THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

ANALYTICAL SOLUTION TO CONVECTION-RADIATION OF A CONTINUOUSLY MOVING FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY

ABSTRACT
In this article, the simultaneous convection-radiation heat transfer of a moving fin of variable thermal conductivity is studied. The differential transformation method (DTM) is applied for an analytic solution for heat transfer in fin with two different profiles. Fin profiles are rectangular and exponential. The accuracy of analytic solution is validated by comparing it with the numerical solution that is obtained by fourth-order Runge-Kutta method. The analytical and numerical results are shown for different values of the embedding parameters. DTM results show that series converge rapidly with high accuracy. The results indicate that the fin tip temperature increases when ambient temperature increases. Conversely, the fin tip temperature decreases with an increase in the Peclet number, convection-conduction and radiation-conduction parameters. It is shown that the fin tip temperature of the exponential profile is higher than the rectangular one. The results indicate that the numerical data and analytical method are in a good agreement with each other.
KEYWORDS
PAPER SUBMITTED: 2011-04-25
PAPER REVISED: 2012-01-05
PAPER ACCEPTED: 2012-01-05
DOI REFERENCE: https://doi.org/10.2298/TSCI110425005M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE 4, PAGES [1049 - 1060]
REFERENCES
  1. Sakiadis, B. C., Boundary-layer Behaviour on Continuous Solid Surface: I. Boundary Layer Equations for Two Dimensional and Axisymmetric Flow, AICHE. J., 7 (1961), 26.
  2. Erickson, L. E., fan, L. T., Fox, V. G., Heat and Mass Transfer on a Continuous Moving Flat Plate with Suction or Injection. Ind. Eng. Chem. Fund., 5 (1966), 19.
  3. Cortell, R., Flow and Heat Transfer in a Moving Fluid over a Moving Flat Surface, Theoretical and Computational Fluid Dynamics, 21 (2007), pp. 435-446.
  4. Sparrow, E. M., Abraham, J. P., Universal Solutions for the Streamwise Variation of the Temperature of a Moving Sheet in the Presence of a Moving Fluid, Int. J. Heat Mass Transfer, 48 ( 2005), pp. 3047- 3056.
  5. Char, M. I., Chen, C. K., Cleaver, J. W., Conjugate Force Convection Heat Transfer from a Continuous, Moving Flat Sheet, Int. J. Heat and Fluid Flow, 11(3) (1990), pp. 257-261.
  6. Al-Sanea, S. A., Mixed Convection Heat Transfer along a Continuously Moving Heated Vertical Plate with Suction or Injection, Int. J. Heat Mass Transfer, 47 (2004), pp. 1445-1465.
  7. Abel, S., Prasad K. V., Mahaboob A., Buoyancy Force and Thermal Radiation Effects in MHD Boundary Layer Visco-elastic Fluid Flow over Continuously Moving Stretching Surface, Int. J. Thermal Science, 44 (2005), pp. 465-476.
  8. Lee S. L., Tsai, J. S., Cooling of a Continuous Moving Sheet of Finite Thickness in the Presence of Natural Convection, Int. J. Heat Mass Transfer, 33 (1990), 3, pp. 457-464.
  9. Choudhury, S. R., Jaluria, Y., Forced Convective Heat Transfer from a Continuously Moving Heated Cylindrical Rod in Material Processing, ASME Journal of Heat Transfer, 116 (1994) pp. 724-734.
  10. Mendez, F., Trevino, C., Heat Transfer Analysis on a Moving Flat Sheet Emerging into a Quiescent Fluid, J. Thermophysics and Heat Transfer, 16 (2002), pp. 373-378.
  11. Fox, V. G., Erickson, L. E., fan, L. T., The Laminar Boundary Layer on a Moving Continuous Flat Sheet Immersed in a Non-Newtonian Fluid, AICHE. J., 15 (1969), 3, pp. 327-333.
  12. Howell, T. G., Jeng, D. R., De Witt, K. J., Momentum and Heat Transfer on a Continuous Moving Surface in a Power Law Fluid, Int. J. Heat Mass Transfer, 40 (1997), 8, pp. 1853-1861.
  13. Torabi, M., Yaghoobi, H., Saedodin, S., Assessment of Homotopy Perturbation Method in Nonlinear Convective-Radiative Non-Fourier Conduction Heat Transfer Equation with Variable Coefficient, Thermal Science, (In Press)
  14. Sahu, A. K., Mathur, M. N., Chaturani, P., Bharatiya, S. S., Momentum and Heat Transfer from a Continuous Surface to a Power-Law Fluid, Acta Mechanica, 142 (2000), pp. 119-131.
  15. Zheng, L. C., Zhang, X. X., Skin Friction and Heat Transfer in Power-Law Fluid Laminar Boundary Layer along a Moving Surface, Int. J. Heat Mass Transfer, 45 (2002), pp. 2667-2672.
  16. Ganji, D. D., Ganji, Z. Z., Ganji, H. D., Determination of Temperature Distribution for Annual Fins with Temperature-Dependent Thermal Conductivity by HPM, Thermal Science, 15 (2011), 1, pp. 111-115.
  17. Aziz, A., Khani, F., Convection-Radiation from a Continuously Moving Fin of a Variable Thermal Conductivity, Journal of the Franklin Institute, 348 (2011), pp. 640-651.
  18. Zhou, J. K., Differential Transformation Method and its Application for Electrical Circuits, Hauzhang University press, Wuhan, China, 1986.
  19. Rashidi, M. M., Erfani, E., New Analytical Method for Solving Burgers, and Nonlinear Heat Transfer Equation and Comparison with HAM, Comput. Phys. Commun., 180 (2009), pp. 1539-1544.
  20. Joneidi, A. A., Ganji, D. D., Babaelahi, M., Differential Transformation Method to Determine Fin Efficiency of Convective Straight Fins with Temperature Dependent Thermal Conductivity, Int. Commun. Heat Mass Transfer, 36 (2009), pp. 757-762.
  21. Moradi, A., Ahmadikia, H., Analytical Solution for Different Profiles of Fin with Temperature- Dependent Thermal Conductivity, Mathematical Problems in Engineering, doi:10.1155/2010/568263.
  22. Chang, S. H., Chang, I. L., A New Algorithm for Calculating One-dimensional Differential Transformation of Nonlinear Functions, Appl. Math. Comput., 195 (2008), pp. 799-808.
  23. Chang, S. H., Chang, I. L., A New Algorithm for Calculating Two-dimensional Differential Transformation of Nonlinear Functions, Appl. Math. Comput., 215 (2009), pp. 2486-2494.
  24. Jang, B., Solving Linear and Nonlinear Initial Value Problems by the Projected Differential Transform Method, Comput. Phys. Commun., 181 (2010), pp. 848-854.
  25. Rashidi, M. M., Erfani, E., A New Analytical Study of MHD Stagnation-point Flow in Porous Medium with Heat Transfer, Computer& Fluid, 40 (2011), pp. 172-178.
  26. Rashidi, M. M., The Modified Differential Method for Solving MHD Boundary-layer Equations, Comp. Phys. Commun., 180 (2009), pp. 2210-2217.
  27. Franco, A., An Analytic Method for the Optimum Thermal Design of Convective Longitudinal Fin Arrays, Heat Mass Transfer, 45 (2009), pp. 1503-1517.

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence