The Graetz-Nusselt problem for the curved channel using spectral collocation method

This paper investigates the Graetz-Nusselt problem for a curved channel. The solution of the energy equation for constant wall temperature boundary condition is developed via the separation of variable technique. The associated eigenvalue problem is handled numerically with the help of the spectral collocation method, and the Simpson's 1/3 rule is employed to compute the coefficient of the solution series. The impact of curvature on temperature profile, mean temperature, and Nusselt numbers at both upper and lower walls of the curved channel is presented through tables and graphs and discussed in detail. The analysis reveals an attenuation in the net heat transfer rate through the channel with raising the curvature parameter. The local Nusselt number at the upper wall of the curved channel decreases while at the lower wall it follows an increasing trend with enhancing the channel curvature. In addition, the net heat transfer rate through the curved channel is significantly higher than its counterpart for a straight channel. It is believed that the availability of such a solution will be an important contribution in the field of biomedical sciences, engineering sciences and development of many industrial types of equipment.

Automated summary

This study investigates the Graetz-Nusselt problem in a curved channel, developing a solution using variable separation technique and numerical methods. The analysis reveals that curvature affects temperature profiles, mean temperature, and Nusselt numbers, with an attenuation in net heat transfer rate as curvature parameter increases. Additionally, the net heat transfer rate through the curved channel is significantly higher than for a straight channel, making this solution potentially valuable for biomedical, engineering, and industrial applications.