Unsteady stagnation point flow past a permeable stretching/shrinking Riga plate in Al₂O₃-Cu/H₂O hybrid nanofluid with thermal radiation

Abstract

Purpose The investigation of fluid flow and heat transfer is incredibly significant in the present era, particularly in the engineering and manufacturing industries. Hence, this study aims to concern with analysing the unsteady stagnation point flow towards a permeable stretching/shrinking Riga plate of Al2O3-Cu/H2O. The effect of thermal radiation on the boundary layer flow is also taken into account. Design/methodology/approach The multi-variable differential equations with partial derivatives are transformed into third-order and second-order differential equations by applying appropriate transformations. The reduced mathematical model is solved in the MATLAB system by using the bvp4c procedure. This solution approach is capable of producing multiple solutions once the necessary assumptions are provided. Findings The results of various control parameters were analysed, and it has been observed that raising the solution viscosity from 0% to 0.5% and 1% improves the coefficient of skin friction and thermal conductivity by almost 1.0% and 1.9%. Similar response and observation can be witnessed in the addition of modified Hartmann number where the highest values dominate about 10.7% improvement. There is a substantial enhancement in the heat transfer rate, approximately 1.8% when the unsteadiness parameter leads around 30% in the boundary layer flow. In contrast, the increment in thermal radiation promotes heat transfer deterioration. Further, more than one solution is proven, which invariably leads to a stability analysis, which validates the first solution’s feasibility. Originality/value The present results are new and original for the study of flow and heat transfer on unsteady stagnation point flow past a permeable stretching/shrinking Riga plate in Al2O3-Cu/H2O hybrid nanofluid with thermal radiation.

Dual solutions of unsteady two-dimensional electro-magneto-hydrodynamics (EMHD) axisymmetric stagnation-point flow of a hybrid nanofluid past a radially stretching/shrinking Riga surface with radiation effect

“…Following Hashim and Sharjeel (2018) and Zainal et al (2021b), the transformation of the partial differential equations ( 2) and ( 6) are conducted using the following similarity transformations:…”

“…The cylindrical coordinate ( r, φ, z ) is considered with the assumption that the flow is axisymmetric ( ∂/∂φ = 0) and in the region z ≥ 0. The velocity of the stretching/shrinking plate u w ( r, t ) = cr /(1− α t ), where the constant c represents the physical model of a shrinking Riga plate (Zainal et al , 2021b). Furthermore, assumption is given by u e ( r, t ) = cr /(1 − α t ) for the free stream velocity, with 0 ≤ t < 1/ α and α is a constant showing the expansion/contraction strength of the Riga plate.…”

“…contracting; whereas for a negative value of α , the surface of Riga plate becomes larger with time, e.g. expanding (Fang et al , 2012; Zainal et al , 2021b). The surface and ambient temperatures are constant and, respectively, denoted as T w and T ∞ .…”

“…Following Hashim and Sharjeel (2018) and Zainal et al (2021b), the transformation of the partial differential equations (2) and (6) are conducted using the following similarity transformations: where ψ is the stream function and Re r = r u e ( r , t )/ ν f is the local Reynolds number, which are: …”

Dual Solutions of Unsteady Mixed Convection Hybrid Nanofluid Flow Past a Vertical Riga Plate with Radiation Effect

“…Additionally, the hybrid nanofluid outperformed the Al 2 O 3 /H 2 O nanofluid and water in terms of skin friction coefficient and heat transfer rate. Then, Zainal et al [50] broadened this investigation to include the unsteady flow over a stretching/shrinking Riga plate with thermal radiation. This investigation also obtained dual solutions with only one stable solution.…”