## THERMAL SCIENCE

International Scientific Journal

### APPROXIMATE SOLUTIONS AND CONSERVATION LAWS OF THE PERIODIC BASE TEMPERATURE OF CONVECTIVE LONGITUDINAL FINS IN THERMAL CONDUCTIVITY

**ABSTRACT**

In this paper, the residual power series method (RPSM) is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the RPSM is efficient for examining numerical behavior of nonlinear models. Further, the conservation of heat is studied using the multiplier method.

**KEYWORDS**

PAPER SUBMITTED: 2018-10-15

PAPER REVISED: 2018-11-23

PAPER ACCEPTED: 2019-01-15

PUBLISHED ONLINE: 2019-03-09

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Supplement 1**, PAGES [S267 - S273]

- G. B. Whitham. Linear and Nonlinear Waves, John Whiley, New york, 1974
- G.P Agrawal, Nonlinear fiber optics 5th edition; Academic Press: New York, 2013
- Ferziger. J. H., A note on numerical accuracy, Int. J. Num. M. in fluids, 8 (1988), pp. 995-996
- Inc. M., et al., A new method for approximate solutions of some nonlinear equations: Residual power series method, Advances in Mechanical Engineering, 8 (2016), pp.1-7
- Maysaa. A.Q., et al., Approximate optical solitons of bright and dark optical solitons in birefrigent fibers, Optik, 140 (2017), pp.45-61
- Yang., Y.T., et al., A double decomposition method for solving the annular hyperbolic profile fins with variable thermal conductivity, Heat Transfer Eng, 31 (2010), pp.1165-1172
- Yang. Y. T., et al., A double decomposition method for solving the periodic base temperature in convective longitudinal fins, Energy Conversion and Management, 49 (2008), pp. 2910-2916
- Duan .,J. S., et al., A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations, Applied Mathematics and Computation, 218 (2011), pp. 4090-4118
- Buhe., E., et al., Symmetry reductions, exact solutions, and conservation laws of the generalized Zakharov equations, Journal of Mathematical Physics, 56 (2015), pp. 101501
- Anco., S. C. et al., Direct construction method for conservation laws of partial differential equations Part II: General treatment, European Journal of Applied Mathematics, 13 (2002), pp. 567-585
- Inc., M et al., Exact solutions and conservation laws of the Bogoyavlenskii equation, Acta physica polonica A, 13 (2018), pp. 1133-1137
- Seadawy .,A. R, Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves,, Eur. Phys. J. Plus, 132 (2017), pp. 29
- Seadawy .,A. R, Ionic acoustic solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equations in quantum plasma, Mathematical Methods and Applied Sciences, 40 (2017), pp. 1598-1607
- Seadawy .,A. R, Three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma, Comput. Math. Appl, 71 (2016), pp. 201-2012
- Seadawy .,A. R, Approximation solutions of derivative nonlinear Schrodinger equation with computational applications by variational method,, Eur. Phys. J. Plus, 132 (2017), pp.10
- Aliyu., A. I et al., Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Sixth-Order Nonlinear Ramani Equation, Symmetry, 10 (2018), pp. 341
- Chunyu., Y et al., Amplification, reshaping, fission and annihilation of optical solitons in dispersion-decreasing fiber, Nonlinear Dynamics, 92 (2018), pp. 203-213
- Wenyi., L et al., Soliton structures in the (1+1)-dimensional Ginzburg-Landau equation, with a parity-time-symmetric potential in ultrafast optics, Chinese Physical B, 27 (2018), pp. 030504
- Weitian., Y et al., Interactions of solitons, dromion-like structures and butterfly-shaped pulses for variable coefficient nonlinear Schrödinger equation, Optik, 159 (2018), pp. 21-30