A Comparative Study between Analytical and Numerical Solution of Unsteady State One-Dimensional Heat Transfer for Different Materials

The present investigation includes a comparative study of numerical solution methods with analytical solution for one dimensional transient conduction problems. For this purpose, six different materials were selected and distributed in two groups (metallic and nonmetallic) materials. Group of metallic materials were such as pure copper, pure Aluminum and Iron, whereas a group of nonmetallic materials such as sandstone, concrete and building brick. Four numerical solution methods were selected as (finite difference, thermal capacitance, and finite element) and also Ansys program to compare them with analytical solution. The simulation results showed that the error ratio between numerical solutions and analytical solution would be higher at the transient period in all materials, while this ratio decreased when the case of the materials would reaches steady state, and the results indicated that the materials having high thermal conductivity would give less error ratio in the beginning of simulation than other materials which had low thermal conductivity.