Fractional-order Model for Cooling of a Semi-infinite Body by Radiation

Document Type : Original Paper

Author

Department of Mathematics, University of Kurdistan, Sanandaj, Iran

Abstract

‎In this paper‎, ‎the fractional-order model for cooling of a semi-infinite body by radiation is considered‎.
‎In the supposed semi-infinite body‎, ‎the equation of heat along with an initial condition and an asymptotic boundary condition form an equivalent equation in which the order of derivatives is halved‎.
‎This equation and a boundary condition introduced by the radiation heat transfer give rise to an initial value problem‎, ‎whose differential equation is nonlinear and fractional order‎.
‎The semi-analytical solution to this nonlinear model was determined asymptotically at small and large times‎.
‎Moreover‎, ‎two numerical methods including Grunwald-Letnikov approximation and Muntz-Legendre approximation yield numerical solutions to the problem‎.

Keywords

Main Subjects


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