Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation

Afridi, Muhammad Idrees; Qasim, Muhammad

doi:10.1016/j.ijthermalsci.2017.09.014

Cited by 110 publications

(51 citation statements)

References 37 publications

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“…In this study, the nonlinear and coupled Equations , and with boundary conditions are solved numerically using Runge–Kutta–Fehlberg method with shooting technique for different values of parameters. Table reveals the comparison of the present results with the previously declared results of Ishak et al, Chen and Smith, and Afrdi and Qasim, where it was observed that there is a good agreement between them. The good agreement is related to the observation that increase in the size of the needle reduces the skin friction significantly.…”

Section: Resultssupporting

confidence: 81%

“…Under the aforementioned assumptions, the boundary layer equations of the viscous flow over a thin needle subject to variable viscosity are:

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

\begin{matrix} trueleft \\ u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial r} = U_{\infty} \frac{d U_{\infty}}{d x} + \frac{1}{r ρ_{f}} \frac{\partial}{\partial r} (r μ_{f} (T) \frac{\partial u}{\partial r}) - \frac{σ B_{0}^{2} (u - U_{\infty})}{ρ_{f}} \\ + \frac{1}{ρ_{f}} [(1 - C_{\infty}) ρ_{f_{\infty}} β g (T - T_{\infty}) - (ρ_{p} - ρ_{f_{\infty}}) g (C - C_{\infty}], \end{matrix}

\begin{matrix} trueleft \\ u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial r} = \frac{α_{f}}{r} \frac{\partial}{\partial r} (r \frac{\partial T}{\partial r}) + τ [D_{B} \frac{\partial C}{\partial r} \frac{\partial T}{\partial r} + \frac{D_{T}}{T_{\infty}} {((), \frac{\partial T}{\partial r})}^{2}] + \frac{Q_{0}}{{false(ρ C_{p} false)}_{f}} (T - T_{\infty}) \\ + α_{<...>} \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The developed governing equations can be simplified into the dimensionless form by employing the following stream function and similarity variables:

\begin{array}{l} u = 2 U f' false(η false), v = - \frac{υ_{f}}{r} f + η \frac{υ_{f}}{r} f' false(η false), η = \frac{U r^{2}}{υ_{f} x}, \\ θ false(η false) = \frac{T - T_{\infty}}{T_{f} - T_{\infty}}, ϕ false(η false) = \frac{C - C_{\infty}}{C_{\infty}}, \end{array}}

where velocity components

u

and

v

satisfy Equation identically. Further,

U = U_{w} + U_{\infty} \neq 0

is the composite velocity and

U_{\infty}

is the constant free stream velocity.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Joule heating effect on two‐phase nanofluid flow was considered by Dogonchi and Ganji . In the past, the boundary layer flow over a continuously moving thin needle (Ishak et al), forced convection flow on nonisothermal thin needle (Chen and Smith and entropy generation and heat transfer in boundary layer flow over a thin needle with nonlinear Rosseland radiation (Afridi and Quasim) moving in parallel stream have been carried out.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

2019

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The current study focuses on investigating the influence of transverse magnetic field, variable viscosity, buoyancy, variable Prandtl number, viscous dissipation, Joulian dissipation, and heat generation on the flow of nanofluids over thin needle moving in parallel stream. The theory of nanofluids that includes the Buongiorno model featured by slip mechanism, such as Brownian motion and thermophoresis, has been implemented. Further, convective boundary condition and zero mass flux condition are considered. The nondimensionally developed boundary layer equations have been solved by Runge-Kutta-Fehlberg method with shooting technique for different values of parameters. The most relevant outcomes of the present study are that the augmented magnetic field strength, viscosity parameter, buoyancy ratio parameter, and the size of the needle undermine the flow velocity, establishing thicker velocity boundary layer while Richardson number and Brownian motion show opposite trend. Another most important outcome is that increase in the size of the needle, viscous dissipation, convective heating, and heat generation upsurges the fluid temperature, leading to improvement in thermal boundary layer. The effects of different natural parameters on wall shear stress and heat and mass transfer rates have been discussed. K E Y W O R D S buoyancy, Joule heating, thin needle, variable Prandtl number, variable viscosity, viscous dissipation

show abstract

Section: Resultssupporting

confidence: 81%

“…Under the aforementioned assumptions, the boundary layer equations of the viscous flow over a thin needle subject to variable viscosity are:

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

\begin{matrix} trueleft \\ u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial r} = U_{\infty} \frac{d U_{\infty}}{d x} + \frac{1}{r ρ_{f}} \frac{\partial}{\partial r} (r μ_{f} (T) \frac{\partial u}{\partial r}) - \frac{σ B_{0}^{2} (u - U_{\infty})}{ρ_{f}} \\ + \frac{1}{ρ_{f}} [(1 - C_{\infty}) ρ_{f_{\infty}} β g (T - T_{\infty}) - (ρ_{p} - ρ_{f_{\infty}}) g (C - C_{\infty}], \end{matrix}

\begin{matrix} trueleft \\ u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial r} = \frac{α_{f}}{r} \frac{\partial}{\partial r} (r \frac{\partial T}{\partial r}) + τ [D_{B} \frac{\partial C}{\partial r} \frac{\partial T}{\partial r} + \frac{D_{T}}{T_{\infty}} {((), \frac{\partial T}{\partial r})}^{2}] + \frac{Q_{0}}{{false(ρ C_{p} false)}_{f}} (T - T_{\infty}) \\ + α_{<...>} \end{matrix}

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The developed governing equations can be simplified into the dimensionless form by employing the following stream function and similarity variables:

\begin{array}{l} u = 2 U f' false(η false), v = - \frac{υ_{f}}{r} f + η \frac{υ_{f}}{r} f' false(η false), η = \frac{U r^{2}}{υ_{f} x}, \\ θ false(η false) = \frac{T - T_{\infty}}{T_{f} - T_{\infty}}, ϕ false(η false) = \frac{C - C_{\infty}}{C_{\infty}}, \end{array}}

where velocity components

u

and

v

satisfy Equation identically. Further,

U = U_{w} + U_{\infty} \neq 0

is the composite velocity and

U_{\infty}

is the constant free stream velocity.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

2019

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show abstract

“…Numerous research articles have been reported in recent years discussing the flow profiles as well as the entropy generation in the prescribed models. For example, Afridi and Qasim [34] proposed a model comprising of nanofluid with the addition of thermal radiation and viscous dissipation by a moving needle discussing the entropy generation. Lopez et al [35] reported a radiative flow past a vertical porous micro-channel.…”

Section: Introductionmentioning

confidence: 99%

Entropy Generation and Consequences of Binary Chemical Reaction on MHD Darcy–Forchheimer Williamson Nanofluid Flow Over Non-Linearly Stretching Surface

Rasool

Zhang

Chamkha

et al. 2019

Entropy

212

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The current article aims to present a numerical analysis of MHD Williamson nanofluid flow maintained to flow through porous medium bounded by a non-linearly stretching flat surface. The second law of thermodynamics was applied to analyze the fluid flow, heat and mass transport as well as the aspects of entropy generation using Buongiorno model. Thermophoresis and Brownian diffusion is considered which appears due to the concentration and random motion of nanoparticles in base fluid, respectively. Uniform magnetic effect is induced but the assumption of tiny magnetic Reynolds number results in zero magnetic induction. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations. The numerical method is used for solving the so-formulated highly nonlinear problem. The graphical presentation of results highlights that the heat flux receives enhancement for augmented Brownian diffusion. The Bejan number is found to be increasing with a larger Weissenberg number. The tabulated results for skin-friction, Nusselt number and Sherwood number are given. A decent agreement is noted in the results when compared with previously published literature on Williamson nanofluids.

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Designing artificial neural network of nanoparticle diameter and solid–fluid interfacial layer on single‐walled carbon nanotubes/ethylene glycol nanofluid flow on thin slendering needles

Shafiq

Çolak

Sindhu

2021

Numerical Methods in Fluids

115

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In this study, an artificial neural network (ANN) has been developed to predict the boundary layer flow of a single‐walled carbon nanotubes nanofluid toward three different nonlinear thin isothermal needles of paraboloid, cone, and cylinder shapes with convective boundary conditions. Different effects of particle diameter and solid–fluid interface coating have been taken into account in the thermal conductivity model of nanofluid in which ethylene glycol has been used as the base fluid. Single and dual phase approach is used to establish the management model under the phenomenon of zero heat and mass flux. A dataset has been developed for different scenarios of the fluid model by changing the relevant parameters with the Runge–Kutta based shooting technique. Two different ANN models have been developed to predict Nusselt number and skin friction coefficient (SFC) values. The values obtained from ANN models have been compared with the numerical data, which are the target values. In addition, mean square error and R values have also been examined in order to analyze the prediction performance of ANN models more comprehensively. The calculated R values for Nusselt number and SFC were obtained as 0.9999. The results obtained showed that ANN can predict Nusselt number and SFC values with high accuracy.

show abstract

Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation

Cited by 110 publications

References 37 publications

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

Entropy Generation and Consequences of Binary Chemical Reaction on MHD Darcy–Forchheimer Williamson Nanofluid Flow Over Non-Linearly Stretching Surface

Designing artificial neural network of nanoparticle diameter and solid–fluid interfacial layer on single‐walled carbon nanotubes/ethylene glycol nanofluid flow on thin slendering needles

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