... is approximately 1.33%, significantly higher when compared to the linearly shrinking disk. Moreover, the existence of dual solutions attributed to the nonlinear stretching/shrinking disk is unveiled, with the first solution being identified as the stable and reliable solution through temporal stability analysis...

...Iskandar Waini; Farah Nadzirah Jamrus; Natalia C. Roșca; Alin V. Roșca; Ioan Pop Purpose This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation...

...Waqar Khan Usafzai; Ioan Pop; Cornelia Revnic Purpose This paper aims to present dual solutions for the two-dimension copper oxide with silver (CuO–Ag) and zinc oxide with silver (ZnO–Ag) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip. Design...

... ′ = differentiation with respect to η. © Emerald Publishing Limited 2022 Emerald Publishing Limited Licensed re-use rights only Hybrid nanofluid Shrinking disk Convective boundary condition Numerical simulations Dual solutions F = base fluid; hnf...

.... Nur Adilah Liyana Aladdin can be contacted at: nuradilah@upnm.edu.my 27 10 2020 05 03 2021 15 03 2021 © Emerald Publishing Limited 2021 Emerald Publishing Limited Licensed re-use rights only Dual solutions MHD Chemical reaction Hybrid nanofluid Stagnation point...

... et al., 2018) Ioan Pop can be contacted at: ipop@math.ubbcluj.ro 24 09 2019 01 12 2019 16 02 2020 17 02 2020 © Emerald Publishing Limited 2021 Emerald Publishing Limited Licensed re-use rights only Stability analysis MHD Dual solutions Hybrid...

... the stability of the dual solutions obtained as time evolves. Findings The outcome shows that the flow is unlikely to exist unless satisfactory suction strength is imposed on the shrinking sheet. Besides, the heat transfer rate on the shrinking sheet decreases with the increase of . However, the increase...

... stability analysis is used to determine the stability of the dual solutions obtained as time evolves. Findings Results show that two solutions are found for the limited range of the stretching/shrinking parameter λ , and then these solutions are terminated at λ = λ c . The rise...

... variables. The deriving ODEs are solved numerically by using the bvp4c solver in MATLAB software. Stability analysis also has been performed to determine the stable solution among the dual solutions obtain. For method validation purposes, a comparison of numerical results has been made with the previous...

... and discussed. Findings Numerical results clarify that the dual solutions arise for the shrinking case (λ < 0). The critical values expand for the stronger magnetic field. Besides, the skin friction and the heat transfer coefficients enhance with the rise of the magnetic field and the hybrid...

... analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans...

... by considering dual solutions. Design/methodology/approach It is assumed that the needle can move in the same or opposite direction of the free stream. Also the solid phase and fluid phase are in thermal equilibrium. The basic partial differential equations become dimensionless using a similarity...

...   f ‴ + 2 f f ″ − f ′ 2 − B ( f ′ +   η 2   f ″ ) = 0 , Stability analysis Unsteady flow Dual solutions Hybrid nanofluid Permeable disc Heat transfer augmentation is substantial in industrial and engineering sectors. Pure fluids...

.... Findings Dual solutions for hybrid nanofluid flow obtained for a specific range of the stretching/shrinking parameter values. The values of the skin friction coefficient increases but the local Nusselt number decreases for the first solution with the increasing of the magnetic parameter. Enhancing copper...

... variables, the similarity equations are obtained and then solved using bvp4c in MATLAB. The effects of several physical parameters on the skin friction and heat transfer rate, as well as the velocity and temperature profiles are analysed and discussed. Findings The outcomes show that dual solutions...

... is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration...

... a moving thin needle with Dufour and Soret effects are the important originality of the present study. Besides, the temporal stability of the dual solutions is examined for time. γ = eigenvalue; η = similarity variable; θ = dimensionless temperature...

... to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value The case of suction...

... for the heavy duty engines (Babu et al., 2017). Hybrid nanofluid Stagnation point Exponentially shrinking Vertical sheet Buoyancy effects Dual solutions Stability analysis a,b = constant; C_f = skin friction coefficient...

... 2020 © 2020 Emerald Publishing Limited 2020 Emerald Publishing Limited Licensed re-use rights only Dual solutions Hybrid nanofluid Non-axisymmetric flow Stagnation point flow Stretching/shrinking sheet C_fx = skin friction coefficient along...