Soluciones Analíticas y Numéricas para un Problema de Transferencia de Calor en Materiales Bicapa
DOI:
https://doi.org/10.70567/mc.v41i21.113Palavras-chave:
Transferencia de calor, Materiales compuestos, Resistencia térmicaResumo
Este artículo presenta un análisis teórico de un problema de transferencia de calor unidimensional en un material bicapa con difusión, advección, generación o pérdida de calor interna linealmente dependiente de la temperatura en cada capa, y generación de calor debido a fuentes externas. Además, se considera la resistencia térmica ofrecida por la interfaz entre los materiales. La situación de interés se modela matemáticamente, se encuentran soluciones analíticas explícitas utilizando técnicas de Fourier, y se formula un esquema de diferencias finitas convergente para simular casos particulares. La solución es coherente con resultados previos. Se incluye un ejemplo numérico que muestra coherencia entre los resultados obtenidos y la física del problema. Las conclusiones extraídas en este trabajo amplían la comprensión teórica de la transferencia de calor en materiales bicapa y también pueden contribuir a mejorar el diseño térmico de sistemas de ingeniería multicapa.
Referências
Bandhauer T., Garimella S., y Fuller T. A critical review of
thermal issues in lithium-ion batteries. J. Electrochem. Soc.,
158(3):R1-R25, 2011. https://doi.org/10.1149/1.3515880
Becker S. Analytic one dimensional transient conduction into a
living perfuse/non-perfuse two layer composite system. Heat Mass
Transfer, 48:317-327, 2012.
https://doi.org/10.1007/s00231-011-0886-5
Becker S. y Herwing H. One dimensional transient heat conduction in
segmented fin-like geometries with distinct discrete peripheral
convection. Int. J. Therm. Sci., 71:148-162, 2013.
https://doi.org/10.1016/j.ijthermalsci.2013.04.004
Carson J. Modelling thermal diffusivity of heterogeneous materials
based on thermal diffusivities of components with implications for
thermal diffusivity and thermal conductivity measurement. Int. J.
Thermophys., 43(108), 2022.
https://doi.org/10.1007/s10765-022-03037-6
Caunce J., Barry S., y Mercer G. A spatially dependent model for
washing wool. Appl. Math. Model., 32(4):389-404, 2008.
https://doi.org/10.1016/j.apm.2006.12.010
Choobineh L. y Jain A. An explicit analytical model for rapid
computation of temperature field in a three-dimensional integrated
circuit (3d ic). Int. J. Therm. Sci., 87:103-109, 2015.
https://doi.org/10.1016/j.ijthermalsci.2014.08.012
Dias C. A method of recursive images to solve transient heat
diffusion in multilayer materials. Int. J. Heat Mass Transfer,
85:1075-1083, 2015.
https://doi.org/10.1016/j.ijheatmasstransfer.2015.01.138
Esho I., Shah K., y Jain A. Measurements and modeling to determine
the critical temperature for preventing thermal runaway in li-ion
cells. Appl. Therm. Eng., 145:287-294, 2018.
https://doi.org/10.1016/j.applthermaleng.2018.09.016
Hickson R., Barry S., y Mercer G. Critical times in multilayer
diffusion. part 1: exact solutions.Int. J. Heat Mass Transfer,
52:5776-5783, 2009.
https://doi.org/10.1016/j.ijheatmasstransfer.2009.08.013
Jain A., Zhou L., y Parhizi M. Multilayer one-dimensional
convection-diffusion-reaction (cdr) problem: Analytical solution
and imaginary eigenvalue analysis. Int. J. Heat Mass Transfer,
177:121465, 2021.
https://doi.org/10.1016/j.ijheatmasstransfer.2021.121465
Johansson B. y Lesnic D. A method of fundamental solutions for
transient heat conduction in layered materials. Eng. Anal. Boundary
Elem., 33(12):1362-1367, 2009.
https://doi.org/10.1016/j.enganabound.2009.04.014
Kim A. Complete analytic solutions for
convection-diffusion-reaction-source equations without using an
inverse laplace transform. Sci. Rep., 10:8040, 2020.
https://doi.org/10.1038/s41598-020-63982-w
Liu C. y Ball W. Analytical modeling of diffusion-limited
contamination and decontamination in a two-layer porous medium.
Adv. Water. Resour., 21(4):297-313, 1998.
https://doi.org/10.1016/S0309-1708(96)00062-0
Liu G. y Si B. Analytical modeling of one-dimensional diffusion in
layered systems with position-dependent diffusion coefficients.
Adv. Water. Resour., 31(2):251-268, 2008.
https://doi.org/10.1016/j.advwatres.2007.08.008
Liu G. y Si B. Multi-layer diffusion model and error analysis
applied to chamber-based gasfluxes measurements. Agric. For.
Meteorol., 149(1):169-178, 2009.
https://doi.org/10.1016/j.agrformet.2008.07.012
Mantzavinos D., Papadomanolaki M., Saridakis Y., y Sifalakis A.
Fokas transform method for a brain tumor invasion model with
heterogeneous diffusion in 1 + 1 dimensions. Appl. Numer.Math.,
104:47-61, 2016. https://doi.org/10.1016/j.apnum.2014.09.006
McGinty S., McKee S., Wadsworth R., y McCormick C. Modelling
drug-eluting stents. Math.Med. Biol., 28(1):1-29, 2011.
https://doi.org/10.1093/imammb/dqq003
Mitragotri S., Anissimov Y., Bunge A., Frasch H., Guy R., Hadgraft
J., Kasting G., Lane M., y Roberts M. Mathematical models of skin
permeability: An overview. Int. J. Pharm.,418(1):115-129, 2011.
https://doi.org/10.1016/j.ijpharm.2011.02.023
Monte F.d. Transient heat conduction in one-dimensional composite
slab. a 'natural' analytic approach. Int. J. Heat Mass Transfer,
43(19):3607-3619, 2000.
https://doi.org/10.1016/S0017-9310(00)00008-9
Monte F.d. An analytic approach to the unsteady heat conduction
processes in one-dimensional composite media. Int. J. Heat Mass
Transfer, 45(6):1333-1343, 2002.
https://doi.org/10.1016/S0017-9310(01)00226-5
Pasupuleti R., Wang Y., Shabalin I., Li L., Liu Z., y Grove S.
Modelling of moisture diffusion in multilayer woven fabric
composites. Comput. Mater. Sci., 50(5):1675-1680, 2011.
https://doi.org/10.1016/j.commatsci.2010.12.028
Pennes H., Shah K., y Jain A. Analysis of tissue and arterial blood
temperature in the resting human forearm. J. Appl. Phys.,
1(2):93-122, 1948. https://doi.org/10.1152/jappl.1948.1.2.93
Rodrigo M. y Worthy A. Solution of multilayer diffusion problems
via the laplace transform.J. Math. Anal. Appl., 444(1):475-502,
2016. https://doi.org/10.1016/j.jmaa.2016.06.042
Rubio D., Tarzia D., y Umbricht G. Heat transfer process with
solid-solid interface: Analytical and numerical solutions. WSEAS
trans. Math., 20:404-414, 2021.
https://doi.org/10.37394/23206.2021.20.42
Rubio D., Umbricht G., Saintier N., Morvidone M., y Tarzia D.
Non-invasive study to determine changes in physical properties of
multilayer materials. MRS. Adv., 7:1115-1119, 2022.
https://doi.org/10.1557/s43580-022-00463-4
Shah K., Chalise D., y Jain A. Experimental and theoretical
analysis of a method to predict thermal runaway in li-ion cells. J.
Power Sources, 330:167-174, 2016.
https://doi.org/10.1016/j.jpowsour.2016.08.133
Skyllas-Kazacos M., Chakrabarti M., Hajimolana S., Mjalli F., y
Saleem M. Progress in flow battery research and development. J. Electrochem. Soc., 158(8):R55-R79, 2011. https://doi.org/10.1149/1.3599565
Umbricht G. y Rubio D. Optimal estimation of thermal diffusivity in an energy transfer problem. WSEAS trans. Fluid Mech., 16:222-231, 2021. https://doi.org/10.37394/232013.2021.16.21
Umbricht G., Rubio D., Echarri R., y Hasi C.E. A technique to estimate the transient coefficient of heat transfer by convection. Lat. Am. Appl. Res., 50(3):229-234, 2020a. https://doi.org/10.52292/j.laar.2020.179
Umbricht G., Rubio D., y Tarzia D. Estimation technique for a contact point between two materials in a stationary heat transfer problem. Math. Modell. Eng. problem, 7(4):607-613, 2020b. https://doi.org/10.18280/mmep.070413
Umbricht G., Rubio D., y Tarzia D. Estimation of a thermal conductivity in a stationary heat transfer problem with a solid-solid interface. Int. J. Heat. Technol., 39(2):337-344, 2021. https://doi.org/10.18280/ijht.390202
Umbricht G., Rubio D., y Tarzia D. Determination of thermal conductivities in multilayer materials. WSEAS trans. Heat Mass Transfer, 17:188-195, 2022a. https://doi.org/10.37394/232012.2022.17.20
Umbricht G., Tarzia D., y Rubio D. Determination of two homogeneous materials in a bar with solid-solid interface. Math. Modell. Eng. problem, 9(3):568-576, 2022b. https://doi.org/10.18280/mmep.090302
Yavaraj R.and Senthilkumar D. Numerical analysis of non-fourier heat conduction dynamics in the composite layer. J. Mech. Eng. Sci., 17(3):9597-9615, 2023. https://doi.org/10.15282/jmes.17.3.2023.6.0760
Yuan W.b., Yu N., Li L.y., y Fang Y. Heat transfer analysis in multi-layered materials with interfacial thermal resistance. Compos. Struct., 293(1):115728, 2022.https://doi.org/10.1016/j.compstruct.2022.115728
Zhou L., Parhizi M., y Jain A. Theoretical modeling of heat transfer in a multilayer rectangular body with spatially-varying convective heat transfer boundary condition. Int. J. Therm. Sci., 170:107156, 2021. https://doi.org/10.1016/j.ijthermalsci.2021.107156
Downloads
Publicado
Edição
Seção
Licença
Copyright (c) 2024 Asociación Argentina de Mecánica Computacional
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Esta publicação é de acesso aberto diamante, sem custos para autores ou leitores.
Somente os artigos que foram aceitos para publicação e apresentados no congresso da AMCA serão publicados.
