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.
Some peculiarities of the asymmetric Graetz problem
A numerical simulation and an analysis of the steady state forced convection heat transfer with plane laminar flow confined by two parallel plates that are kept at constant but different temperatures are presented. We name this heat transfer configuration shortly the asymmetric Graetz problem. The essential features of the asymmetric in comparison to the symmetric Graetz problem are the reversal of the heat flux and the jump of the Nusselt number from positive to negative region at the plate having the temperature closer to the fluid inlet temperature. These phenomena occur at different axial positions, which depend on the thermal asymmetry and the fluid inlet conditions. The numerical results agree excellently with an analytical solution obtained in terms of Kummer confluent hypergeometric function and Hermite polynomials.
Magnetic plasma confinement for laser ion source.
A laser ion source (LIS) can easily provide a high current beam. However, it has been difficult to obtain a longer beam pulse while keeping a high current. On occasion, longer beam pulses are required by certain applications. For example, more than 10 micros of beam pulse is required for injecting highly charged beams to a large sized synchrotron. To extend beam pulse width, a solenoid field was applied at the drift space of the LIS at Brookhaven National Laboratory. The solenoid field suppressed the diverging angle of the expanding plasma and the beam pulse was widened. Also, it was observed that the plasma state was conserved after passing through a few hundred gauss of the 480 mm length solenoid field.