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Grounded in second-language acquisition (SLA) field, with a particular focus on the positive psychology (PP) theoretical perspective, this study examined the potential interplay between learning engagement (LE) and language learning strategies (LLSs), and their impact on language learning achievement of Saudi English as a foreign language (EFL) learners.

This quantitative study adopted a cross-sectional design using an online questionnaire distributed to 168 Saudi EFL college-level students in Saudi Arabia. Various statistical analyses (descriptive analyses, correlations and simple linear regression) were used.

The findings revealed that the most frequently LLSs used were metacognitive, followed by compensation, cognitive, affective, social and memory strategies. High levels of behavioral, followed by cognitive, emotional and agentic, engagement were reported. There was a significant and positive correlation between LLS and LE. LLS use and LE were significant predictors of language learning achievement.

The findings contribute to the domain of second language (L2) educational research and SLA field by emphasizing the importance of researching positive psychological factors such as engagement in relation to individual learners' learning strategies and styles to enhance learners' language learning achievement. A number of pedagogical implications for policymakers, educational stakeholders and foreign language teachers were provided.

The purpose of this paper is to study the effects of thermal radiation and homogeneous-heterogeneous reactions in the three-dimensional hybrid nanofluid flow past a permeable stretching/shrinking sheet.

The combination of aluminum oxide (Al₂O₃) and copper (Cu) nanoparticles with total volumetric concentration is numerically analyzed using the existing correlations of hybrid nanofluid. With the consideration that both homogeneous and heterogeneous reactions are isothermal while the diffusion coefficients of both autocatalyst and reactant are same, the governing model is simplified into a set of differential (similarity) equations.

Using the bvp4c solver, dual solutions are presented, and the stability analysis certifies the physical/real solution. The findings show that the suction parameter is requisite to induce the steady solution for shrinking parameter. Besides, the fluid concentration owing to the shrinking sheet is diminished with the addition of surface reaction.

The present findings are novel and can be a reference point to other researchers to further analyze the heat transfer performance and stability of the working fluids.

The evaluation of high thermal efficiency has actively highlighted the unique behaviour of hybrid nanofluid. Thus, the purpose of this paper is to emphasize the hybrid nanofluid’s stagnation point in three-dimensional flow with magnetic field.

The defined ordinary differential equations systems are addressed using the bvp4c solver.

The results indicate that using dual solutions is possible as long as the physical parameters remain within their specified ranges. Hybrid nanofluid flow has been recognised for its superior heat transfer capabilities in comparison to both viscous flow and nanofluid flow. Furthermore, it has been demonstrated in the current study that augmenting the volume concentration of nanoparticles leads to a corresponding enhancement in the rate of heat transfer. When the velocity gradients ratio is augmented, there is a corresponding reduction in the thermal performance. The separation value grows as the magnetic parameter rises, which signifies the expansion of the boundary layer.

The originality of the paper highlights the general mathematical hybrid model of the three-dimensional problem with the magnetohydrodynamics (MHD) effect in the stagnation point flow. The comprehensive examination of the suggested model has not yet been thoroughly addressed in prior research.

The purpose of this paper is to numerically analyze the stagnation point flow of Cu-Al2O3/water hybrid nanofluid with mixed convection past a flat plate and circular cylinder.

The similarity equations that reduced from the boundary layer and energy equations are solved using the bvp4c solver. The duality of solutions is observed within the specific range of the control parameters, namely, mixed convection parameter λ, curvature parameter γ and nanoparticles volumetric concentration ϕ1 for alumina, while for copper ϕ2. The stability analysis is also designed to justify the particular solutions’ stability. Additionally, the idea to obtain the solution for large value of λ and γ is also presented in this paper.

Two solutions exist in opposing and assisting flows up to a critical value λc where λc lies in the opposing region. An upsurge of the curvature parameter tends to extend the critical value (delay the separation process), whilst increase the heat transfer performance of the working fluid. Meanwhile, the application of hybrid Cu-Al2O3/water nanofluid also can decelerate the separation of laminar boundary layer flow and produce higher heat transfer rate than the Cu–water nanofluid and pure water.

The results are new and original. This study benefits to the other researchers, specifically in the observation of the fluid flow characteristics and heat transfer rate of the hybrid nanofluid. Also, this paper features with the mathematical formulation for the solution with large values of λ and γ.

This paper aims to explore on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder by adding the effect of chemical reaction, B together with the magnetic field, M.

A set of reduced ordinary differential equations from the governing equations of partial differential equations is obtained through similarities requirements. The resulting equations are solved using bvp4c in MATLAB2019a. The impact of various physical parameters such as curvature parameter, ϒ, chemical reaction rate, B, magnetic field, M and Schmidt numbers, Sc on shear stress, f′′0 local heat flux, -θ′(0) and mass transfer, -∅′(0) also for velocity, f′(η), temperature, θ(η) and concentration, ∅(η) profiles have been plotted and briefly discussed. In this work, some vital characteristics such as local skin friction, Cf, local Nusselt number, Nux and local Sherwood number, Shx are chosen for physical and numerical analysis.

The findings expose that the duality of solutions appears in a shrinking region ( ε < 0). The value of skin friction, heat transfer rate and mass transfer rate reduction for existing of M, but in contrary result obtain for larger ϒ, B and Sc. Furthermore, the hybrid nanofluid demonstrates better heat transfer compared to nanofluid.

The hybrid nanofluid has widened its applications such as in electronic cooling, manufacturing, automotive, heat exchanger, solar energy, heat pipes and biomedical, as their efficiency in the heat transfer field is better compared to nanofluid.

The findings on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder with the effect of chemical reaction, B and magnetic field, M is new and the originality is preserved for the benefits of future researchers.