From Experiments to Numerical Modeling: A Tool for Teaching Heat Transfer in Mechanical Engineering
In this work the numerical simulation of transient heat
transfer in a cylindrical probe is done. An experiment was conducted
introducing a steel cylinder in a heating chamber and registering its
surface temperature along the time during one hour. In parallel, a
mathematical model was solved for one dimension transient heat
transfer in cylindrical coordinates, considering the boundary
conditions of the test. The model was solved using finite difference
method, because the thermal conductivity in the cylindrical steel bar
and the convection heat transfer coefficient used in the model are
considered temperature dependant functions, and both conditions
prevent the use of the analytical solution. The comparison between
theoretical and experimental results showed the average deviation is
below 2%. It was concluded that numerical methods are useful in
order to solve engineering complex problems. For constant k and h,
the experimental methodology used here can be used as a tool for
teaching heat transfer in mechanical engineering, using mathematical
simplified models with analytical solutions.
[1] W.F. Wu, Y.H. Feng and X.X. Zhang. "Heat transfer analysis during
rolling of thin slab in CSP", Acta Metallurgica Sinica (English letters),
Vol.19, No.4, 2006, pp. 244-250.
[2] S. H. Han, S.W. Baek, S.H. Kang and C.Y. Kim. "Numerical analysis of
heating characteristics of a slab in a bench scale reheating furnace", Int.
J. Heat Mass Transfer, Vol.50, No.9-10, 2007, pp. 2019-2023.
[3] A. Jaklic, F.Vode and T. Kolenko. "Online simulation model of the slabreheating
process in a pusher-type furnace", Applied Thermal
Engineering, Vol.27, No.5-6, 2007, pp. 1105-1114.
[4] S. J. Barnett, M.N. Soutsos S.G. Millard and J.H. Bungey. "Strength
development of mortars containing ground granulated blast-furnace slag:
Effect of curing temperature and determination of apparent activation
energies", Cement and Concrete Research, Vol.36, No.3, 2006, pp. 434-
440.
[5] L. Zashkova. "Mathematical modelling of the heat behaviour in the
ceramic chamber furnaces at different temperature baking curves",
Simulation Modelling Practice and Theory, Vol. 16, No.10, 2008, pp.
1640-1658.
[6] M.Y. Kim. "A heat transfer model for the analysis of transient heating of
the slab in a direct-fired walking beam type reheating furnace".
International Journal of Heat and Mass Transfer, Vol.50, No.19-20,
2007, pp. 3740-3748.
[7] M. Hendrickx, C. Silva, F. Oliveira, P. Tobbacka. Desarrollo de
fórmulas empíricas para las temperaturas de esterilización óptimas de
los alimentos calentados por conducci├│n con estudios de coeficientes de
transferencia de calor y método de superficie infinita. Tesis Escuela
Superior de Biotecnología Dr. Antonio Bernardino de Almeida,
Portugal, 2003.
[8] J. García, S. Hervás, J. Rico, A. Sánchez, F. Villatoro. "Comparación de
métodos numéricos para la simulaci├│n de Intercambiadores de Calor
enterrados verticales. Aplicaci├│n a intercambiadores de calor
enterrados". Anales de ingeniería mecánica; Revista de la Asociación
Española de Ingeniería Mecánica, año 15, No.4, 2004, 2481 - 2489.
[9] L. Patiño, Y. Orquín, J. Urchuenguía, P. De Córdoba. "Modelado y
soluci├│n numérica de la conducci├│n de calor transitoria en el subsuelo.
Aplicaci├│n a intercambiadores de calor enterrados". Anales de
ingeniería mecánica; Revista de la Asociación Española de Ingeniería
Mecánica, año 15, No.4, 2004, pp. 2509 - 2517
[10] A. Molina. "Problemática actual en la enseñanza de la ingeniería: una
alternativa para su solución". Ingenierías, Vol. III, No.7, 2000, (abriljunio).
[11] P. Salcedo. Ingeniería de software educativo, teorías y metodologías que
la sustentan, 2002, http:/www.inf.udec.cl.
[12] L. Pineda, X. Arrieta, M. Delgado. "Tecnologías didácticas para la
ense├▒anza aprendizaje de la f├¡sica en educaci├│n superior". Télématique,
Vol.8, ed. 1, 2009.
[13] J. Delors. Los cuatro pilares de la educaci├│n. Ediciones Unesco,
Caracas, 1996.
[14] F. Incropera and D.P. Hewitt. Fundamentos de Transferencia de Calor.
México: Prentice Hall, 1999.
[15] A. Mills. Transferencia de calor. Santafé de Bogot├í: McGraw-Hill,
1997.
[16] S.C. Chapra, P.R. Canale. Métodos numéricos para ingenieros. 5th
Edition. Caracas: McGraw-Hill, 2007
[17] S. W. Churchill and H.H.S. Chu, "Correlating equations for laminar and
turbulent free convection from a horizontal cylinder", Int. J. Heat Mass
Transfer, Vol.18, 1975, pp. 1049-1053.
[1] W.F. Wu, Y.H. Feng and X.X. Zhang. "Heat transfer analysis during
rolling of thin slab in CSP", Acta Metallurgica Sinica (English letters),
Vol.19, No.4, 2006, pp. 244-250.
[2] S. H. Han, S.W. Baek, S.H. Kang and C.Y. Kim. "Numerical analysis of
heating characteristics of a slab in a bench scale reheating furnace", Int.
J. Heat Mass Transfer, Vol.50, No.9-10, 2007, pp. 2019-2023.
[3] A. Jaklic, F.Vode and T. Kolenko. "Online simulation model of the slabreheating
process in a pusher-type furnace", Applied Thermal
Engineering, Vol.27, No.5-6, 2007, pp. 1105-1114.
[4] S. J. Barnett, M.N. Soutsos S.G. Millard and J.H. Bungey. "Strength
development of mortars containing ground granulated blast-furnace slag:
Effect of curing temperature and determination of apparent activation
energies", Cement and Concrete Research, Vol.36, No.3, 2006, pp. 434-
440.
[5] L. Zashkova. "Mathematical modelling of the heat behaviour in the
ceramic chamber furnaces at different temperature baking curves",
Simulation Modelling Practice and Theory, Vol. 16, No.10, 2008, pp.
1640-1658.
[6] M.Y. Kim. "A heat transfer model for the analysis of transient heating of
the slab in a direct-fired walking beam type reheating furnace".
International Journal of Heat and Mass Transfer, Vol.50, No.19-20,
2007, pp. 3740-3748.
[7] M. Hendrickx, C. Silva, F. Oliveira, P. Tobbacka. Desarrollo de
fórmulas empíricas para las temperaturas de esterilización óptimas de
los alimentos calentados por conducci├│n con estudios de coeficientes de
transferencia de calor y método de superficie infinita. Tesis Escuela
Superior de Biotecnología Dr. Antonio Bernardino de Almeida,
Portugal, 2003.
[8] J. García, S. Hervás, J. Rico, A. Sánchez, F. Villatoro. "Comparación de
métodos numéricos para la simulaci├│n de Intercambiadores de Calor
enterrados verticales. Aplicaci├│n a intercambiadores de calor
enterrados". Anales de ingeniería mecánica; Revista de la Asociación
Española de Ingeniería Mecánica, año 15, No.4, 2004, 2481 - 2489.
[9] L. Patiño, Y. Orquín, J. Urchuenguía, P. De Córdoba. "Modelado y
soluci├│n numérica de la conducci├│n de calor transitoria en el subsuelo.
Aplicaci├│n a intercambiadores de calor enterrados". Anales de
ingeniería mecánica; Revista de la Asociación Española de Ingeniería
Mecánica, año 15, No.4, 2004, pp. 2509 - 2517
[10] A. Molina. "Problemática actual en la enseñanza de la ingeniería: una
alternativa para su solución". Ingenierías, Vol. III, No.7, 2000, (abriljunio).
[11] P. Salcedo. Ingeniería de software educativo, teorías y metodologías que
la sustentan, 2002, http:/www.inf.udec.cl.
[12] L. Pineda, X. Arrieta, M. Delgado. "Tecnologías didácticas para la
ense├▒anza aprendizaje de la f├¡sica en educaci├│n superior". Télématique,
Vol.8, ed. 1, 2009.
[13] J. Delors. Los cuatro pilares de la educaci├│n. Ediciones Unesco,
Caracas, 1996.
[14] F. Incropera and D.P. Hewitt. Fundamentos de Transferencia de Calor.
México: Prentice Hall, 1999.
[15] A. Mills. Transferencia de calor. Santafé de Bogot├í: McGraw-Hill,
1997.
[16] S.C. Chapra, P.R. Canale. Métodos numéricos para ingenieros. 5th
Edition. Caracas: McGraw-Hill, 2007
[17] S. W. Churchill and H.H.S. Chu, "Correlating equations for laminar and
turbulent free convection from a horizontal cylinder", Int. J. Heat Mass
Transfer, Vol.18, 1975, pp. 1049-1053.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51060", author = "D. Zabala and Y. Cárdenas and G. Núñez", title = "From Experiments to Numerical Modeling: A Tool for Teaching Heat Transfer in Mechanical Engineering", abstract = "In this work the numerical simulation of transient heat
transfer in a cylindrical probe is done. An experiment was conducted
introducing a steel cylinder in a heating chamber and registering its
surface temperature along the time during one hour. In parallel, a
mathematical model was solved for one dimension transient heat
transfer in cylindrical coordinates, considering the boundary
conditions of the test. The model was solved using finite difference
method, because the thermal conductivity in the cylindrical steel bar
and the convection heat transfer coefficient used in the model are
considered temperature dependant functions, and both conditions
prevent the use of the analytical solution. The comparison between
theoretical and experimental results showed the average deviation is
below 2%. It was concluded that numerical methods are useful in
order to solve engineering complex problems. For constant k and h,
the experimental methodology used here can be used as a tool for
teaching heat transfer in mechanical engineering, using mathematical
simplified models with analytical solutions.", keywords = "Heat transfer experiment, thermal conductivity,finite difference, engineering education.", volume = "6", number = "11", pages = "2329-4", }
