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.
An iterative method for the solution of eigenvalue problems
where the values of the constants A1 , A2 and B1, B2 are not simultaneously zero. Several methods have been proposed to determine the proper elements (i.e. eigenvalues and eigenfunctions) of Sturm-Liouville equations. Most of them have been reviewed by Kopal [1], but we shall examine one of them, the so called Rayleigh-Ritz method, in order to explain the main defect they have in common and to judge their general efficiency. This method was originally proposed by Ritz [2]. By transformations whose details will not be given here but which are described in many classical texts it leads to the solutions of equations of the form:
Heat Transfer to Longitudinal Laminar Flow Between Cylinders
Consideration is given to the fully developed heattransfer characteristics for longitudinal laminar flow betweem cylinders arranged in an equilateral triangular array. The analysis is carried out for the condition of uniform heat transfer per unit length. Solutions are obtained for the temperature distributiom, and from these, Nusselt numbers are derived for a wide range of spacingto-diameter ratios. it is found that as the spacing ratio increases, so also does the wall-to-bulk temperature difference for a fixed heat transfer per unit length. Corresponding to a uniform surface temperature around the circumference of a cylinder, the circumferential variation of the local heat flux is computed. For spacing ratios of 1.5 to 2.0 amd greater, uniform peripheral wall temperature and uniform peripheral heat flux are simultaneously achieved. A simplified analysis which neglects circumferential variations is also carried out, and the results are compared with those from the more exact formulation. (auth)