Numerical study of magnetohydrodynamics and thermal radiation on Williamson nanofluid flow over a stretching cylinder with variable thermal conductivity

Bilal, Muhammad; Sagheer, Muhammad; Hussain, Shafqat

doi:10.1016/j.aej.2017.12.006

Cited by 78 publications

(32 citation statements)

References 34 publications

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“…Except thermal conductivity, the physical behaviors of the fluid are deliberated to be constant. By using the above supposition, the equations of continuity, momentum, energy, and mass can be formulated 48

\frac{\partial}{\partial x} false(r u false) + \frac{\partial}{\partial y} false(italicrv false) = 0,

\begin{matrix} trueleft \\ u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial r} & = & ν true(\frac{1}{italicr} \frac{\partial u}{\partial r} + \frac{\partial^{2} u}{\partial {italicr}^{2}} true) + ν true(\frac{Γ}{\sqrt{2} italicr} {true(\frac{\partial italicu}{\partial italicr} true)}^{2} + \sqrt{2} normalΓ \frac{\partial italicu}{\partial italicr} \frac{\partial^{2} italicu}{\partial r^{2}} true) - \frac{italicν}{k'} u - \frac{σ_{1} {italicB}_{0}^{2}}{italicρ} u \\ + g {italicβ}_{1} false(T - {italicT}_{normal∞} false) + g {italicβ}_{2} false(C - {italicC}_{normal∞} false) = 0, \end{matrix}

\begin{matrix} trueleft \\ u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial r} & = & \frac{1}{italicr} \frac{\partial}{\partial r} true(α \frac{\partial T}{\partial r} true) + τ \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Inspiring the following dimensionless resemblance transformations, the partial differential equation is converted to a nondimensional system ordinary differential equation (ODE) 48 :

\begin{matrix} true \\ left η = \frac{r^{2} - R^{2}}{2 R} {(\frac{u_{0}}{l ν})}^{\frac{1}{2}}, ψ = {(\frac{ν u_{0}}{l})}^{\frac{1}{2}} x R f false(η false), u = \frac{u_{0} x}{l} f' false(η false), \\ left v = - {(\frac{ν u_{0}}{l} \frac{R}{r})}^{\frac{1}{2}} f false(η false), θ false(η false) = \frac{T - T_{\infty}}{T_{normalw} - T_{\infty}}, φ false(η false) = \frac{C - C_{\infty}}{C_{normalw} - C_{\infty}} . \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In Equation (3),

α

is given as follows 48 :

α = α_{normal∞} false(1 + β θ false(η false) false),

where

α_{\infty}

is thermal conductivity and

β

represents thermal conductivity parameter.…”

Section: Mathematical Formulationmentioning

confidence: 99%

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Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

Ibrahim

Negera

2020

Heat Trans

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The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge‐Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.

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\frac{\partial}{\partial x} false(r u false) + \frac{\partial}{\partial y} false(italicrv false) = 0,

\begin{matrix} trueleft \\ u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial r} & = & ν true(\frac{1}{italicr} \frac{\partial u}{\partial r} + \frac{\partial^{2} u}{\partial {italicr}^{2}} true) + ν true(\frac{Γ}{\sqrt{2} italicr} {true(\frac{\partial italicu}{\partial italicr} true)}^{2} + \sqrt{2} normalΓ \frac{\partial italicu}{\partial italicr} \frac{\partial^{2} italicu}{\partial r^{2}} true) - \frac{italicν}{k'} u - \frac{σ_{1} {italicB}_{0}^{2}}{italicρ} u \\ + g {italicβ}_{1} false(T - {italicT}_{normal∞} false) + g {italicβ}_{2} false(C - {italicC}_{normal∞} false) = 0, \end{matrix}

\begin{matrix} trueleft \\ u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial r} & = & \frac{1}{italicr} \frac{\partial}{\partial r} true(α \frac{\partial T}{\partial r} true) + τ \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Inspiring the following dimensionless resemblance transformations, the partial differential equation is converted to a nondimensional system ordinary differential equation (ODE) 48 :

\begin{matrix} true \\ left η = \frac{r^{2} - R^{2}}{2 R} {(\frac{u_{0}}{l ν})}^{\frac{1}{2}}, ψ = {(\frac{ν u_{0}}{l})}^{\frac{1}{2}} x R f false(η false), u = \frac{u_{0} x}{l} f' false(η false), \\ left v = - {(\frac{ν u_{0}}{l} \frac{R}{r})}^{\frac{1}{2}} f false(η false), θ false(η false) = \frac{T - T_{\infty}}{T_{normalw} - T_{\infty}}, φ false(η false) = \frac{C - C_{\infty}}{C_{normalw} - C_{\infty}} . \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

Ibrahim

Negera

2020

Heat Trans

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“…Shafiq et al 38 analysed the characteristics of MHD convective tangential hyperbolic nanofluid fluid flow. The behaviour of the MHD bioconvective flow due to the gyrotactic microorganism in a stratified medium was observed by Alsaedi et al 39 and Waqas et al 40 MHD flow under the effect of thermal radiation and chemical reaction is being discussed by Lu et al, [41][42][43][44] Bilal and colleagues 45,46 and Suleman et al 47 Blowing effect due to species transfer has many engineering applications as pointed out by Fang and Jing. 48 Stefan blowing effects on nanofluid with microorganism over permeable surface and solid rotating stretchable disc have been studied by Hajmohammadi et al 49 and Latiff et al, 50 respectively.…”

Section: Introductionmentioning

confidence: 95%

Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc

Zohra

Uddin

Basir

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part N:

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Microfluidic-related technologies and micro-electromechanical systems–based microfluidic devices have received applications in science and engineering fields. This article is the study of a mathematical model of steady forced convective flow past a rotating disc immersed in water-based nanofluid with microorganisms. The boundary layer flow of a viscous nanofluid is studied with multiple slip conditions and Stefan blowing effects under the magnetic field influence. The microscopic nanoparticles move randomly and have the characteristics of thermophoresis, and it is being considered that the change in volume fraction of the nanofluid does not affect the thermo-physical properties. The governing equations are nonlinear partial differential equations. At first, the nonlinear partial differential equations are converted to system of nonlinear ordinary differential equations using suitable similarity transformations and then solved numerically. The influence of relevant parameters on velocities, temperature, concentration and motile microorganism density is illustrated and explained thoroughly. This investigation indicated that suction provides a better medium to enhance the transfer rate of heat, mass and microorganisms compared to blowing. This analysis has a wide range engineering application such as electromagnetic micro pumps and nanomechanics.

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“…Hashim et al 22 presented the Runge‐Kutta numerical scheme implemented to analyze Williamson nanoliquid flow characteristics through a radially stretching sheet and showed that temperature of the liquid amplifies as the thermophoresis parameter values rises. Bilal et al 23 perceived magnetohydrodynamics (MHD) heat and mass transfer flow of Williamson nanofluid flow over a stretching cylinder with radiation.…”

Section: Introductionmentioning

confidence: 99%

Heat and mass transfer analysis of MWCNT‐kerosene nanofluid flow over a wedge with thermal radiation

Sreedevi¹,

Reddy²

2020

Heat Trans

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A comparison between the unsteady and steady magnetohydrodynamics Tiwari-Das model Williamson nanofluid flow through a wedge occupied by carbon nanotubes of multiwalled type nanoparticles and kerosene as base fluid is presented in this analysis. A suitable similarity variable technique is adopted to transmute the governing partial differential equations into a set of nonlinear ordinary differential equations (ODEs). To solve these ODEs together along with boundary conditions, we have utilized finite element analysis. The behavior of concentration, temperature, and velocity sketches for diverse values of the pertinent parameters is plotted through graphs. The impact on the above parameters on the rates of velocity, heat, and concentration is also evaluated and depicted through tables. It is noted that as the values of nanoparticle volume fraction parameter rises, the rates of temperature increase in both the unsteady and steady cases.

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Numerical study of magnetohydrodynamics and thermal radiation on Williamson nanofluid flow over a stretching cylinder with variable thermal conductivity

Cited by 78 publications

References 34 publications

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc

Heat and mass transfer analysis of MWCNT‐kerosene nanofluid flow over a wedge with thermal radiation

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