Materials 2011, 4(12), 2108-2118; doi:10.3390/ma4122108
Article

Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution

Department of Mechanical Engineering, University of Maine, Orono, ME 04469, USA
Received: 19 October 2011; in revised form: 2 December 2011 / Accepted: 5 December 2011 / Published: 8 December 2011
(This article belongs to the Special Issue Advances in Functionally Graded Materials)
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Abstract: This work investigates transient heat conduction in a functionally graded plate (FGM plate) subjected to gradual cooling/heating at its boundaries. The thermal properties of the FGM are assumed to be continuous and piecewise differentiable functions of the coordinate in the plate thickness direction. A linear ramp function describes the cooling/heating rates at the plate boundaries. A multi-layered material model and Laplace transform are employed to obtain the transformed temperatures at the interfaces between the layers. An asymptotic analysis and an integration technique are then used to obtain a closed form asymptotic solution of the temperature field in the FGM plate for short times. The thermal stress intensity factor (TSIF) for an edge crack in the FGM plate calculated based on the asymptotic temperature solution shows that the asymptotic solution can capture the peak TSIFs under the finite cooling rate conditions.
Keywords: functionally graded material; heat conduction; cooling rate; temperature; asymptotic solution

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MDPI and ACS Style

Jin, Z. Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution. Materials 2011, 4, 2108-2118.

AMA Style

Jin Z. Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution. Materials. 2011; 4(12):2108-2118.

Chicago/Turabian Style

Jin, Zhihe. 2011. "Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution." Materials 4, no. 12: 2108-2118.

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