Transient heat conduction in a functionally graded strip in contact with well stirred fluid with an outside heat source

The transient heat conduction model is established for a functionally graded strip which is in contact with well stirred fluid. The fluid receives heat from an outside source. Exact solutions for the temperature distribution for both the functionally graded strip and the fluid are performed by the methods of Laplace transform and inverse Laplace theorem. An iterative procedure is proposed to find the roots of the transcendental equation. Numerical results of the temperature are obtained and the computational accuracy in terms of the roots is demonstrated. The effects of the graded parameter and the heat transfer parameter on the temperature distribution of both the functionally graded strip and the fluid are discussed, which are helpful for the design optimization of the graded material. The thickness of the functionally graded strip on the temperature distribution is specially analyzed, which provides practical references for geometrical optimization of the structure.