ALBERT

Description: The problem of the stability of a fluid with time-dependent heating has been investigated by Morton (1957), Lick (1965) and Foster (1965). Morton and Lick assumed that the rate of change of the temperature profile is small compared with the growth rate of the disturbances (quasi-static assumption). This assumption is invalid near the onset of instability (as defined by ∂/∂t = 0), and Foster has therefore used an initial-value approach.In this paper the range of validity of the quasi-static assumption is discussed, and results of a time-scaled analysis and calculations based on this are compared with the work of Foster; the agreement is found to be good. We restrict our attention to a semi-infinite fluid initially at a constant temperature; at time t = 0 a temperature difference ΔT is applied at the (lower) horizontal boundary (case (A) of Foster).

Description: In this paper we consider two-dimensional steady cellular motion in a fluid heated from below at large Rayleigh number and Prandtl number of order unity. This is a boundary-layer problem and has been considered by Weinbaum (1964) for the case of rigid boundaries and circular cross-section. Here we consider cells of rectangular cross-section with three sets of velocity boundary conditions: all boundaries free, rigid horizontal boundaries and free vertical boundaries (referred to here as periodic rigid boundary conditions), and all boundaries rigid; the vertical boundaries of the cells are insulated. It is shown that the geometry of the cell cross-section is important, such steady motion being not possible in the case of free boundaries and circular cross-section; also that the dependence of the variables of the problem on the Rayleigh number is determined by the balances in the vertical boundary layers.We assume only those boundary layers necessary to satisfy the boundary conditions and obtain a Nusselt number dependence $N sim R^{frac{1}{3}}$ for free vertical boundaries. For the periodic rigid case, Pillow (1952) has assumed that the buoyancy torque is balanced by the shear stress on the horizontal boundaries; this is equivalent to assuming velocity boundary layers beside the vertical boundaries (rather than the vorticity boundary layers demanded by the boundary conditions) and leads to a Nusselt number dependence N ∼ R¼. If it is assumed that the flow will adjust itself to give the maximum heat flux possible the two models are found to be appropriate for different ranges of the Rayleigh number and there is good agreement with experiment.An error in the application of Rayleigh's method in this paper is noted and the correct method for carrying the boundary-layer solutions round the corners is given. Estimates of the Nusselt numbers for the various boundary conditions are obtained, and these are compared with the computed results of Fromm (1965). The relevance of the present work to the theory of turbulent convection is discussed and it is suggested that neglect of the momentum convection term, as in the mean field equations, leads to a decrease in the heat flux at very high Rayleigh numbers. A physical argument is given to derive Gill's model for convection in a vertical slot from the Batchelor model, which is appropriate in the present work.

Description: SUMMARYEwo milk yield data obtained by the lamb suckling technique from nutritional experiments were analysed statistically to obtain estimates of the several components of variation. Diurnal variation was studied. The fitting of a sinusoidal curve removed a significant amount of variation.There was a highly significant correlation between successive milk yields obtained at 4 h intervals. Number of lambs suckled and body weight of ewe at parturition had a significant effect on total daily milk yield.The variation within ewes after the removal of diurnal variation and between ewes after the removal of the effects of number of lambs suckled and body weight at parturition were computed. These sources of variation were combined in a general equation which enabled the prediction of the standard errors associated with daily milk production for a given sampling technique. The practical application of the predicted standard errors is discussed.

Description: SUMMARYMilk yield data obtained by the lamb-suckling technique on twenty-four ewes over a period of 5 consecutive days in the second and third week of their lactation have been related to lamb body weights and lamb body-weight changes over the same period. The regression equation obtained wasThe equation was used to estimate the milk consumption of lambs over the range of lamb body weights and lamb body-weight changes studied. The standard errors of these estimates have been computed for comparison with those obtained directly from the lamb suckling technique.The role of the prediction equation in estimating daily milk consumption of lambs is discussed.