the time needed for the conduction of heat via thermal waves at a limited speed which is known as thermal relaxation time. The modification in Fourier law gives hyperbolic energy equation for temperature profile. Christov [33] further inserted Oldroyd's upper convective derivative to maintain material invariant formulation. This upgraded model is known as Cattaneo- Christov heat flux model. The aqueous fluid flow by two rotating disks with the impact of CC heat flux is studied by Hayat et al. [34]. Dogonchi et al. [35] scrutinized the squeezed flow of nanofluid encompassing CC heat flux and thermal radiation effects. Lu et al. [36] discussed the unsteady squeezing nanofluid flow between parallel disks comprising CNTs with CC heat flux model and HH reactions. The recent advance studies on CC heat flux is done by many researchers [37–40].

The aforementioned literature survey (Table 1) reveals that unsteady nanofluid flow containing CNTs with CC heat flux under the influence of hall current between two rotating stretchable disks is not yet discussed. Additional impacts like HH reactions and thermal stratification of the presented mathematical model may be considered as added features toward the novelty of the problem. The problem is solved numerically by using the bvp4c function of MATLAB software.


**Table 1.** A comparison table depicting uniqueness of presented mathematical model.

(×) shows effect is absent and (√) shows the presence of effect.
