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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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Effect of β on f′(η).
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pone.0153481.g003: Effect of β on f′(η).

Mentions: This section focuses on the physical interpretation of the behaviour of the embedded parameters on the solutions. For this purpose, we display graphical results in Figs 3–12. Table 2 includes the numerical values of wall temperature gradient θ′(0) for different value of β, γ and M. The entries of this table are obtained at suitable choice of ℏ. It is observed that θ′(0) has direct relationship with the thermal relaxation time. However it is a decreasing function of the fluid relaxation time β. The presence of magnetic field also causes diminution in the magnitude of heat transfer rate from the surface.


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

Rubab K, Mustafa M - PLoS ONE (2016)

Effect of β on f′(η).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0153481.g003: Effect of β on f′(η).
Mentions: This section focuses on the physical interpretation of the behaviour of the embedded parameters on the solutions. For this purpose, we display graphical results in Figs 3–12. Table 2 includes the numerical values of wall temperature gradient θ′(0) for different value of β, γ and M. The entries of this table are obtained at suitable choice of ℏ. It is observed that θ′(0) has direct relationship with the thermal relaxation time. However it is a decreasing function of the fluid relaxation time β. The presence of magnetic field also causes diminution in the magnitude of heat transfer rate from the surface.

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