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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.

8 May 2007: 2(m2 1). 2u. XY= Mm2h2. (2.24). We posit a solution in the form. ... 4.1) for openchannel flow is replaced by 24/105 = 0.229 for a circular constraining geometry andK/m = 0.137m2/(1 m2) for a V-shaped constrainer.

13 Nov 2007: Method. Glass beads 24 Rotating drume. 0.25–0.35 24 Smooth inclined planef. ... 0.5 0.04 24–31 Rough inclined planeg. 1.26 9–11 Shear gauge, smooth chute flowh.

25 Jan 2007: E. Huppert. Parameter Value Units. a (5.0+ 0.24( T- 20)) x U 0.015 cm2 s-' CC 4.14 J O C - '. 2.66 J cm-3 O C - '

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.

16 Jan 2007: expressed as wt.%, as a function of the amount of K2CO 3 or NaNO 3 present in solution at 24.2C. ... Lower and upper layer properties were: initial temperatures 46 and 15C; initial concentrations 37 and 24%; initial densities 1.26 and 1.23 g cm 3; and

25 Jan 2007: J. Fluid Mech. (1989), voZ. 198, p p. 293-319. Printed in Great Britain. 293. Phase changes following the initiation of a hot turbulent flow over a cold solid surface. By HERBERT E. HUPPERT Department of Applied Mathematics and Theoretical Physics,

25 Jan 2007: Substituting (18), (19) and (24) into (21), we obtain the following implicit relationship between T and Tl :. ( 2 5 ). Substituting (20) and (21) into ( 2 2 ) , and using (23a, c ) in ... a = pcDH;' (To--T). (24). Tl = Tmp2c2k' D J H i l ( T o - T ) (T-T,

22 Jan 2007: Inserting equations (2.23) and (2.24) into equations (2.12)–(2.16) andlinearizing in the perturbed quantities leads to the following nonlinear ordinarydifferential equation for the disturbance amplitude:.