Unsteady conductive heat transfer on the cylindrical surface of a plume conduit
A.G. Kirdyashkin, A.A. Kirdyashkin
Sobolev Institute of Geology and Mineralogy SB RAS, Novosibirsk, Russia
Keywords: unsteady conductive heat transfer, mantle plumes, plume conduit, specific heat flux, thermal power
Abstract
Studies of nonstationary conductive heat transfer on a cylindrical surface are presented in the approximation when the thickness of the thermal boundary layer is less than the surface diameter. The temperature profiles at the cylindrical surface and the specific heat flux on this surface are obtained. Using the experimentally established law for the stationary mode of thermal conduction of a cylindrical surface (Nu = 0.5), the value of the Fourier number at which the stationary mode occurs (Fo = 1.27) is determined. For mantle plumes having conduit diameters d = (7.4 ¸ 85)×103 m, the time of plume ascent to the surface t a and the time of establishment of the stationary conductive heat transfer t s are estimated depending on the dimensionless value Ka = N / NH , where N is the thermal power at the base of the plume, and NH is the thermal power transferred from the plume conduit to the surrounding mantle in stationary mode. For Ka = 0.97 ¸ 1.58 ( t a / t s = ¥ ¸ 1) and Ka = 1.58 ¸ 129 ( t a / t s = 1 ¸ 0.005), the effect of unsteady heat transfer to the sur-rounding mantle on the plume ascent to the surface is shown and it is established that for Ka > 4 ( t a / t s < 0.19, d > 15 km), the effect of unsteadiness during the plume rise may be neglected.
|
