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


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.


Unsteady mixed convection Magnetic effects 


Roman letters


skin friction coefficient in the x-direction


skin friction coefficient in the y-direction


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


Eckert number


electric field


dimensionless stream function

G, H

similarity velocity functions, m·s–1


Grashof number

H, h

total enthalpy and static enthalpy, respectively


Hartman number


thermal conductivity, W·m–1·K


magnetic parameter


Mach number


characteristic length, m


Nusselt number


Prandtl number


Reynolds number


Stanton number


dimensional time


dimensionless time


temperature, K

u, v, w

velocity components, m·s–1


characteristic velocity, m·s–1

x, y, z

curvilinear coordinates system

Greek letters


skin friction coefficient in the x-direction


semi-angle of the cone


pressure gradient parameter


ratio of specific heats

η, ξ

transformed co-ordinates


dynamic viscosity, kg·m–1·s–1


konematic viscosity, m2·s–1


density, kg·m–3


dimensional stream function, m2·s–1


angular velocity of the cone


angular velocity of the cone at t=0


a continuous function of time



initial conditions at the wall


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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