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

Abstract

A mathematical model for the unsteady, two-dimensional mixed convection stagnation point flow over a Riga plate is presented in this study. Convective boundary conditions, time-dependent derivatives, mixed convection, radiation effects, and the Grinberg term were all incorporated into the formulation of the governing equations and boundary conditions. By incorporating similarity transformations, ordinary differential (similarity) equations (ODEs) are derived from the partial differential equations (PDEs) of the flow model. The boundary value problem of the fourth-order accuracy code (bvp4c) was implemented in MATLAB (2017b, The MathWorks, Inc., MA. USA, 2017) to solve the mathematical model numerically. Due to the plate's shrinking motion, two (dual) solutions are possible (first and second solutions). Based on the stability analysis, it was found that the first solution is stable and physically realizable in practice, while the second solution is not stable and not physically realizable in practice. It was found that the increase in the mixed convection parameter, modified Hartmann number, and unsteadiness parameter improved the hybrid nanofluid's temperature profile. In addition, increasing the unsteadiness parameter decreased the velocity profile and the skin friction coefficient. Thus, the numerical results suggested that the augmentation of the modified Hartmann number, mixed convection parameter, and unsteadiness parameter can enhance the heat transfer performance in this flow model. This study offers valuable insight into fundamental transport phenomena such as the transmission of momentum, heat, or mass. Hence, it provides valuable information on the gradients of essential factors to control the boundary layer flow pattern.

Mixed convection hybrid nanofluid flow over a stationary permeable vertical cone with thermal radiation and convective boundary condition

“…They reported that mixed convection had proliferated the microorganism transfer rate and the $$y$$‐direction flow velocity. The following papers can also be referred to for additional reading on the studies about mixed convection hybrid nanofluid flow (see [19–25]).…”

Thermal Radiation Effect on Unsteady MHD Rear Stagnation Point in Al2O3-Cu/H2O Hybrid Nanofluids

“…Analytical solutions to heat conduction issues with three different forms of periodic boundary conditions were discovered by Xu et al (2023), along with applications of these solutions. In their study conducted in 2023, Yahaya et al (2023) identified the presence of dual solutions throughout the computational process, instigating an investigation into the stability of the solution. The analysis correctly identified the first solution as stable and meaningful from a physical standpoint.…”

Stability Analysis of Unsteady Flow and Heat Transfer of Rear Stagnation Point in Hybrid Nanofluids with Thermal Radiation and Magnetic Impact

“…Fang and Jing [3] discovered the exact solutions in the unsteady rear stagnation point flow. The analytical and numerical study of the heat transfer and boundary layer flow in the unsteady flow of nanofluid may be obtained in Saidin et al, [4], Fathinia and Hussein [5], Yahaya et al, [6], and Xu et al, [7].…”