Showing papers on "Magnetic Prandtl number published in 1981"
TL;DR: In this paper, an approximate solution of two-dimensional convection in the limit of low Prandtl number is presented in which the buoyancy force is balanced by the inertial terms.
Abstract: An approximate solution of two-dimensional convection in the limit of low Prandtl number is presented in which the buoyancy force is balanced by the inertial terms. The results indicate that inertial convection becomes possible when the Rayleigh number exceeds a critical value of about 7 × 103. Beyond this value the velocity and temperature fields become independent of the Prandtl number except in thin boundary layers. The convective heat transport approaches the law Nu = 0·175 R¼ for the Nusselt number Nu. These results are in reasonably close agreement with the numerical results described in the preceding paper by Clever & Busse (1980).
54 citations
TL;DR: In this article, natural convection in a rectangular cavity is considered for the problem where one vertical wall is heated and the other is cooled using a modified Oseen technique in a manner similar to Gill's solution.
28 citations
TL;DR: In this article, the low Prandtl number flow of a conducting fluid about a semi-infinite vertical plate in the presence of a strong cross magnetic field was investigated numerically.
Abstract: The low Prandtl number flow of a conducting fluid about a semi-infinite vertical plate in the presence of a strong cross magnetic field is investigated numerically. The range of Prandtl numbers examined extends down to values appropriate to liquid-metal reactor coolants. A numerical scheme is employed that takes advantage of the established limiting similarity states at the leading edge and downstream.
18 citations
TL;DR: In this article, the effect of the vertical magnetic field of uniform strength on the stability of natural convection in a thin horizontal fluid layer subject to horizontal as well as vertical temperature gradient has been studied on the basis of linear theory.
Abstract: The effect of the vertical magnetic field of uniform strength on the stability of natural convection in a thin horizontal fluid layer subject to horizontal as well as vertical temperature gradient has been studied on the basis of linear theory. The boundaries are taken to be rigid, perfectly thermally and electrically conducting having prescribed temperatures and the horizontal temperature gradient is assumed to be small. The analysis is restricted to the case when Prandtl number is greater than magnetic Prandtl number which is met by a large margin under most terristrial conditions. It has been found that the preferred mode of disturbance is stationary and will be a transverse roll or a longitudinal roll depending on three parameters namely Prandtl number, Chandrasekhar number and the ratio of Prandtl number to magnetic Prandtl number. The critical Rayleigh numbers for various values of the above three parameters have been reported.
5 citations
TL;DR: In this article, a nonlinear hydromagnetic connection is investigated using the modal equations for cellular convection, and the boundary layer method is used assuming large Rayleigh number R, moderate Prandtl number σ and for different ranges of the Chandrasekhar number Q.
Abstract: Nonlinear hydromagnetic connection is investigated using the modal equations for cellular convection. The boundary layer method is used assuming large Rayleigh number R , moderate Prandtl number σ and for different ranges of the Chandrasekhar number Q . The heat flux F is determined for the value of the horizontal wave number which maximizes F . For a weak field, the inertial force dominates over the Lorentz force. F is independent of Q , but it increases with R and σ. For a moderate field, the Lorentz force is significant. F increases with R and σ and decreases as Q increases. For a strong field, the Lorentz force dominates over the inertial force. F is independent of σ, but it increases with R and decreases as Q increases.
1 citations
TL;DR: In this paper, it was shown that stars of the highly centrally condensed type are likely to excite only the fundamental mode of pulsation and that the radial velocity and light curves will not be complicated by the superposition of higher modes.
Abstract: displacement of the overtones increases monatomically with mode number. Furthermore, the maximum relative displacement of the higher modes remains constant with increasing radius for n = 5 and these maxima decrease with increasing mode number. The results certainly suggest that stars of the highly centrally condensed type are likely to excite only the fundamental mode of pulsation and that the radial velocity and light curves will not be complicated by the superposition of higher modes. The non-linear analysis would probably confirm that the higher modes contribute very little to the overall amplitude of displacement and that a non-skewed radial velocity curve with a sinusoidal profile could be expected.
TL;DR: In this article, the authors investigated the effect of arbitrary Prandtl number convection in a layer with nearly insulating boundaries and showed that the heat transported by the stable rolls reaches its peak at a critical P = B1/3/5.77 beyond which the heat flux decreases with increasing P. The stable square pattern convection represents the preferred stable convection.
Abstract: Arbitrary Prandtl number convection in a layer with nearly insulating boundaries is investigated. For B1/3 > 3.95P (P is the Prandtl number and B being the ratio between the thermal conductivities of the boundary and of the fluid) two-dimensional rolls are stable. The heat transported by the stable rolls reaches its peak at a critical P = B1/3/5.77 beyond which the heat flux decreases with increasing P. For B1/3 = 3.95P rolls become unstable to disturbances in the form of rolls oriented at a right angle to the original rolls. For B1/3 > 3.95P square pattern convection represents the preferred stable convection. The stable square pattern transports the maximum amount of heat at a critical P = B1/3/3.7.