The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer

Asfour, Hanaa A.

doi:10.1002/htj.21660

Heat Trans

2020

DOI: 10.1002/htj.21660

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The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer

Hanaa A. Asfour

Abstract: This investigation aims to study Hall's current effect on the peristaltic flow of a Jeffrey nanofluid with variable thermal conductivity in an inclined asymmetric channel. Joule heating and oblique magnetic field effects are taken into consideration. A system of ordinary differential equations is obtained under the approximation of low Reynolds number and long wavelength, which consists of momentum, energy, and concentration equations. The influences of penitent physical parameters on the distribution of veloc… Show more

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Cited by 5 publications

(16 citation statements)

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“…">The expression

v = - \frac{\partial ψ}{\partial y}

in eq. 15 on page 5, as given by Abdel‐Hameed Asfour, 1 is wrong. The correction is

v = - \frac{\partial ψ}{\partial x}

. …”

mentioning

confidence: 98%

“…16 and 20 are as follows, respectively;

0 = \frac{\partial p}{\partial x} + \frac{1}{1 + λ_{1}} (\frac{\partial^{3} ψ}{\partial y^{3}}) - \frac{M^{2}}{1 + m^{2}} \cos^{2} (γ) {true(\frac{\partial ψ}{\partial y} + 1 true)}^{2} + G_{r} θ + B_{r} φ + \frac{R_{e}}{F_{r}} normalsin (β),

0 = \frac{1}{1 + λ_{1}} (\frac{\partial^{4} ψ}{\partial y^{4}}) - \frac{M^{2}}{1 + m^{2}} \cos^{2} (γ) \frac{\partial}{\partial y} {true(\frac{\partial ψ}{\partial y} + 1 true)}^{2} + G_{r} \frac{\partial θ}{\partial y} + B_{r} \frac{\partial φ}{\partial y} .

Note that Equation (2) is obtained by using eq. 17 on page 5, as given by Abdel‐Hameed Asfour 1 to eliminate the pressure from Equation (1). The corrected form of Equations (1) and (2) are as follows 2 :

0 = - \frac{\partial p}{\partial x} + \frac{1}{1 + λ_{1}} (\frac{\partial^{3} ψ}{\partial y^{3}}) - \frac{M^{2}}{1 + m^{2}} \cos^{2} (γ) (\frac{\partial ψ}{\partial y} + 1) + G_{r} (normalsin (β)) θ + B_{r}

…”

mentioning

confidence: 99%

“…">The condition presented in eq. 3 as given by Abdel‐Hameed Asfour 1 is wrong as it can not guarantee the channel nonclogging due to possible clashing between the channel walls. The correct condition is that

a_{1}, b_{1}, d_{1}, d_{2}, normala normaln normald ϕ

satisfies 3

a_{1}^{2} + b_{1}^{2} + 2 a_{1} b_{1} \cos ϕ \leq {(d_{1} + d_{2})}^{2} .

Now, from fig.…”

mentioning

confidence: 99%

“…The correct condition is that

a_{1}, b_{1}, d_{1}, d_{2}, normala normaln normald ϕ

satisfies 3

a_{1}^{2} + b_{1}^{2} + 2 a_{1} b_{1} \cos ϕ \leq {(d_{1} + d_{2})}^{2} .

Now, from fig. 1 as given by Abdel‐Hameed Asfour 1 since

a_{1} \leq d_{1}

and

b_{1} \leq d_{2}

implies that

a_{1}^{2} + b_{1}^{2} \leq d_{1}^{2} + d_{2}^{2},

and to contain the phase angle in a relation that guarantees no collision will occur between the channel walls, we can write

{2 a}_{1} a_{2} normalcos ϕ \leq 2 d_{1} d_{2},

hence by adding, we get,

a_{1}^{2} + b_{1}^{2} + {2 a}_{1} b_{1} normalcos ϕ \leq d_{1}^{2} + d_{2}^{2} + 2 d_{1} d_{2} .

So the correct condition for the channel walls can be written as in Equation (5). Eq.…”

mentioning

confidence: 99%

“…Eq. 10 on page 4 as given by Abdel‐Hameed Asfour 1 is given by

k (θ) = k_{0} (1 + α θ)

. This expression has a typo, and the corrected form is

k (T) = k_{0} (1 + α θ)

and thus

\frac{k (T)}{k_{0}} = k (θ) = (1 + α θ),

where

T

is the dimensional temperature, and

θ

is the nondimensional temperature (see Mekheimer and Abdelmaboud 4 ).…”

mentioning

confidence: 99%

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Comments on the paper “The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer” by Hanaa Abdel‐Hameed Asfour

Elogail

2020

Heat Trans

View full text Add to dashboard Cite

“…">The expression

v = - \frac{\partial ψ}{\partial y}

in eq. 15 on page 5, as given by Abdel‐Hameed Asfour, 1 is wrong. The correction is

v = - \frac{\partial ψ}{\partial x}

. …”

mentioning

confidence: 98%

“…16 and 20 are as follows, respectively;

0 = \frac{\partial p}{\partial x} + \frac{1}{1 + λ_{1}} (\frac{\partial^{3} ψ}{\partial y^{3}}) - \frac{M^{2}}{1 + m^{2}} \cos^{2} (γ) {true(\frac{\partial ψ}{\partial y} + 1 true)}^{2} + G_{r} θ + B_{r} φ + \frac{R_{e}}{F_{r}} normalsin (β),

0 = \frac{1}{1 + λ_{1}} (\frac{\partial^{4} ψ}{\partial y^{4}}) - \frac{M^{2}}{1 + m^{2}} \cos^{2} (γ) \frac{\partial}{\partial y} {true(\frac{\partial ψ}{\partial y} + 1 true)}^{2} + G_{r} \frac{\partial θ}{\partial y} + B_{r} \frac{\partial φ}{\partial y} .

0 = - \frac{\partial p}{\partial x} + \frac{1}{1 + λ_{1}} (\frac{\partial^{3} ψ}{\partial y^{3}}) - \frac{M^{2}}{1 + m^{2}} \cos^{2} (γ) (\frac{\partial ψ}{\partial y} + 1) + G_{r} (normalsin (β)) θ + B_{r}

…”

mentioning

confidence: 99%

a_{1}, b_{1}, d_{1}, d_{2}, normala normaln normald ϕ

satisfies 3

a_{1}^{2} + b_{1}^{2} + 2 a_{1} b_{1} \cos ϕ \leq {(d_{1} + d_{2})}^{2} .

Now, from fig.…”

mentioning

confidence: 99%

“…The correct condition is that

a_{1}, b_{1}, d_{1}, d_{2}, normala normaln normald ϕ

satisfies 3

a_{1}^{2} + b_{1}^{2} + 2 a_{1} b_{1} \cos ϕ \leq {(d_{1} + d_{2})}^{2} .

Now, from fig. 1 as given by Abdel‐Hameed Asfour 1 since

a_{1} \leq d_{1}

and

b_{1} \leq d_{2}

implies that

a_{1}^{2} + b_{1}^{2} \leq d_{1}^{2} + d_{2}^{2},

and to contain the phase angle in a relation that guarantees no collision will occur between the channel walls, we can write

{2 a}_{1} a_{2} normalcos ϕ \leq 2 d_{1} d_{2},

hence by adding, we get,

a_{1}^{2} + b_{1}^{2} + {2 a}_{1} b_{1} normalcos ϕ \leq d_{1}^{2} + d_{2}^{2} + 2 d_{1} d_{2} .

So the correct condition for the channel walls can be written as in Equation (5). Eq.…”

mentioning

confidence: 99%

“…Eq. 10 on page 4 as given by Abdel‐Hameed Asfour 1 is given by

k (θ) = k_{0} (1 + α θ)

. This expression has a typo, and the corrected form is

k (T) = k_{0} (1 + α θ)

and thus

\frac{k (T)}{k_{0}} = k (θ) = (1 + α θ),

where

T

is the dimensional temperature, and

θ

is the nondimensional temperature (see Mekheimer and Abdelmaboud 4 ).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Comments on the paper “The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer” by Hanaa Abdel‐Hameed Asfour

Elogail

2020

Heat Trans

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Rheological effects on peristaltic transport of Bingham fluid through an elastic tube with variable fluid properties and porous walls

et al. 2020

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The peristaltic pumping of non‐Newtonian material configured by a tube is quite interesting phenomenon to examine the behavior of physiological fluids. The present paper investigates the role of variable viscosity and thermal conductivity on the peristaltic mechanism of Bingham fluid in an elastic tube with porous and convective boundary conditions. The long wavelength and small Reynolds number approximation is used to obtain the analytical solutions for velocity, plug flow velocity, streamlines, flow rate, and temperature. The theoretical determination of flux is calculated using the equilibrium condition, and an application to flow through an artery is highlighted by using the tension relation in an elastic tube. It is observed that the rate of flow within the elastic tube declined with variation of variable viscosity. An enhanced temperature distribution near the tube axis has been observed with increment of variable viscosity. An increasing influence of the porous parameter in the bolus size can also be seen from the streamlines plotted.

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Novel design of intelligent Bayesian networks to study the impact of magnetic field and Joule heating in hybrid nanomaterial flow with applications in medications for blood circulation

Awan,

Awais,

Shamim

et al. 2023

Tribology International

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The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer

Cited by 5 publications

References 36 publications

Comments on the paper “The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer” by Hanaa Abdel‐Hameed Asfour

Comments on the paper “The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer” by Hanaa Abdel‐Hameed Asfour

Rheological effects on peristaltic transport of Bingham fluid through an elastic tube with variable fluid properties and porous walls

Novel design of intelligent Bayesian networks to study the impact of magnetic field and Joule heating in hybrid nanomaterial flow with applications in medications for blood circulation

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