%0 Journal Article
%T An Exact Analytical Solution for Convective Heat Transfer in Elliptical Pipes
%J AUT Journal of Mechanical Engineering
%I Amirkabir University of Technology
%Z 2588-2937
%A Shahmardan, M. M.
%A Norouzi, M.
%A Sedaghat, M. H.
%D 2017
%\ 12/01/2017
%V 1
%N 2
%P 131-138
%! An Exact Analytical Solution for Convective Heat Transfer in Elliptical Pipes
%K Convective Heat Transfer
%K Exact Solution
%K Elliptical Pipe
%K Aspect Ratio
%R 10.22060/mej.2017.12310.5311
%X In this paper, an analytical solution for convective heat transfer in straight pipes withthe elliptical cross section is presented. The solution is obtained for steady-state fluid flow and heattransfer under the constant heat flux at walls using the finite series expansion method. Here, the exactsolution of Nusselt number as well as temperature distribution in terms of aspect ratio is presented as thecorrelation in the Cartesian coordinate system and validated with the previous investigations. It is shownthat the minimum amount of Nusselt number, as well as the maximum absolute value of dimensionlesstemperature at the center of the cross section, are related to the aspect ratio equal to 1 (circular pipe). Thesolution indicated that the amount of Nusselt number is increased by changing the geometry of crosssection from circular to an elliptical shape and it finally tends to 4356/833 at large enough aspect ratios.Our results also show that 95% of the increase in Nusselt number to the circular cylinder is related toaspect ratio equal to 18.36. The present method of solution could be used to obtain the exact solution ofconvective heat transfer in elliptical pipes for other thermal boundary conditions and fluid rheologicalbehaviors.
%U https://ajme.aut.ac.ir/article_2752_c6b926525682a13dc365340f595ce402.pdf