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THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD

Year 2018, Volume: 4 Issue: 5, 2287 - 2302, 25.06.2018
https://doi.org/10.18186/thermal.438485

Abstract

In this paper, thermal
performance of convective-radiative straight fin with temperature-dependent
thermal conductivity in the presence of uniform magnetic field is analyzed
using partial Noether method. The exact analytical solution is used to
investigate the effects of magnetic field, convective, radiative,
thermo-geometric and thermal conductivity (non-linear) parameters on the
thermal performance of the fin
.
The results reveal that as the magnetic, convective
and radiative parameters increase, the temperature of the fin decreases rapidly
and by implication, the rate of heat transfer through the fin increases.
The study provides a platform for comparison of results of any other method of
analysis of the problem with the results of the exact analytical solutions in
this paper. Also, such an analytical tool is valuable as a design and
optimization approach for large scale (not necessarily in size) finned heat
exchangers where each fin/row are analytically analyzed and where the
surrounding fluid is influenced by a magnetic field
.

References

  • [1] Aziz, A. Enamul-Huq.S. (1973). Perturbation solution for convecting fin with temperature dependent thermal conductivity, Journal of Heat Transfer 97, 300–301.
  • [2] Aziz, A., (1977). Perturbation solution for convecting fin with internal heat generation and temperature dependent thermal conductivity, International Journal of Heat and Mass Transfer, 1253-5.
  • [3] Campo, A. Spaulding, R. J., (1999). Coupling of the methods of successive approximations and undetermined coefficients for the prediction of the thermal behaviour of uniform circumferential fins,” Heat and Mass Transfer, 34 (6), 461–468.
  • [4] Chiu, C. H., Chen, C. K.. (2002). A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, International Journal of Heat and Mass Transfer 45, 2067-2075.
  • [5] Arslanturk, A. (2005). A decomposition method for fin efficiency of convective straight fin with temperature dependent thermal conductivity, International Communications in Heat and Mass Transfer Transfer, 32(6), 831–841.
  • [6] Ganji, D. D. 2006. The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Physics Letters A A, 355, 337–341.
  • [7] He, J.H. (1999). Homotopy perturbation method, Computer Methods in Applied Mechanics and Engineering, 178, 257–262. [8] Chowdhury M. S. H., Hashim I. (2008). Analytical solutions to heat transfer equations by homotopy-perturbation method revisited, Physical Letters A, 372, 1240-1243.
  • [9] Rajabi, A. (2007). Homotopy perturbation method for fin efficiency of convective straight fins with temperature dependent thermal conductivity .Physics Letters A364, 33-37.
  • [10] Chowdhury,M. S. H., Hashim, I. Abdulaziz, O. (2009). Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems, Communications in Nonlinear Science and Numerical Simulation 14, 371-378.
  • [11] Mustafa, I. (2008). Application of Homotopy analysis method for fin efficiency of convective straight fin with temperature dependent thermal conductivity. Mathematics and Computers Simulation 79, 189 – 200.
  • [12] Hosseini, K. Daneshian, B. Amanifard, N. Ansari, R. (2012). Homotopy Analysis Method for a Fin with Temperature Dependent Internal Heat Generation and Thermal Conductivity, International Journal of Nonlinear Science. 14(2), 201-210.
  • [13] Domairryand, G. Fazeli, M. (2009). Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity. Communication in Nonlinear Science and Numerical Simulation 14, pp. 489-499.
  • [14] Coskun, S. B. and Atay, M. T. (2007). analysis of convective straight and radial fins with temperature dependent thermal conductivity using variational iteration method with comparision with respect to finite element analysis. Mathematical Problem in Engineering, 15.
  • [15] Languri, E. M. Ganji, D. D. Jamshidi, N. (2008). Variational Iteration and Homotopy perturbation methods for fin efficiency of convective straight fins with temperature dependent thermal conductivity. 5th WSEAS Int .Conf .On FLUID MECHANICS (fluids 08) Acapulco, Mexico January 25 -27.
  • [16] Coskun, S. B. and Atay, M. T. (2008). Fin efficiency analysis of convective straight fin with temperature dependent thermal conductivity using variational iteration method, Applied Thermal Engineering, 28, 2345–2352.
  • [17] Atay, M. T. Coskun. S. B. (2008). Comparative analysis of power-law fin-type problems using variational iteration method and finite element method, Mathematical Problems in Engineering.
  • [18] Khani, F. Ahmadzadeh,R.M. HamediNejad, H. (2009). Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, Communications in Nonlinear Science and Numerical Simulation 14 (8), 3327-3338.
  • [19] Sobamowo. M. G. (2016). Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering 99, 1316–1330
  • [20] Joneidi.,A. A.,Ganji, D. D. Babaelahi. M. (2009). Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. International Communication in Heat and Mass transfer 36, 757-762
  • [21] Moradi, M. Ahmadikia, H. (2010). Analytical Solution for different profiles of fin with temperature dependent thermal conductivity. Hindawi Publishing Corporation Mathematical Problem in Engineering.
  • [22] Mosayebidorcheh, Ganji, D. D. Farzinpoor. M. (2014). Approximate Solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient, Propulsion and Power Research, 41-47.
  • [23] Ghasemi,S. E. Hatami, M. Ganji, D. D. (2014). Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation, Cases Studies in Thermal Engineering, 4, 1-8.
  • [24] Ganji, D. D. Dogonchi, A. S. (2014). Analytical investigation of convective heat transfer of a longitudinal fin with temperature-dependent thermal conductivity, heat transfer coefficient and heat generation, International Journal of Physical Sciences, 9 (21), 466-474.
  • [25] Fernandez, A. (2009). On some approximate methods for nonlinear models. Applied Mathematics and Computation, 215 (1), 168-74.
  • [26] Aziz, A. and Bouaziz, M. N. (2011). A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity, Energy Conversion and Management, 52, 2876-2882.
  • [27] Abdel Latif M.S., Abdel Kader A.H., Nour H.M. (2015). Exact implicit solution of nonlinear heat transfer in rectangular straight fin using symmetry reduction methods, Applications And Applied Mathematics-An International Journal., 10 (2),864-877.
  • [28] Abdel Kader A.H., Abdel Latif M.S., Nour H.M. (2016). General exact solution of the fin problem with variable thermal conductivity, Propulsion and Power Research, 5(1), 63-69.
  • [29] Abdel Kader A.H., Abdel Latif M.S., Nour H.M. (2016). General exact solution of the fin problem with the power law temperature - dependent thermal conductivity, Mathematical Methods in the Applied Sciences, 39 (6), 1513-1521.
  • [30]Abdel Kader .A, H. Abdel Latif, M. S. and Nour, H. M. (2016). Exact solution of fin problem with linear temperature-dependent thermal conductivity. Journal of Applied Mathematics and Computational Mechanics, 15(4), 51-61.
  • [31] Kara, A. H. , Mahomed F. M., Naeem I, W. C. Sofo. (2007). Partial Noether and the first integrals via partial Lagrangian. Mathematical Methods in the Applied Sciences, 30 (16), 2079-2089.
  • [32] Naheem I., Mahomed F. M. (2008). Noether, partial Neother operators and the first integrals for a linear system. Journal of Mathematical Analysis and Applications., 342, 70-82.
  • [33] Noether, E. (1918) Invariant Variations probleme, Nachr. K¨onig Gesell Wissen, G¨ottingen’, Math. Phys. Kl. Heft 2, 235-257. (English translation in Transport Theory and Statical Physics 1971 1, 186-207.)
  • [34]Naeem I and Mahomed F M (2008) Partial Noether operators and first integrals for a system with two degrees of freedom, Journal of Nonlinear Mathematical Physics, 15, 165-178.
  • [35]Naeem I and Mahomed F M (2008) Noether, partial Noether operators and first integrals or a linear system, Journal of Mathematical Analysis and Applications, 342, 70-82.
  • [36] Naeem, I., Mahomed, F. M. (2009). Approximate partial Noether operators and first integrals for coupled nonlinear oscillators. Nonlinear Dynamics, 57(1-2), 303-311.
  • [37] Amirkolaei, R. S., Ganji, D. D. Slarian H. (2014). Determination of temperature distribution for porous fin which is exposed to uniform magnetic field to a vertical isothermal surface by homotopy analysis method and collocation method. Indian Journal of Scientific Research, 1(2), 215-222.
  • [38] Hoshyar, H., Ganji, D. D. Majidian, A. R. (2016). Least square method for porous fin in the presence of uniform magnetic field. Journal of Applied Fluid Mechanics, 9 (2), 661-668.
Year 2018, Volume: 4 Issue: 5, 2287 - 2302, 25.06.2018
https://doi.org/10.18186/thermal.438485

Abstract

References

  • [1] Aziz, A. Enamul-Huq.S. (1973). Perturbation solution for convecting fin with temperature dependent thermal conductivity, Journal of Heat Transfer 97, 300–301.
  • [2] Aziz, A., (1977). Perturbation solution for convecting fin with internal heat generation and temperature dependent thermal conductivity, International Journal of Heat and Mass Transfer, 1253-5.
  • [3] Campo, A. Spaulding, R. J., (1999). Coupling of the methods of successive approximations and undetermined coefficients for the prediction of the thermal behaviour of uniform circumferential fins,” Heat and Mass Transfer, 34 (6), 461–468.
  • [4] Chiu, C. H., Chen, C. K.. (2002). A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, International Journal of Heat and Mass Transfer 45, 2067-2075.
  • [5] Arslanturk, A. (2005). A decomposition method for fin efficiency of convective straight fin with temperature dependent thermal conductivity, International Communications in Heat and Mass Transfer Transfer, 32(6), 831–841.
  • [6] Ganji, D. D. 2006. The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Physics Letters A A, 355, 337–341.
  • [7] He, J.H. (1999). Homotopy perturbation method, Computer Methods in Applied Mechanics and Engineering, 178, 257–262. [8] Chowdhury M. S. H., Hashim I. (2008). Analytical solutions to heat transfer equations by homotopy-perturbation method revisited, Physical Letters A, 372, 1240-1243.
  • [9] Rajabi, A. (2007). Homotopy perturbation method for fin efficiency of convective straight fins with temperature dependent thermal conductivity .Physics Letters A364, 33-37.
  • [10] Chowdhury,M. S. H., Hashim, I. Abdulaziz, O. (2009). Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems, Communications in Nonlinear Science and Numerical Simulation 14, 371-378.
  • [11] Mustafa, I. (2008). Application of Homotopy analysis method for fin efficiency of convective straight fin with temperature dependent thermal conductivity. Mathematics and Computers Simulation 79, 189 – 200.
  • [12] Hosseini, K. Daneshian, B. Amanifard, N. Ansari, R. (2012). Homotopy Analysis Method for a Fin with Temperature Dependent Internal Heat Generation and Thermal Conductivity, International Journal of Nonlinear Science. 14(2), 201-210.
  • [13] Domairryand, G. Fazeli, M. (2009). Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity. Communication in Nonlinear Science and Numerical Simulation 14, pp. 489-499.
  • [14] Coskun, S. B. and Atay, M. T. (2007). analysis of convective straight and radial fins with temperature dependent thermal conductivity using variational iteration method with comparision with respect to finite element analysis. Mathematical Problem in Engineering, 15.
  • [15] Languri, E. M. Ganji, D. D. Jamshidi, N. (2008). Variational Iteration and Homotopy perturbation methods for fin efficiency of convective straight fins with temperature dependent thermal conductivity. 5th WSEAS Int .Conf .On FLUID MECHANICS (fluids 08) Acapulco, Mexico January 25 -27.
  • [16] Coskun, S. B. and Atay, M. T. (2008). Fin efficiency analysis of convective straight fin with temperature dependent thermal conductivity using variational iteration method, Applied Thermal Engineering, 28, 2345–2352.
  • [17] Atay, M. T. Coskun. S. B. (2008). Comparative analysis of power-law fin-type problems using variational iteration method and finite element method, Mathematical Problems in Engineering.
  • [18] Khani, F. Ahmadzadeh,R.M. HamediNejad, H. (2009). Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, Communications in Nonlinear Science and Numerical Simulation 14 (8), 3327-3338.
  • [19] Sobamowo. M. G. (2016). Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering 99, 1316–1330
  • [20] Joneidi.,A. A.,Ganji, D. D. Babaelahi. M. (2009). Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. International Communication in Heat and Mass transfer 36, 757-762
  • [21] Moradi, M. Ahmadikia, H. (2010). Analytical Solution for different profiles of fin with temperature dependent thermal conductivity. Hindawi Publishing Corporation Mathematical Problem in Engineering.
  • [22] Mosayebidorcheh, Ganji, D. D. Farzinpoor. M. (2014). Approximate Solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient, Propulsion and Power Research, 41-47.
  • [23] Ghasemi,S. E. Hatami, M. Ganji, D. D. (2014). Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation, Cases Studies in Thermal Engineering, 4, 1-8.
  • [24] Ganji, D. D. Dogonchi, A. S. (2014). Analytical investigation of convective heat transfer of a longitudinal fin with temperature-dependent thermal conductivity, heat transfer coefficient and heat generation, International Journal of Physical Sciences, 9 (21), 466-474.
  • [25] Fernandez, A. (2009). On some approximate methods for nonlinear models. Applied Mathematics and Computation, 215 (1), 168-74.
  • [26] Aziz, A. and Bouaziz, M. N. (2011). A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity, Energy Conversion and Management, 52, 2876-2882.
  • [27] Abdel Latif M.S., Abdel Kader A.H., Nour H.M. (2015). Exact implicit solution of nonlinear heat transfer in rectangular straight fin using symmetry reduction methods, Applications And Applied Mathematics-An International Journal., 10 (2),864-877.
  • [28] Abdel Kader A.H., Abdel Latif M.S., Nour H.M. (2016). General exact solution of the fin problem with variable thermal conductivity, Propulsion and Power Research, 5(1), 63-69.
  • [29] Abdel Kader A.H., Abdel Latif M.S., Nour H.M. (2016). General exact solution of the fin problem with the power law temperature - dependent thermal conductivity, Mathematical Methods in the Applied Sciences, 39 (6), 1513-1521.
  • [30]Abdel Kader .A, H. Abdel Latif, M. S. and Nour, H. M. (2016). Exact solution of fin problem with linear temperature-dependent thermal conductivity. Journal of Applied Mathematics and Computational Mechanics, 15(4), 51-61.
  • [31] Kara, A. H. , Mahomed F. M., Naeem I, W. C. Sofo. (2007). Partial Noether and the first integrals via partial Lagrangian. Mathematical Methods in the Applied Sciences, 30 (16), 2079-2089.
  • [32] Naheem I., Mahomed F. M. (2008). Noether, partial Neother operators and the first integrals for a linear system. Journal of Mathematical Analysis and Applications., 342, 70-82.
  • [33] Noether, E. (1918) Invariant Variations probleme, Nachr. K¨onig Gesell Wissen, G¨ottingen’, Math. Phys. Kl. Heft 2, 235-257. (English translation in Transport Theory and Statical Physics 1971 1, 186-207.)
  • [34]Naeem I and Mahomed F M (2008) Partial Noether operators and first integrals for a system with two degrees of freedom, Journal of Nonlinear Mathematical Physics, 15, 165-178.
  • [35]Naeem I and Mahomed F M (2008) Noether, partial Noether operators and first integrals or a linear system, Journal of Mathematical Analysis and Applications, 342, 70-82.
  • [36] Naeem, I., Mahomed, F. M. (2009). Approximate partial Noether operators and first integrals for coupled nonlinear oscillators. Nonlinear Dynamics, 57(1-2), 303-311.
  • [37] Amirkolaei, R. S., Ganji, D. D. Slarian H. (2014). Determination of temperature distribution for porous fin which is exposed to uniform magnetic field to a vertical isothermal surface by homotopy analysis method and collocation method. Indian Journal of Scientific Research, 1(2), 215-222.
  • [38] Hoshyar, H., Ganji, D. D. Majidian, A. R. (2016). Least square method for porous fin in the presence of uniform magnetic field. Journal of Applied Fluid Mechanics, 9 (2), 661-668.
There are 37 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

M. G. Sobamowo

Publication Date June 25, 2018
Submission Date May 1, 2017
Published in Issue Year 2018 Volume: 4 Issue: 5

Cite

APA Sobamowo, M. G. (2018). THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD. Journal of Thermal Engineering, 4(5), 2287-2302. https://doi.org/10.18186/thermal.438485
AMA Sobamowo MG. THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD. Journal of Thermal Engineering. June 2018;4(5):2287-2302. doi:10.18186/thermal.438485
Chicago Sobamowo, M. G. “THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD”. Journal of Thermal Engineering 4, no. 5 (June 2018): 2287-2302. https://doi.org/10.18186/thermal.438485.
EndNote Sobamowo MG (June 1, 2018) THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD. Journal of Thermal Engineering 4 5 2287–2302.
IEEE M. G. Sobamowo, “THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD”, Journal of Thermal Engineering, vol. 4, no. 5, pp. 2287–2302, 2018, doi: 10.18186/thermal.438485.
ISNAD Sobamowo, M. G. “THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD”. Journal of Thermal Engineering 4/5 (June 2018), 2287-2302. https://doi.org/10.18186/thermal.438485.
JAMA Sobamowo MG. THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD. Journal of Thermal Engineering. 2018;4:2287–2302.
MLA Sobamowo, M. G. “THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD”. Journal of Thermal Engineering, vol. 4, no. 5, 2018, pp. 2287-02, doi:10.18186/thermal.438485.
Vancouver Sobamowo MG. THERMAL PERFORMANCE ANALYSIS OF CONVECTIVE-RADIATIVE FIN WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY IN THE PRESENCE OF UNIFORM MAGNETIC FIELD USING PARTIAL NOETHER METHOD. Journal of Thermal Engineering. 2018;4(5):2287-302.

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IMPORTANT NOTE: JOURNAL SUBMISSION LINK http://eds.yildiz.edu.tr/journal-of-thermal-engineering