Variation of parameters, Nonlinear differential equations, Heat transfer applications


Nonlinear problems arise in many heat transfer applications, and several analytical and numerical methods for solving these problems are described in the literature. Here, the method of variation of parameters is shown to be a relatively simple method for obtaining solutions to four specific heat transfer problems: 1. a radiating annular fin, 2. conduction-radiation in a plane-parallel medium, 3. convective and radiative exchange between the surface of a continuously moving strip and its surroundings, and 4. convection from a fin with temperature-dependent thermal conductivity and variable cross-sectional area. The results for each of these examples are compared to those obtained using other analytical and numerical methods. The accuracy of the method is limited only by the accuracy with which the numerical integration is performed. The method of variation of parameters is less complex and relatively easy to implement compared to other analytical methods and some numerical methods. It is slightly more computationally expensive than traditional numerical approaches. The method presented may be used to verify numerical solutions to nonlinear heat transfer problems.

Original Publication Citation

Travis J. Moore, Matthew R. Jones, Solving nonlinear heat transfer problems using variation of parameters, International Journal of Thermal Sciences, Volume 93, 2015, Pages 29-35, ISSN 1290-0729, (

Document Type

Peer-Reviewed Article

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Ira A. Fulton College of Engineering and Technology


Mechanical Engineering

University Standing at Time of Publication

Associate Professor

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Engineering Commons