An Exact Analytical Solution for Convective Heat Transfer in Elliptical Pipes

In this paper, an analytical solution for convective heat transfer in straight pipes with the elliptical cross section is presented. The solution is obtained for steady-state fluid flow and heat transfer under the constant heat flux at walls using the finite series expansion method. Here, the exact solution of Nusselt number as well as temperature distribution in terms of aspect ratio is presented as the correlation in the Cartesian coordinate system and validated with the previous investigations. It is shown that the minimum amount of Nusselt number, as well as the maximum absolute value of dimensionless temperature at the center of the cross section, are related to the aspect ratio equal to 1 (circular pipe). The solution indicated that the amount of Nusselt number is increased by changing the geometry of cross section 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 to aspect ratio equal to 18.36. The present method of solution could be used to obtain the exact solution of convective heat transfer in elliptical pipes for other thermal boundary conditions and fluid rheological behaviors.