Temperature Distribution in Convective Fins with Variable Thermal Conductivity
Consider a convective straight fin with temperature-dependent thermal conductivity. The dimensionless problem reduces to (see  for details) with , , where the dimensionless quantities and parameters are defined as follows: , , , and .[more]
The plots of the temperature distribution are obtained using the shooting technique (red curve) and the differential transformation method (dashed blue curve).
Excellent agreement is found between the two methods.[less]
The -order Taylor series expansion function of is of the form . At , this is the Maclaurin series, . The differential transformation of the function is given by . The differential inverse transform of is defined by . Table 1 in  gives a list of properties of the differential transformation. For instance, if then . In this Demonstration, and .
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 M. J. Jang, C. L. Chen, and Y. C. Liu, "On Solving the Initial-Value Problems Using the Differential Transformation Method," Applied Mathematics and Computation, 115(2–3), 2000 pp. 145–160. doi: 10.1016/S0096-3003(99)00137-X.
 A. A. Joneidi, D. D. Ganji, and M. Babaelahi, "Differential Transformation Method to Determine Fin Efficiency of Convective Straight Fins with Temperature Dependent Thermal Conductivity," International Communications in Heat and Mass Transfer, 36(7), 2009 pp. 757–62. doi: 10.1016/j.icheatmasstransfer.2009.03.020.