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We prove that a finite solvable group G admitting a Frobenius group F H of automorphisms of coprime order with kernel F and complement H so that [G, F ] = G and C C G (F ) (h) = 1 for every 1 = h ∈ H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.

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-Mixed convection of ethylene glycol (EG) and water mixture based Al2O3 nanofluids in a lid-driven square enclosure heated from the left wall and cooled from the top wall was investigated numerically in this study. The Grashof number was kept at a constant value of 10 4 . Reynolds number was assumed to vary in a range so that the Richardson number gets values in the range of 0.1 to 10. Three different nanoparticle volume fractions were considered: 0%, 4% and 8%. Six different volume ratios of EG to water were taken into consideration, 0:100 %, 20:80 %, 40:60%, 60:40%, 80:20% and 100:0%. The results show that an increase in the average Nusselt number is seen with an increase in the volume fraction of nanoparticles and with a decrease in the Richardson number. The results also show that average Nuselt number shows a considerable increase with an increase of EG volume fraction in the base fluid.

No abstract