Abstract
A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the physical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbationmethod, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.
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The project was supported by the National Special Fund for Major Research Instrument Development (2011YQ140145), 111 Project (B07009), the National Natural Science Foundation of China (11002013), and Defense Industrial Technology Development Program (A2120110001 and B2120110011).
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Wang, C., Qiu, ZP. Fuzzy finite difference method for heat conduction analysis with uncertain parameters. Acta Mech Sin 30, 383–390 (2014). https://doi.org/10.1007/s10409-014-0036-7
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DOI: https://doi.org/10.1007/s10409-014-0036-7