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Zeitschrift für Naturforschung A Contents Vol. 69a (2014)

Z. Naturforsch. 69a, 195 – 198 (2014)

doi:10.5560/ZNA.2014-0008

Invariance, Conservation Laws, and Exact Solutions of the Nonlinear Cylindrical Fin Equation

Saeed M. Ali¹, Ashfaque H. Bokhari¹, Fiazuddin D. Zaman¹, and Abdul H. Kara²

¹Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

²School of Mathematics, Centre for Differential Equations Continuum Mechanics and Applications University of the Witwatersrand Johannesburg, Wits 2050, South Africa

Received August 6, 2013 / revised January 6, 2014 / published online April 2, 2014

Reprint requests to: A. H. K.; E-mail: abdul.kara@wits.ac.za

Fins are heat exchange surfaces which are used widely in industry. The partial differential equation arising from heat transfer in a fin of cylindrical shape with temperature dependent thermal diffusivity are studied. The method of multipliers and invariance of the differential equations is employed to obtain conservation laws and perform double reduction.

Key words: Nonlinear Cylindrical Fin Equation; Exact Solutions; Conservation Laws.

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