In present paper, the symplectic method was introduced for the two dimensional transient heat conduction problems. Based on the fundamental equations, the symplectic space constituted by original variable temperature and dual variable heat flux density has been built, which was reduced to finding the eigen solutions and eigen values, so the analytic solutions of temperature field in Hamilton system are obtained. Finally, the distribution of temperature was analyzed with different thickness ratio, time steps. The results showed that symplectic method is effective to study two dimensional transient heat conduction.
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