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Cattaneo-Christov Heat Flux Model for MHD Three-Dimensional Flow of Maxwell Fluid over a Stretching Sheet.

Rubab K, Mustafa M - PLoS ONE (2016)

Bottom Line: The governing partial differential equations even after employing the boundary layer approximations are non linear.It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted.Penetration depth of temperature is a decreasing function of thermal relaxation time.

View Article: PubMed Central - PubMed

Affiliation: School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan.

ABSTRACT
This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.

No MeSH data available.


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ℏ− curves for the functions f(η), g(η) and θ(η).
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pone.0153481.g002: ℏ− curves for the functions f(η), g(η) and θ(η).

Mentions: Note that the series solutions given in Eqs (28)–(30) contain an auxiliary parameters ℏ which has an important role in controlling the convergence of homotopic solutions. To select an appropriate value of ℏ, we have plotted the so-called ℏ− curves for f′′(0), g′′(0) and θ′(0) in Fig 2. Here the valid range of ℏ lies where the ℏ− curves are parallel to ℏ− axis. From Fig 2, we expect that series solutions for f, g and θ would converge in the range −1.5 ≤ ℏ ≤ −0.4. Table 1 is plotted to see the convergence rate of the solutions. We observe that tenth-order approximations are sufficient for convergent solutions at ℏ = −0.8.


Cattaneo-Christov Heat Flux Model for MHD Three-Dimensional Flow of Maxwell Fluid over a Stretching Sheet.

Rubab K, Mustafa M - PLoS ONE (2016)

ℏ− curves for the functions f(η), g(η) and θ(η).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4836741&req=5

pone.0153481.g002: ℏ− curves for the functions f(η), g(η) and θ(η).
Mentions: Note that the series solutions given in Eqs (28)–(30) contain an auxiliary parameters ℏ which has an important role in controlling the convergence of homotopic solutions. To select an appropriate value of ℏ, we have plotted the so-called ℏ− curves for f′′(0), g′′(0) and θ′(0) in Fig 2. Here the valid range of ℏ lies where the ℏ− curves are parallel to ℏ− axis. From Fig 2, we expect that series solutions for f, g and θ would converge in the range −1.5 ≤ ℏ ≤ −0.4. Table 1 is plotted to see the convergence rate of the solutions. We observe that tenth-order approximations are sufficient for convergent solutions at ℏ = −0.8.

Bottom Line: The governing partial differential equations even after employing the boundary layer approximations are non linear.It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted.Penetration depth of temperature is a decreasing function of thermal relaxation time.

View Article: PubMed Central - PubMed

Affiliation: School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan.

ABSTRACT
This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.

No MeSH data available.


Related in: MedlinePlus