Author : Muhammad Nadeem, Afifa Maqsood, Muhammad Moaz Safer, Hira Fatima, Abdul Raheem and Tazeem Fatima

In this study, the Crank-Nicolson scheme (CNS) was employed to calculate the transient temperature distribution within a rectangular shaft. The shaft boundary was discretized into ten equal intervals, each with a grid point. The length of each interval, δx, was 0.01. Eleven grid points were utilized, with the temperatures at the first and eleventh grid points maintained at 0°C throughout the computation. The computational procedure for determining the transient temperature at the grid points was used to develop a MATLAB computer program. The computed results were then compared to the exact solutions. The accuracy of the CNS was evaluated through the use of tables and graphs.

Keywords: Rectangular shaft, Transitory Temperature Distribution, Crank-Nicolson Scheme