Solving nonlinear heat transfer problems using variation of parameters

Abstract

a b s t r a c tNonlinear 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.

Variation of parameters method for a three-dimensional problem of condensation film on an inclined rotating disk

“…The method of variation of parameters is generally used to solve nonhomogeneous linear differential equations [21]. However, it is known from the literature that it can also be used to solve nonlinear equations [14][15][16][17][18][19][20]. In linear equations, while the term disrupting homogeneity is only the function of the independent variable, in nonlinear equations, this term is also the function of the dependent variable.…”

“…This method has recently been used by Moore [18] for the first time in a doctoral thesis for non-linear heat transfer problems. Other studies by Moore and Jones [19,20] have also been included in the literature as the first studies where the method was used in the problems of heat transfer. This study is the first study in which the nonlinear fluid condensation problem was solved by the variation of parameters method.…”

Droplets and Sprays

“…The approaches to droplet heating discussed so far are based on the assumption that the heat conduction equation is linear and the heat conduction process follows the Fourier law (see [19,20,21,22] for possible approaches to the solution to the non-linear problem and [23,24,25,26,27,28,29] for the analysis of non-Fourier models of heat transfer).…”

Performance analysis of pin fins with temperature dependent thermal parameters using the variation of parameters method

“…Ancak, bu yöntemin lineer olmayan diferansiyel denklemlerin çözümünde de etkin bir şekilde kullanılabileceği literatürden bilinmektedir [17]- [21]. Mohyud_Din ve diğ.…”