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25 Jan 2007: 0.01 (for Ra, = lo@), convection continues in the melt until t = 0.24, by which time the system is about 40% solidified.

10 Mar 2009: Conservation of volume. v = 0. (2.24)2. Momentum balance. ρDv. Dt= p (ρ ρb)g ẑ μ2v, (2.25). ... After some algebra and use of(2.24), we obtain. ρD. Dt. [1.

9 Mar 2004: Received 24 April 2000 and in revised form 7 December 2000).

9 Feb 2004: 5H1 2(H0U1)′=0, (24)3U1 H ′1 H ′0ϕ1. 1. 2H0ϕ. ′1=0, (25)ϕ1=2720. ... 4y2)], (38). and then subsequent substitution into (24) yields a second-order differential equation forH1(y), namely(1.

9 Mar 2004: e-mail: grae@esc.cam.ac.uk; heh1@esc.cam.ac.uk. (Received 24 July and in revised form 27 March 1997). ... 24/3λRa1/3 (3.1). between the Nusselt number Nu for thermal convection in the liquid region and theRayleigh number.

30 Jul 2013: 24). The perturbation equations are given, at O(βN), by. 1. η.

21 Dec 2012: Carbon budgets have been introduced to capemissions [24] (Figure 1). The power sector is the single largest emitter. ... and are designed to capemissions [24] (green line).

16 Jan 2007: J. Fluid M e c h. (1990). vol. 212, p p. 209-240. Printed in Great Britain 209. The fluid mechanics of solidification. By H E R B E R T E. H U P P E R T Institute of Theoretical Geophysics and Department of Applied Mathematics and Theoretical.

16 Jul 2010: nly. 24 HUPPERT & SPARKS. compositional film is to substitute the film thickness into the compositional Rayleigh number, which can be re-expressed as. ... 24. I. A. -.:---n;o • • Pl AA GIOCl A S E.

23 Dec 2021: 2πϕ r0. 0. h00. s0[h0(r), z]dzr dr =V, (2.24). where s0[h0(r), z] is the initial saturation distribution. ... By applying scaling analysis to (2.14) and (2.24) and rearranging, we find thefollowing relations between the dimensions of radius, height,