Exact solutions of Stokes' second problem for hybrid nanofluid flow with a heat source

Abstract

In this study, Stokes' second problem for Cu-Al2O3/water hybrid nanofluid is considered along with the effects of buoyancy force and a heat source. Using Laplace transforms, transient velocity, skin friction coefficient, and local Nusselt number are established in closed forms involving exponentials and error functions. The exact solutions have been compared with the numerical solutions as well as with available exact solutions, which show excellent agreement. It is found that the temperature, skin friction coefficient, and local Nusselt number are strongly affected and increased owing to the increase in the volume fractions of copper and alumina nanoparticles and heat source parameter. On the other hand, the mixed convection parameter noticeably enhances the flow velocity. When the heat source is absent, the skin friction coefficients are oscillating and the heat transfer approaches an asymptotic value. However, for a higher heat source parameter, when time increases, the amplitude of oscillation of the skin friction coefficients gradually increases and the magnitude of heat transfer exponentially increases. Both eventually go to infinity after a long period of time.

MHD oscillatory flow of hybrid nanofluid along a vertical plate with ramped wall temperature, heat source, and thermal radiation: An exact solution

“…Furthermore, because the nanoparticles and base fluid create a solid combination to produce the hybrid nanofluid, it is believed that the nanoparticles size is uniform and that variations in thermo-physical properties owing to nanoparticles aggregation are ignored. T A B L E 2 Nanofluid and hybrid nanofluid thermo-physical relations 6,19 Properties Relations…”

“…In view of the aforementioned assumptions and following Roy and Pop 19 and Nandi and Kumbhakar, 27 the governing boundary layer equations (continuity, momentum, and energy) can be formulated as…”

“…Following Roy and Pop, 19 the below-mentioned appropriate dimensionless variables are adopted to transform the governing equations as well as the associated boundary conditions into a dimensionless form:…”

“…17 Berrehal et al 18 examined the impact of heat source/sink and nanoparticles form on hydromagnetic nanofluid flow along an elongating surface with entropy production. Roy and Pop 19 addressed the sway of heat production and free convection on hybrid nanofluid flow via an oscillating vertical plate analytically.…”

Impact of Smoluchowski Temperature and Maxwell Velocity Slip Conditions on Axisymmetric Rotated Flow of Hybrid Nanofluid past a Porous Moving Rotating Disk

“…Acharya et al [24] discussed the characteristics of Hall current through a moving disk by including the Cu/TiO 2 nanomaterials suspended into base fluid water along with subject to thermal radiation and magnetic effects. Recently, several researchers [25][26][27][28][29][30][31][32][33][34] explored the significance of hybrid nanofluid flow with different aspects.…”