Heat transfer for laminar thermally developing flow in parallel-plates using the asymptotic method
Heat transfer for laminar, thermally developing flow in parallel-plates is investigated using the asymptotic method. There are two asymptotes for local, and mean Nusselt numbers (Nuz and Num) in the parallel-plates thermal entrance problem at both uniform wall temperature (UWT) and uniform heat flux (UHF). The first asymptote corresponds to very small value of dimensionless axial coordinate (z∗). The second asymptote corresponds to very high value of dimensionless axial coordinate (z∗). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model can be determined. Comparisons of the asymptotic model with the analytical and numerical solutions available in the literature are presented.
Non-uniform heat transfer to fluids flowing in conduits
The general theory of the temperature distribution in a fluid flowing in a heated conduit is discussed. Equations are derived for the temperature distribution throughout the fluid stream, and an expression is presented for the Nusselt modulus as a function of downstream position. A definite criterion is proposed for estimation of the thermal entry length. In addition, it is shown that the asymptotic value of the Nusselt modulus depends not only upon the geometry and the hydrodynamics of the system, but also upon the temperature boundary conditions imposed. A simple procedure is given for computation of the heat transfer coefficient when velocity and effective thermometric conductivity distributions are available. Both round pipes and parallel wall conduits are considered.
The crystal structure of stilpnomelane. Part II. The full cell
Summary The structural formula of stilpnomelane averaged from 37 representative literature analyses and based on the determined structure is (Ca,Na,K)4(Ti0·1Al2·3Fe35·5Mn0·8Mg9·3)[Si63Al9](O,OH)216·nH2O. Ferrostilpnomelanes have up to 12 R 3+ cations in the octahedral sheet, ferristilpnomelanes commonly have between 24 and 30 R 3+ cations, rarely up to 37. The two groups can be distinguished by accurate X-ray powder diffraction, ferrostilpnomelanes having d 001 less and a greater than have ferristilpnomelanes. The unit cell is triclinic, a = b∼21·8 Å, γ = 120°, d 001∼12·2 Å, P . Hexagonal groups or ‘islands’ of 24 silicon-oxygen tetrahedra co-ordinate to the octahedral sheet, the centres of the ‘islands’ are displaced by 5a/12, 8b/12 on either side of the octahedral sheet as a result of warping of this sheet to permit articulation with the smaller tetrahedral sheet. The 24-tetrahedra ‘islands’ are linked laterally by 6-member rings of inverted tetrahedra, which in turn link at their apices to like rings connecting the next sheet of ‘islands’. Thus a single tetrahedral layer is 4 tetrahedra thick and has symmetry 6/m. The 6-member rings of tetrahedra act as hinges permitting up to 0·5 Å extension or contraction of the tetrahedral sheet to accommodate variations in the octahedral sheet dimensions with varying R 2+/R 3+ ratio.