The Efficiency of The Gaver-Stehfest Method Transient Response of A Spiral Fin

Year 2021, Volume: 5 Issue: 4, 194 - 200, 20.12.2021

Bilal Sungur , İbrahim Keles

https://doi.org/10.26701/ems.899389

Abstract

In this study, a practical combined approach was applied by the Gaver-Stehfest method to examine the impermanent reaction of a spiral fin whose tip is isolated with the base tip exposed to changes in fluid temperature. The heat transmission of the fin under the stable temperature effect of the base is examined. The environment temperature is saved stationary and no heat source or sink is available. Results are improved for minor- and major -time worth when the base is exposed to the unit step variation form in temperature. The changes in heat flux and temperature at the base formed depending on the parameters that make up the spiral fin are graphically shown. The available numerical results show that it is fully consistent when compared with the literature.

Keywords

Laplace transform, Transient response, Spiral fin, Heat transfer, Gaver-Stehfest method

References

• CHU, H.-S., CHEN, C.-K., WENG, C.-I., (1982). Applications of Fourier series technique to transient heat transfer problem. Chemical Engineering Communications. 16(1–6): 215–25. https://doi.org/10.1080/00986448208911098
• Chu, H.S., Chen, C.K., Weng, C.I., (1983). Transient response of circular pins. Journal of Heat Transfer. 105(1): 205–8. doi: 10.1115/1.3245547.
• Chu, H. Sen., Weng, C.I., Chen, C.K., (1983). Transient Response of Composite Straight Fin. Advances in the Astronautical Sciences. 50(pt 1): 539–49. https://doi.org/10.1115/1.3245579
• Mokheimer, E.M.A., (2002). Performance of annular fins with different profiles subject to variable heat transfer coefficient. International Journal of Heat and Mass Transfer. 45(17): 3631–42. https://doi.org/10.1016/S0017-9310(02)00078-9
• Cheng, C.-Y., (1994). Transient response of annular fins of various shapes subjected to constant base heat fluxes. Journal of Physics D: Applied Physics. 27(11): 2302. https://doi.org/10.1088/0022-3727/27/11/009
• Lee, Y.-M., Haji-Sheikh, A., Fletcher, L.S., Peterson, G.P., (1994). Effective thermal conductivity in multidimensional bodies. Journal of Heat Transfer. 116(1):17-27. https://doi.org/10.1115/1.2910853
• Liaw, S.P., Yeh, R.H., (1994). Fins with temperature dependent surface heat flux—I. Single heat transfer mode. International Journal of Heat and Mass Transfer. 37(10): 1509–15. https://doi.org/10.1016/0017-9310(94)90152-X
• Wang, C.Y., (1994). Diffusive transport across a wavy plate composed of annular sectors.
• Yeh, R.-H., (1994). Optimum spines with temperature dependent thermal parameters. International Journal of Heat and Mass Transfer. 37(13): 1877–84. https://doi.org/10.1016/0017-9310(94)90328-X
• Yeh, R.-H., (1994). Optimization of longitudinal fins with temperature-dependent thermal parameters. Heat Transfer Engineering. 15(3): 25–34. https://doi.org/10.1080/01457639408939828
• Chen Cha’O-Kuang, L.-T.Y., (1999). Application of the Taylor transformation to the transient temperature response of an annular fin. Heat Transfer Engineering. 20(1): 78–87. https://doi.org/10.1080/014576399271736
• Laor, K., Kalman, H., (1996). Performance and optimum dimensions of different cooling fins with a temperature-dependent heat transfer coefficient. International Journal of Heat and Mass Transfer. 39(9): 1993–2003. https://doi.org/10.1016/0017-9310(95)00296-0
• Zubair, S.M., Al-Garni, A.Z., Nizami, J.S., (1996). The optimal dimensions of circular fins with variable profile and temperature-dependent thermal conductivity. International Journal of Heat and Mass Transfer. 39(16): 3431–9. https://doi.org/10.1016/0017-9310(96)00011-7
• Bouaziz, M.N., Rechak, S., Hanini, S., Bal, Y., Bal, K., (2001). Étude des transferts de chaleur non linéaires dans les ailettes longitudinales. International Journal of Thermal Sciences. 40(9): 843–57. https://doi.org/10.1016/S1290-0729(01)01271-6
• Campo, A., Stuffle, R.E., (1997). Symbolic mathematics for the calculation of thermal efficiencies and tip temperatures in annular fins of uniform thickness. International Journal of Heat and Mass Transfer. 40(2): 490–2. https://doi.org/10.1016/0017-9310(96)00093-2
• Wang, J.S., Luo, W.J., Hsu, S.P., (2008). Transient Response of a Spiral Fin with its Base Subjected to the Variation of Heat Flux. Journal of Applied Sciences. 8(10): 1798–811. https://doi.org/10.3923/jas.2008.1798.1811
• Knight, J.H., Raiche, A.P., (1982). Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method. Geophysics. 47(1): 47–50. https://doi.org/10.1190/1.1441280
• Abate, J., Whitt, W., (1992). The Fourier-series method for inverting transforms of probability distributions. Queueing Systems. 10(1): 5–87. https://doi.org/10.1007/BF01158520
• Kou, S.G., Wang, H., (2003). First passage times of a jump diffusion process. Advances in Applied Probability.: 504–31. https://doi.org/10.1239/aap/1051201658
• Badescu, A., Breuer, L., Da Silva Soares, A., Latouche, G., Remiche, M.-A., Stanford*, D., (2005). Risk processes analyzed as fluid queues. Scandinavian Actuarial Journal. 2005(2): 127–41. https://doi.org/10.1080/03461230410000565
• Schoutens, W., Van Damme, G., (2011). The β-variance gamma model. Review of Derivatives Research. 14(3): 263–82. https://doi.org/10.1007/s11147-010-9057-y
• Montella, C., (2008). LSV modelling of electrochemical systems through numerical inversion of Laplace transforms. I–The GS–LSV algorithm. Journal of Electroanalytical Chemistry. 614(1–2): 121–30. https://doi.org/10.1016/j.jelechem.2007.11.010
• Kawakatsu, H., (2005). Numerical inversion methods for computing approximate p-values. Computational Economics. 26(3–4): 103–16. https://doi.org/10.1007/s10614-005-9011-5
• Egonmwan, A.O., (2012). The numerical inversion of the Laplace transform. LAP Lambert Academic Publishing
• Valkó, P.P., Vajda, S., (2002). Inversion of noise-free Laplace transforms: towards a standardized set of test problems. Inverse Problems in Engineering. 10(5): 467–83. https://doi.org/10.1080/10682760290004294
• Mashayekhizadeh, V., Dejam, M., Ghazanfari, M.H., (2011). The application of numerical Laplace inversion methods for type curve development in well testing: a comparative study. Petroleum Science and Technology. 29(7): 695–707. https://doi.org/10.1080/10916460903394060
• Zhang, J., (2007). Some innovative numerical approaches for pricing American options.
• Hassanzadeh, H., Pooladi-Darvish, M., (2007). Comparison of different numerical Laplace inversion methods for engineering applications. Applied Mathematics and Computation. 189(2): 1966–81. https://doi.org/10.1016/j.amc.2006.12.072
• Cheng, A.H.D., Sidauruk, P., Abousleiman, Y., (1994). Approximate inversion of the Laplace transform. Mathematica Journal. 4(2): 76–82.