Unsteady stagnation point flow of Oldroyd-B nanofluid with heat generation/absorption and nonlinear thermal radiation

Hayat, Tasawar; Qayyum, Sumaira; Waqas, M.; Alsaedi, Ahmed

doi:10.1007/s40430-018-1007-x

Cited by 8 publications

(4 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The correlation of investigative outcomes is made with the current literature for the specific estimations of stream parameters. These correlations are shown in Table 1 with those of Hayat et al, 46 Pop et al, 49 and Hayat et al 50 The results are found in close concurrence with the current outcomes within acceptable limits.…”

Section: The Runge‐kutta‐gill Methodssupporting

confidence: 85%

“…Superficially, mutually the nanofluid and the pane are set at a steady temperature T w , here T T > w ∞ are utilized for the warmed extended float up, and T T < w ∞ relates to the frozen float up. The nanofluid coherence, force, energy, and nanoparticle division conditions can be communicated as 46 :…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Superficially, mutually the nanofluid and the pane are set at a steady temperature

T_{w}

, here

T_{w} > T_{\infty}

are utilized for the warmed extended float up, and

T_{w} < T_{\infty}

relates to the frozen float up. The nanofluid coherence, force, energy, and nanoparticle division conditions can be communicated as 46 :

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

\begin{matrix} trueleft \\ \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = u_{e} \frac{\partial u_{e}}{\partial t} + u_{e} \frac{\partial u_{e}}{\partial x} + υ \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B_{0}^{2}}{ρ} (u - u_{e}) \pm g β_{T} (T - T_{\infty}) \\ \pm g β_{C} (\hat{ψ} - {\overset{ψ}{true}}_{\infty}), \end{matrix}

\frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α_{m} \frac{\partial^{2} T}{\partial y^{2}} + τ ([], D_{B} \frac{\partial \overset{ψ}{true}}{\partial y} \frac{\partial T}{\partial y} + \frac{D_{T}}{T_{\infty}} {(\frac{\partial T}{\partial y})}^{2}),

\frac{\partial \overset{ψ}{true}}{<...>}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Unsteady natural convection magnetohydrodynamic stagnation point flow with assisting and opposing characteristics: Buongiorno model

et al. 2020

View full text Add to dashboard Cite

In this investigation, the flow of an unsteady mixed convection boundary layer viscous nanofluid on a stretchable sheet is considered. The flow examination is affected by a magnetic field. The reason for the examination exhibited is to create models for nanomaterials that incorporate the Brownian movement and thermophoresis phenomena. The created nonlinear standard differential condition is illuminated numerically utilizing the Runge-Kutta-Gill technique and the start program. The different factors of speed, temperature, and concentration are reported and discussed. The examination shows that the speed, temperature, and concentration are lower in contrast with the consistent stream on account of an assisting flow, whereas the opposite situation is noticed in the opposing flow case. The effects of Brownian movement and thermophoresis in the concentration case are totally different.

show abstract

Section: The Runge‐kutta‐gill Methodssupporting

confidence: 85%

Section: Mathematical Formulationmentioning

confidence: 99%

“…Superficially, mutually the nanofluid and the pane are set at a steady temperature

T_{w}

, here

T_{w} > T_{\infty}

are utilized for the warmed extended float up, and

T_{w} < T_{\infty}

relates to the frozen float up. The nanofluid coherence, force, energy, and nanoparticle division conditions can be communicated as 46 :

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

\begin{matrix} trueleft \\ \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = u_{e} \frac{\partial u_{e}}{\partial t} + u_{e} \frac{\partial u_{e}}{\partial x} + υ \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B_{0}^{2}}{ρ} (u - u_{e}) \pm g β_{T} (T - T_{\infty}) \\ \pm g β_{C} (\hat{ψ} - {\overset{ψ}{true}}_{\infty}), \end{matrix}

\frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α_{m} \frac{\partial^{2} T}{\partial y^{2}} + τ ([], D_{B} \frac{\partial \overset{ψ}{true}}{\partial y} \frac{\partial T}{\partial y} + \frac{D_{T}}{T_{\infty}} {(\frac{\partial T}{\partial y})}^{2}),

\frac{\partial \overset{ψ}{true}}{<...>}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Unsteady natural convection magnetohydrodynamic stagnation point flow with assisting and opposing characteristics: Buongiorno model

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Impacts of symmetric/ asymmetric wall zeta potentials in electroosmotic flow of non-Newtonian (Oldroyd-B) liquid are elaborated by Kaushik and Chakraborty (2017). Further analyses covering Oldroyd-B liquid subjected to distinct configurations are given in Waqas et al (2017a); Alshomrani et al (2018); Waqas et al (2018c); Irfan et al (2018b); Hayat et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Effectiveness of improved Fourier-Fick laws in a stratified non-Newtonian fluid with variable fluid characteristics

Waqas

Naz

Hayat

et al. 2019

HFF

Self Cite

View full text Add to dashboard Cite

Purpose The purpose of this paper is to introduce the concept of improved Fourier–Fick laws subjected to variable fluid characteristics. Flow analysis in the stagnation region of Oldroyd-B fluid is elaborated. Heat generation is present. Design/methodology/approach Optimal homotopy analysis method is used to obtain convergent solutions. Findings The outcomes reveal reduction in penetration depths of temperature and concentration due to involvement of thermal and solutal relaxation times of fluxes. Originality/value As per the authors’ knowledge, such analysis has not yet been reported.

show abstract

Investigation of CuO, Al$$_{{2}}$$O$$_{{3}}$$ and Ag nanomaterials on unsteady stagnation point flow of Oldroyd-B–power-law nanofluid with viscous dissipation

2022

View full text Add to dashboard Cite

Unsteady stagnation point flow of Oldroyd-B nanofluid with heat generation/absorption and nonlinear thermal radiation

Cited by 8 publications

References 49 publications

Unsteady natural convection magnetohydrodynamic stagnation point flow with assisting and opposing characteristics: Buongiorno model

Unsteady natural convection magnetohydrodynamic stagnation point flow with assisting and opposing characteristics: Buongiorno model

Effectiveness of improved Fourier-Fick laws in a stratified non-Newtonian fluid with variable fluid characteristics

Investigation of CuO, Al$$_{{2}}$$O$$_{{3}}$$ and Ag nanomaterials on unsteady stagnation point flow of Oldroyd-B–power-law nanofluid with viscous dissipation

Contact Info

Product

Resources

About