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 approximate treatment of forced heat convection in laminar flow between parallel plates
Approximate formulae are derived for the thermal properties occurring in forced heat convection by fully established Poiseuille flow between parallel flat plates. The results are intended to supplement the work of Prins, vander Does de Byeet. al
 1)2), and comparison is made with their available detailed calculations. Fair agreement is obtained, with due regard to physical requirements.
Laminar flow in regular polygonal shaped ducts with circular centered cores
The method of least-squares fitting of harmonic functions to known boundary conditions has been employed to obtain closed-form solutions for laminar flow of an incompressible fluid through the constant area annulus between a regular polygonal duct and a centered circular core. The product of Fanning friction factor and Reynolds number has been determined for the entire range between the extreme case of no core and the other extreme case where the core touches the outerwalls. For the latter case, it is shown that when the number of sides of the polygon approaches infinity, f.Re approaches a minimum value of 6.22. The analysis of this case is further extended to corner angles less than 60°, the minimum imposed by an equilateral triangular duct. 
 
 
 
On a adapte la methode des moindres carres de fonctions harmoniques a des conditions-limites connues pour obtenir des solutions de genre ferme dans le cas de l'ecoulement laminaire d'un fluide incompressible par un anneau a surface constante, entre un conduit en forme de polygone regulier et un noyau circulaire et centre. On a determine le produit facteur de friction de Fanning et du nombre de Reynolds sur une echelle complete comprise entre deux extrěmes, a savoir l'absence de noyau et le contact du noyau avec les parois exterieures; on a demontre dans ce dernier cas que, lorsque le nombre des cǒtes du polygone approche l'infini, f. Re approche une valeur minimum de 6.22. On a etendu l'analyse de ce cas a des angles de coin inferieurs a 60°, qui est le minimum requis pour un conduit en forme de triangle equilateral.