ESTIMATION OF THE LENGTH CONSTANT OF A LONG COOLING FIN BY AN ANCIENT CHINESE ALGORITHM

Abstract

In this paper, an ancient Chinese algorithm is used to estimate the length constant of a long cooling fin, and an approximate solution formulation is obtained. The obtained results show that this method is a simple but promising method without any requirement for advanced calculus.

Dates

  • Submission Date2010-07-10
  • Revision Date2010-09-10
  • Acceptance Date2010-11-18

DOI Reference

10.2298/TSCI11S1149X

References

  1. He, J.-H., Ancient Chinese Algorithm: the Ying Buzu Shu (Method of Surplus and Deficiency) vs. Newton Iteration Method, Applied Math. Mech., 23 (2002), 12, pp. 1255-1260
  2. He, J.-H., Some Asymptotic Methods for Strongly Non-Linear Equations, Int. J. Mod. Phys. B., 20 (2006), 10, pp. 1141-1199
  3. He, J.-H., An Elementary Introduction to Recently Developed Asymptotic Methods and Nanomech-anics in Textile Engineering, Int. J. Mod. Phys. B. 22 (2008), 21, pp. 3487-3578
  4. He, J.-H., Application of He Chengtian's Interpolation to Bethe Equation, Comput. Math. Applicat. 58 (2009), 11-12, pp. 2427-2430
  5. He, J.-H., Max-Min. Approach to Non-Linear Oscillators, Int. J. Nonlin. Sci. Num., 9 (2008), 2, pp. 207-210
  6. He, J.-H., An Improved Amplitude-Frequency Formulation for Non-Linear Oscillators, Int. J. Nonlin. Sci. Num., 9 (2008), 2, pp. 211-212
  7. Zhang, H. L., Application of He's Amplitude-Frequency Formulation to a Non-Linear Oscillator with Discontinuity, Comput. Math. Applicat., 58 (2009), 11-12, pp. 2197-2198
  8. Cai, X. C., Wu, W. Y., He's Frequency Formulation for the Relativistic Harmonic Oscillator, Comput. Math. Applicat., 58 (2009), 11-12, pp. 2358-2359
  9. Fan, J., He's Frequency-Amplitude Formulation for the Duffing Harmonic Oscillator, Comput. Math. Applicat., 58 (2009), 11-12, pp. 2473-2476
  10. Zhao, L., He's Frequency-Amplitude Formulation for Non-Linear Oscillators with an Irrational Force, Comput. Math. Applicat., 58 (2009), 11-12, pp. 2477-2479
  11. Ebaid, A. E., Analytical Periodic Solution to a Generalized Non-Linear Oscillator: Application of He's Frequency-Amplitude Formulation, Mech. Res. Communicat., 37 (2010), 1, pp. 111-112
  12. Ebaid, A. E., Oscillations in an x[(2n + 2)/(2n + 1)] Potential via He's Frequency-Amplitude Formulation, Z. Naturforch. A, 64 (2009), A, pp. 877-878
  13. Ganji, S. S., et al., Application of Amplitude-Frequency Formulation to Non-Linear Oscillation System of the Motion of a Rigid Rod Rocking Back, Math. Method. Appl. Sci., 33 (2010), 2, pp. 157-166
  14. Zeng, D. Q., Lee, Y. Y., Analysis of Strongly Nonlinear Oscillator Using the Max-Min Approach, Int. J. Nonlin. Sci. Num., 10 (2009), 6, pp. 1361-1368
  15. Ren, Z. F., et al., Application of He's Amplitude-Frequency Formulation to Non-Linear Oscillators with Discontinuities, Phys. Script., 80 (2009), 4, 045003
  16. Acton, J. R., Squire, P. T., Solving Equations with Physical Understanding, Adam Hilger Ltd., Bristol, England, 1985
Volume 15, Issue 11, Pages149 -152