Boundary-Layer Disturbances and Surface Heat-Flux Profiles on a Cooled Slender Cone

2022 ◽  
Author(s):  
Laura A. Paquin ◽  
Shaun Skinner ◽  
Stuart J. Laurence
2007 ◽  
Vol 85 (8) ◽  
pp. 869-878 ◽  
Author(s):  
A Ishak ◽  
R Nazar ◽  
I Pop

The laminar boundary-layer flow of a micropolar fluid on a fixed or continuously moving flat plate with uniform surface heat flux is investigated. The plate is assumed to move in the same oropposite direction to the free stream. The resulting system of nonlinear ordinary differential equations is solved numerically using the Keller-box method. Numerical results are obtained for the skin-friction coefficient and the local Nusselt number as well as the velocity, microrotation, and temperature profiles for some values of the governing parameters, namely, the velocity ratio parameter, material parameter, and Prandtl number. The results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.PACS No.: 47.15.Cb


Tectospheric structure can be described in terms of three basic types of surficial boundary layers: chemical (c.b.l.), mechanical (m.b.l.) and thermal (t.b.l.). Beneath old ocean basins the thickness of the c.b.l. ( ca . 40 km) is less than that of either the m.b.l. ( ca . 100 km) or the t.b.l. ( ca . 150 km), but the hypothesis that a similar structure underlies the old continental cratons is difficult to reconcile with seismic observations. We therefore examine an alternate model which postulates a much thicker c.b.l. beneath the cratons whose mantle component consists of a low-density peridotite depleted in its basaltic constituents. On the basis of seismological and petrological data it is inferred that this augmented c.b.l. extends below the m.b.l. to depths exceeding 150 km and acts to stabilize a thick ( > 200 km) t.b.l. against convective disruption. Because of its refractory nature the sub-m.b.l. portion of the c.b.l. constitutes a stable geochemical reservoir which has evidently been impregnated by large-ion lithophile elements fluxing from the deep mantle or from descending slabs. Consequently, its heat production is high ( ca . 0.1 μW/m 3 ) and it contributes significantly to the surface heat flux. The evolutionary history and dynamics of the continental c.b.l. are not well understood, especially the role of double-diffusive instabilities, but the fusion of the continental masses into ‘supercontinents’ and the orogenic compression that this entails are thought to be important processes in c.b.l. formation.


Author(s):  
Md Jashim Uddin

Magnetohydrodynamic (MHD) twodimensional steady convective flow and heat transfer of micropolar fluids flow along an inclined flat plate with variable electric conductivity and uniform surface heat flux has been analyzed numerically in the presence of heat generation. With appropriate transformations the boundary layer partial differential equations are transformed into nonlinear ordinary differential equations. The local similarity solutions of the transformed dimensionless equations for the velocity flow, microrotation and heat transfer characteristics are assessed using Nachtsheim- Swigert shooting iteration technique along with the sixth order Runge-Kutta-Butcher initial value solver. Numerical results are presented graphically in the form of velocity, microrotation, and temperature profiles within the boundary layer for different parameters entering into the analysis. The effects of the pertinent parameters on the local skin-friction coefficient (viscous drag), plate couple stress and the rate of heat transfer (Nusselt number) are also discussed and displayed graphically. Keywords: Convective flow; Micropolar fluid; Heat transfer; Electric conductivity; Inclined plate; Locally self-similar solution DOI: http://dx.doi.org/10.3329/diujst.v6i1.9336 DIUJST 2011; 6(1): 69-79


Sign in / Sign up

Export Citation Format

Share Document