**1. Introduction**

Nanoparticles less than 100 nm in size suspended into a base fluid is recognized as nanofluid. Nanofluids are used in pharmaceutical procedures, microelectronics, fuel cells, hybrid powered machines, and nanotechnology fields. Choi and Eastman [1] were the first to immerse nanoparticles into a base fluid and call it a nanofluid. Through the suspension of nanoparticles, the thermophysical

properties of the conventional fluid are enhanced. The heat transmission characteristics of a nanofluid were pointed out by Wang and Mujumdar [2]. Later on, Eastman et al. [3,4] furthered this study using different base fluids. Murshed et al. [5] experimentally showed that nanofluids that contain smaller amounts of nanoparticles have higher thermal conductivities. Furthermore, increasing the volume of the nanoparticles fraction increases the thermal conductivity of the nanofluids. Maiga et al. [6] addressed the thermal and hydrodynamic behaviors of nanofluids inside a heated tube. Nanofluid flow in a circular tube with heat flux was addressed by Bianco et al. [7]. The flow processes of nanofluids inside a heated cavity were numerically addressed by Tiwari and Das [8]. The heat transmission in nanofluid flows with Brownian and thermophoresis influences was investigated by Buongiorno [9]. The heat transmission processes of nanofluids in a porous medium were examined by Kasaeian et al. [10]. The radiative MHD flow of a nanofluid experiencing a chemical reaction under the influence of thermal radiation was addressed by Ramzan et al. [11]. The impacts of Brownian motion, magnetic field, and nanoparticles volume fraction on nanofluid flow were analyzed by Sheikholeslami and Shehzad [12]. The MHD nanofluid flow over an extending surface with the influence of viscous dissipation was addressed by Besthapu et al. [13]. The heat transmission in a nanofluid flow over an oscillatory stretching sheet with radiation impacts was addressed by Dawar et al. [14]. The same nanofluid with entropy generation and magnetic field impacts was addressed by Alharbi et al. [15]. Nanofluid flow based on four different fluids in a rotating system with a Darcyian model was addressed by Shah et al. [16]. Khan et al. [17] addressed heat transmission in MHD nanofluid flow under the influence of radiation in rotating plates.Khan et al. [18] addressed nanofluid flow over a linear extending sheet under convective conditions. The viscous dissipation impact of MHD nanofluid flow with entropy generation was determined by Dawar et al. [19]. Sheikholeslami [20] examined the radiative and heat transfer in electrohydrodynamic nanofluid flow. Sheikholeslami [21] determined the MHD nanofluid flow with Brownian influence. Dawar et al. [22] addressed the flow of nanofluid over a porous extending sheet with radiation influence. Ramzan et al. [23] examined the MHD nanofluid flow using the couple stress effect. Sajid et al. [24] examined nanofluid flow over a radially extending surface. Attia et al. [25] examined the stagnation point flow in a porous medium over a radially extending surface. But and Ali [26] scrutinized the MHD flow and heat transfer with entropy generation rate over a radially stretching surface. Zeeshan et al. [27] examined ferrofluid flow over a stretching sheet under the influence of ferromagnetism, thermal radiation, and the Prandtl number. Ellahi et al. [28] addressed the impact of a magnetic field on Carreau fluid flow. Recently, the applications and development of nanofluids were discussed by Ellahi [29]. In another article, Ellahi et al. [30] addressed differential equations with application in engineering fields. The applications of heat transfer in nanofluid flows were addressed by Abu-Nada [31]. Hayat et al. [32] discussed the MHD magnetic field impact on Powell-Eyring nanomaterial flow over a nonlinear extending sheet. Hsiao [33] examined the heat convection, conduction, and mass transfer of MHD nanofluid flow over a stretching sheet. Abu-Nada [34] addressed the heat transfer in a nanofluid flow with entropy generation. Hsiao [35] analyzed the viscous dissipation and radiative influences on MHD Maxwell nanofluid flow in a thermal extrusion system. Pour and Nassab [36] examined nanofluid flows under bleeding conditions. Tian et al. [37] addressed the MHD incompressible flow of nanofluid over an extending sheet with thermophoresis and Brownian influences. Recently, Shah et al. [38] addressed the flow of nanofluid over an extending sheet with couple stress impact. Ellahi et al. [39] examined heat transmission in a boundary layer flow with MHD and entropy generation effects. Some recent study about nanofluid flow can be seen in [39–43].

In this article, a thin layer flow of Darcy-Forchheimer nanofluid over a nonlinear radially extending disc is examined. The disc is considered as porous. The homotopy analysis method (HAM) is applied to solve the nonlinear differential equations using appropriate similarities transformations. The HAM is compared with the numerical (ND-Solve) technique through graphs and tables. Section 2 confronts with the problem of formulation. In Section 3, the modeled problem is solved by HAM. In Section 4,

the impacts of embedded parameters on the fluid flow are deliberated. Section 5 presents the concluding remarks of this research.
