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The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip.

Mondal S, Haroun NA, Sibanda P - PLoS ONE (2015)

Bottom Line: The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity.The magnetic field is imposed normally to the sheet.The model equations that describe this fluid flow are solved by using the spectral relaxation method.

View Article: PubMed Central - PubMed

Affiliation: University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Science, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa.

ABSTRACT
In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.

No MeSH data available.


Related in: MedlinePlus

Initial values F′′(0) and h′(0) versus α and M.
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pone.0138355.g002: Initial values F′′(0) and h′(0) versus α and M.

Mentions: Fig 2 depicts the variation of the skin friction coefficients f′′(0) and h′(0) with α < 0 (shrinking sheet) and α > 0 (stretching sheet) for different values of the magnetic parameter M. Here solid and dashed lines represent the trajectories of f′′(0) and h′(0), respectively. Our numerical results reveal that without a magnet (i.e., M = 0), Eqs (14) and (15) have unique solutions when α ≥ −1 and no similarity solution exists for α < −1. It is observed that the similarity solution exists up to a critical value α = αc(< 0), (say) beyond which a solution based on the boundary layer approximations does not exist as the boundary layer separates from the surface. From a physical point of view, a steady solution is not possible unless additional fluid from the stagnation-point is added to the free stream. A steady solution is possible only when ratio of the free stream velocity and shrinking velocity is less than a certain numerical value which again depends on the magnetic field parameter (M). The results show that when M increases, the range of α where similarity solutions exist gradually increases. When α = 1, we find that f′′(0) = 0 because f(η) = η is the solution of Eq (14) subject to the boundary conditions Eq (16). The results show that when f′′(0) ≥ 0, for a given value of α, f′′(0) increases with M. For a shrinking surface, the h′(0) orbits intersect the α-axis but this is not the case for flow over a stretching sheet. For a given value of M, the size of h′(0) decreases with increases in ∣α∣. Also, for any given α, ∣h′(0)∣ increases with M.


The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip.

Mondal S, Haroun NA, Sibanda P - PLoS ONE (2015)

Initial values F′′(0) and h′(0) versus α and M.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4587369&req=5

pone.0138355.g002: Initial values F′′(0) and h′(0) versus α and M.
Mentions: Fig 2 depicts the variation of the skin friction coefficients f′′(0) and h′(0) with α < 0 (shrinking sheet) and α > 0 (stretching sheet) for different values of the magnetic parameter M. Here solid and dashed lines represent the trajectories of f′′(0) and h′(0), respectively. Our numerical results reveal that without a magnet (i.e., M = 0), Eqs (14) and (15) have unique solutions when α ≥ −1 and no similarity solution exists for α < −1. It is observed that the similarity solution exists up to a critical value α = αc(< 0), (say) beyond which a solution based on the boundary layer approximations does not exist as the boundary layer separates from the surface. From a physical point of view, a steady solution is not possible unless additional fluid from the stagnation-point is added to the free stream. A steady solution is possible only when ratio of the free stream velocity and shrinking velocity is less than a certain numerical value which again depends on the magnetic field parameter (M). The results show that when M increases, the range of α where similarity solutions exist gradually increases. When α = 1, we find that f′′(0) = 0 because f(η) = η is the solution of Eq (14) subject to the boundary conditions Eq (16). The results show that when f′′(0) ≥ 0, for a given value of α, f′′(0) increases with M. For a shrinking surface, the h′(0) orbits intersect the α-axis but this is not the case for flow over a stretching sheet. For a given value of M, the size of h′(0) decreases with increases in ∣α∣. Also, for any given α, ∣h′(0)∣ increases with M.

Bottom Line: The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity.The magnetic field is imposed normally to the sheet.The model equations that describe this fluid flow are solved by using the spectral relaxation method.

View Article: PubMed Central - PubMed

Affiliation: University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Science, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa.

ABSTRACT
In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.

No MeSH data available.


Related in: MedlinePlus