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Boundary-layer flow about a vertical spinning cone under mixed thermal boundary conditions and a magnetic field

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Abstract

A similarity analysis was performed to investigate the laminar boundary-layer flow in the presence of a transverse magnetic field over a down-pointing and spinning cone with mixed thermal boundary conditions. Boundary layer velocity and temperature profiles were determined numerically for various values of the magnetic and spin parameters and the Prandtl number. The spin of the cone compresses the velocity profiles towards the surface by inducing an upward flow and decreases the surface temperature. The magnetic field suppresses the velocity profiles and increases the surface temperature. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.

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Abbreviations

B :

Magnetic field strength

F :

Boundary layer stream function

G :

Boundary layer rotational velocity

g :

Gravitational acceleration

Gr :

Grashof number

H :

Boundary layer temperature

L :

Characteristic length

M :

Magnetic parameter

m :

Transformation scale for the magnetic parameter

Pr :

Prandtl number

r :

Local radius of the cone

Re :

Reynolds number

T :

Temperature

U :

Reference velocity

u :

Velocity component in the x direction

v :

Velocity component in the y direction

w :

Velocity component in the θ direction

x :

Coordinate measured along the surface

y :

Coordinate normal to the surface

α :

Thermal diffusivity of the fluid

β :

Coefficient of thermal expansion of the fluid

Γ :

Transformation scale for the temperature

Δ :

Transformation scale for the stream function

δ :

Transformation scale for the normal coordinate

ε :

Mixed thermal boundary condition

η :

Boundary layer normal variable

Θ :

Dimensionless temperature ratio

Λ :

Magnetic field function

κ :

Transformation scale for the spin parameter

λ :

Spin parameter

ν :

Kinematic viscosity of the fluid

Ω :

Angular speed of the cone

ρ :

Density of the fluid

φ :

Vertex half angle

θ :

Angular coordinate

σ :

Electrical conductivity of the fluid

ψ :

Dimensionless stream function

*:

Dimensional variable

r :

Reference value

o :

Ambient value

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Authors and Affiliations

  1. Department of Mechanical Engineering, Trakya University, 22030, Edirne, Turkey

    Mehmet Cem Ece & Ayşegül Öztürk

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  1. Mehmet Cem Ece
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  2. Ayşegül Öztürk
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Correspondence to Mehmet Cem Ece.

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Ece, M.C., Öztürk, A. Boundary-layer flow about a vertical spinning cone under mixed thermal boundary conditions and a magnetic field. Meccanica 44, 177–187 (2009). https://doi.org/10.1007/s11012-008-9159-x

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  • DOI: https://doi.org/10.1007/s11012-008-9159-x

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