Micropolar fluids are special non-Newtonian fluids with microscopic effects like micro rotational and rotational inertia. Eringen has put out the theory of micropolar fluids (Eringen, 1964), (Eringen, 1996). Many academics studied micropolar fluids by outlining many practical uses. Micropolar liquids may be utilized as lubricants since they have lesser friction coefficients than Newtonian liquids (Bansal et al., 2020), (Khonsari, 1990). The significance of micropolar fluids exists in various industries such as the metallic plate cooling, colonial and suspension solutions, liquid crystals, blood (Ikbal et al., 2009), and nuclear power plant (Siddiqa et al., 2021). Recently, nanofluids have so many applications in many industrial sectors, In connection to this, many fluid dynamics experts are currently exhibiting a significant interest in studying them. As the volume percentage of the suspended nanoparticles increases, the thermal conductivity of nanofluids rises (Lee and Eastman, 1999; Wang et al., 1999; Li and Xuan, 2000; Mintsa et al., 2009). Additionally, Wang & Mujumdar’s (Wang and Mujumdar, 2007) comparison of their data with other sources shows that the rate of thermal conduction of nanofluids improves as the size of the particles decreases. As temperature rises, the thermal conductivity likewise rises (Das et al., 2003), (Hayat et al., 2019) and (Gopal et al., 2020). Anwar et al. (Bég et al., 2019) swotted the two-phase stream of a fluids in the presence of a permeable medium. Under the isothermal condition, Kumar et al. (Kumar et al., 2010) carried out the scrutiny of the two-phase stream of micropolar and Newtonian fluid in the channel. The study of two-layered non-miscible liquids in flat mini channels was swotted by Khaled et al. (Khaled and Vafai, 2014) and Umavathi et al. (Umavathi and Anwar Bég, 2020a). Chamkha (Chamkha, 2000) scrutinized the influence of a permeable medium in a two-phase stream of heat-generating or absorbing materials.

Three-phase flows of a couple of stress fluids squeezed between Newtonian fluids are analytically studied by Umavathi et al. (Umavathi et al., 2005). It was noticed that the fluid flow is increased by the pair stress parameter. Umavathi et al. (Umavathi et al., 2008) investigated the three-phase flow of Micropolar fluid. Dragiša et al. (Nikodijevic et al., 2014) analytically studied the three immiscible region flows of Newtonian fluid and all three regions are electrically conducting. Abdul Rauf and Memoona Naz (Abdul and Naz, 2020) investigated the one-dimensional flow of three immiscible region flows in a cylindrical. Hasnain et al. (Hasnain et al., 2022) studied the three-phase flow of Casson liquid with a porous medium squeezed between hybrid nanofluid with clear fluid. They noticed that copper (Cu) nanoparticles increase the temperature. Kumar et al. (Kumar Yadav et al., 2018) analytically studied the three-phase flow of micropolar fluid between clear and hybrid nanofluid. Engineering applications for three-phase flows in porous media include oil production, biofluid transfer, radiator coolant circulation, and more (Dey et al., 2017; Fan et al., 2017; Vamvakidis et al., 2018). Modern methods such as the machine learning are adopted by El-Amin et al. (El-Amin et al., 2023) to study the effect of Nanoparticles in two-phase flow in permeable medium and demonstrated that machine learning approach gives better results than some of the numerical methods. Immiscible fluid flow in different geometries was considered to study flow and heat transfer rate (Umavathi and Anwar Bég, 2020b), (Chen and Jian, 2022). Abdullah et al. (Alzahrani et al., 2023) studied the effect of viscous-Casson fluid in a rotating two-phase flow channel with a chemical reaction and performed a comparative study of different numerical methods.

There is a fascinating new class of sophisticated fluids known as hybrid nanofluids. These nanofluids combine the advantages of traditional nanofluids with those of hybrid materials. They are manufactured by dispersing nanoparticles and other functional components in a base fluid, which results in the creation of a medium that is unique, adaptable, and with increased qualities. In their study, Shamshuddin et al. (Shamshuddin et al., 2023a) educed the HNF model and the development of entropy across a stretchy disk. Shamshuddin et al. (Shamshuddin et al., 2023b) investigated the effects of radiation and other influencing factors on magnetized nanoliquid flow in a permeable cylindrical annulus. They used molybdenum disulfide and magnetite nanoparticles in their research. Shamshuddin et al. (Shamshuddin et al., 2023c) conducted research on a micropolar liquid medium channel while assuming heat radiation and species reactive agents were present. Researchers Shamshuddin et al. (Shahzad et al., 2022) investigated the thermal features of ternary hybrid nanofluids. Additionally, aluminum oxide, copper oxide, silver, and water nano-molecules were used in the research. Taking into account the Hall effect and radiation impacts Shamshuddin et al. (Shamshuddin et al., 2023d) investigated the energy transition that occurs in order to improve the heat transport rate during the flow of a ternary hybrid nanofluid across the surface of a rotating disk. Moreover, this examination is focused on the characteristics of two different kinds of metallic nanoparticles, including Cu and Al₂O₃. In this framework, Cu nanomaterials are used/exercised in a wide variety of products, including heat transfer, antimicrobial materials, catalysts, super solid materials, and sensors [see Refs. (Ahmed et al., 2016; Khan et al., 2021; Khan et al., 2022)]. The advantages or benefits of Cu nanomaterials are competitive, inflated yields under delicate reaction circumstances or situations, and exact reaction durations that seem differently from traditional catalysts (Khan and Alshomrani, 2017). In addition, the Al₂O₃ nanomaterials are widely used in the ceramics, mechanical, and personal care industries (Khan et al., 2017). In recent times, numerous researchers explored the hybrid nanofluids past diverse surfaces (Kavya et al., 2022; Lou et al., 2022; Raju et al., 2022; Upadhya et al., 2022).

In further study, they can use the different nanoparticle with different base fluids. They can study the mass transfer with Soret effect and Dufour effect with non-linear thermal radiation. The aforementioned works’ wide-ranging implications in science and technology have led to the discussion of the three-phase flow of micropolar fluid compressed between transparent fluid and hybrid nanofluid subject to heat radiation and electromagnetic influence. The perturbation technique is carried out to solve the differential equation in our study.

The flow configuration of the problem is schematically shown in Figure 1. In the presence of a magnetic field and electric field, steady and laminar fluid flow through a channel is considered. The fluid flow in the inclined channel is assumed to be a constant pressure gradient. The wall y = −1 is kept at T w 2 , while y = 2 is maintained at T w 1 . The inclined channel is separated into three regions, Region-1 consists of clear fluid and Region-3 consists of a hybrid nanofluid. Both regions are considered in the presence of viscous, Joules and Darcy dissipation region 2 is of a porous medium and consists of micropolar fluid. Density is considered to be constant in all the regions and thermal conductivity and viscosity only with temperature. Copper, Aluminium Oxide—water hybrid nanofluid are considered. The properties of the nanoparticles involved in the study are mentioned in Table 1. Nanoparticles are assumed to be spherical q = 3 and platelets q = 5.7 shape for the fluid flow.

These presumptions allow us to write the steady, microrotation velocity, one-dimensional velocity and temperature governing equations (Umavathi et al., 2008), (Ghasemi and Aminossadati, 2009; Muthtamilselvan et al., 2010; Vajravelu et al., 2013) as follows.

Region 1: μ f d 2 u 1 ′ d y ′ 2 + ρ f g β f T 1 − T w 2 cos ω − ∂ p ∂ x − σ f E 0 + B 0 u 1 ′ B 0 = 0 (1) k f d 2 T 1 d y ′ 2 + μ f d u 1 ′ d y ′ 2 − ∂ q * ∂ y + σ f E 0 + B 0 u 1 ′ 1 2 = 0 (2)

Region 2: μ m f + k d 2 u 2 ′ d y ′ 2 + k d n d y ′ + ρ f g β f T 2 − T w 2 cos ω − μ m f κ u 2 ′ − ∂ p ∂ x − σ m f E 0 + B 0 u 2 ′ B 0 = 0 (3) γ d 2 n d y ′ 2 − k 2 n + d u 2 ′ d y ′ = 0 (4) k m f d 2 T 2 d y ′ 2 + μ m f d u 2 ′ d y ′ 2 + μ m f κ u 2 ′ 2 − ∂ q * ∂ y + σ m f E 0 + B 0 u 2 ′ 2 = 0 (5)

Region 3: μ h n f d 2 u 3 ′ d y ′ 2 + ρ h n f g β h n f T 3 − T w 2 cos ω − ∂ p ∂ x − σ e h n f E 0 + B 0 u 3 ′ B 0 = 0 (6) k h n f d 2 T 3 d y ′ 2 + μ h n f d u 3 ′ d y ′ 2 − ∂ q * ∂ y + σ e h n f E 0 + B 0 u 3 ′ 2 = 0 (7)

Boundary and Interface conditions are assumed to be: u 1 ′ − h = 0 , u 1 ′ 0 = u 2 ′ 0 , μ f d u 1 ′ 0 d y ′ = μ m f 1 + K d u 2 ′ 0 d y ′ + μ m f K N m , u 2 ′ h = u 3 ′ h , u 3 ′ 2 h = 0 , μ m f 1 + K d u 2 ′ h d y ′ + μ m f K N m = μ h n f d u 3 ′ h d y ′ , d N m 0 d y = 0 , d N m 1 d y = 0 T 1 − h = T w 2 , T 1 0 = T 2 0 , k f d T 1 0 d y ′ = k m f d T 2 0 d y ′ , T 2 h = T 3 h , T 3 2 h = T w 1 , k m f d T 2 h d y ′ = k h n f d T 3 h d y ′ (8)

To convert Eqs 1, 2, 3, 4, 5, 6, 7, 8 into dimensionless equations, we use the following dimensionless parameters y = y ′ h , u i = u i ′ ρ f μ f h , θ i = T i − T w 2 T w 1 − T w 2 , G r = g β f T w 1 − T w 2 h 3 v f 2 cos ω , M 2 = B 0 2 h 1 2 σ μ f , E = E 0 ρ f h B 0 μ f , B r = μ f 3 ρ f 2 h 2 T w 1 − T w 2 k f , σ = h κ , P = − ρ f h 3 μ f 2 ∂ p ∂ x , v f = μ f ρ f , ∂ q ∂ y = 4 α 2 T i − T w 2 , N = 2 α h k f , K = k μ m f , n = N h μ m f

The thermophysical properties of hybrid nanofluids are given by (Hayat and Nadeem, 2017): ρ h n f = 1 − ϕ s 1 ρ f + ϕ s 1 ρ s 1 1 − ϕ s 2 + ρ s 2 ϕ s 2 , α h n f = k h n f ρ C p h n f ρ β h n f = 1 − ϕ s 1 ρ β f + ϕ s 1 ρ β s 1 1 − ϕ s 2 + ρ β s 2 ϕ s 2 , μ h n f = μ f 1 − ϕ s 1 5 1 − ϕ s 2 5 ρ C p h n f = ρ C p f 1 − ϕ s 2 1 − ϕ s 1 + ϕ s 1 ρ C p s 1 ρ C p f + ϕ s 2 ρ C p s 2 σ h n f = σ n f σ s 2 + 2 σ n f − 2 ϕ s 2 σ n f − σ s 2 σ s 2 + 2 σ n f + ϕ s 2 σ n f − σ s 2 , σ n f = σ f σ 1 + 2 σ f − 2 ϕ 1 σ f − σ 1 σ 1 + 2 σ f + ϕ 1 σ f − σ 1 (9)

The thermophysical properties of the nanofluid, base fluid and nanoparticles are denoted by the subscripts n f , f , s 1 and s 2 respectively. According to Maxwell thermal conductivity of hybrid nanofluid k h n f is considered as: k h n f = k b f k s 2 + q − 1 k b f − q − 1 ϕ 2 k b f − k s 2 k s 2 + q − 1 k b f + ϕ 2 k b f − k s 2 , k b f = k f k s 1 + q − 1 k f − q − 1 ϕ 1 k f − k s 1 k s 1 + q − 1 k f + ϕ 1 k f − k s 1 (10)