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Heat and Mass Transfer

, Volume 39, Issue 4, pp 297–304 | Cite as

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

  • H. S. TakharEmail author
  • A. J. Chamkha
  • G. Nath
Original

Abstract.

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.

Keywords.

Unsteady mixed convection Magnetic effects 

Nomenclature

Roman letters

Cfx

skin friction coefficient in the x-direction

Cfy

skin friction coefficient in the y-direction

Cp

specific heat at constant pressure, kJ·kg–1·K

Ec

Eckert number

E

electric field

f

dimensionless stream function

G, H

similarity velocity functions, m·s–1

Gr

Grashof number

H, h

total enthalpy and static enthalpy, respectively

Ha

Hartman number

k

thermal conductivity, W·m–1·K

M

magnetic parameter

Ma

Mach number

L

characteristic length, m

Nu

Nusselt number

Pr

Prandtl number

Re

Reynolds number

St

Stanton number

t

dimensional time

t*

dimensionless time

T

temperature, K

u, v, w

velocity components, m·s–1

V

characteristic velocity, m·s–1

x, y, z

curvilinear coordinates system

Greek letters

Cfx

skin friction coefficient in the x-direction

α

semi-angle of the cone

β

pressure gradient parameter

γ

ratio of specific heats

η, ξ

transformed co-ordinates

μ

dynamic viscosity, kg·m–1·s–1

ν

konematic viscosity, m2·s–1

ρ

density, kg·m–3

ψ

dimensional stream function, m2·s–1

Ω

angular velocity of the cone

Ω0

angular velocity of the cone at t=0

ϕ(t)

a continuous function of time

Subscripts

i

initial conditions at the wall

w

condition at the wall

condition in the free stream

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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Engineering, Manchester Metropolitan University, Manchester, M1 5GD, U.K
  2. 2.Department of Mechanical Engineering, Kuwait University, P.O. Box. 5969, Safat 13060, Kuwait
  3. 3.Department of Mathematics, Indian Institute of Science, Bangalore, India

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