Abstract
Artificial neural network (ANN) is used to retrieve one parameter in conduction–radiation heat transfer problem in porous ceramic matrix. Air flows through a 2D rectangular porous ceramic matrix (PCM) with uniform velocity. The PCM is assumed to be conducting and radiating, also a localized heat generation zone is situated at center. All the governing equations together with appropriate boundary conditions are solved by using finite volume method (FVM), to compute the temperature profiles of the gas and the solid phase. Both the temperature profiles are generated for different values of heat transfer coefficient (HTC). The ANN is trained by using the solid and gas temperature profile, along with the corresponding HTC. Neurons in the ANN are trained by using Levenberg–Marquardt (LM). Once the ANN model is trained, it is analyzed and explored to determine one parameter in the problem. The trained ANN model is fed with an unknown solid and gas temperature profiles as input, the ANN gives back the corresponding HTC as output. The retrieval of HTC by LM algorithm is found to be very accurate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- \(A\) :
-
Porous matrix surface area per unit, \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\text{m}}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\text{m}}$}}\)
- \(\eta\) :
-
Dimensionless coordinate
- \(c\) :
-
Specific heat at constant pressure, \({\raise0.7ex\hbox{${\text{J}}$} \!\mathord{\left/ {\vphantom {{\text{J}} {{\text{kg}} \cdot {\text{K}}}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{kg}} \cdot {\text{K}}}$}}\)
- \(\theta\) :
-
Dimensionless temperature
- \(G\) :
-
Emissive power, \({\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{2} }$}}\)
- \(\rho\) :
-
Density, \({\raise0.7ex\hbox{${{\text{kg}}}$} \!\mathord{\left/ {\vphantom {{{\text{kg}}} {{\text{m}}^{3} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{3} }$}}\)
- \(h\) :
-
Heat transfer coefficient, \({\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} \cdot {\text{K}}}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{2} \cdot {\text{K}}}$}}\)
- \(\sigma\) :
-
Stefan–Boltzmann constant, \(5.67 \times 10^{ - 8} {\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} \cdot {\text{K}}^{4} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{2} \cdot {\text{K}}^{4} }$}}\)
- \(i\) :
-
Intensity of radiation, \({\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} \cdot {\text{sr}}}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{2} \cdot {\text{sr}}}$}}\)
- \(\varphi\) :
-
Porosity of porous ceramic matrix
- \(k\) :
-
Thermal conductivity, \({\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}} \cdot {\text{K}}}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}} \cdot {\text{K}}}$}}\)
- \(\Psi_{{{\text{Rad}}}}\) :
-
Non-dimensional radiative heat flux
- \(L_{{\text{x}}}\) :
-
Length in x-direction, \({\text{m}}\)
- \(\omega\) :
-
Scattering albedo of solid
- \(L_{{\text{y}}}\) :
-
Length in y-direction, \({\text{m}}\)
- \(q_{{\text{R}}}\) :
-
Radiative heat flux, \({\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{2} }$}}\)
- E :
-
East direction
- \(\dot{Q}\) :
-
Heat generation rate per unit volume, \({\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{3} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{3} }$}}\)
- W :
-
West direction
- \(S_{{{\text{av}}}}\) :
-
Average source term, \({\raise0.7ex\hbox{${\text{W}}$} \!\mathord{\left/ {\vphantom {{\text{W}} {{\text{m}}^{2} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${{\text{m}}^{2} }$}}\)
- N :
-
North direction
- \(T\) :
-
Temperature, \({\text{K}}\)
- S :
-
South direction
- μ :
-
Velocity, \({\raise0.7ex\hbox{${\text{m}}$} \!\mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\text{s}}$}}\)
- e :
-
Exit of PCM
- g :
-
Gas phase
- \(\beta\) :
-
Extinction coefficient, \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\text{m}}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\text{m}}$}}\)
- i :
-
Inlet of PCM
- \(\delta\) :
-
Unit step function
- s :
-
Solid phase
- \(\varepsilon\) :
-
Emissivity
- *:
-
Non-dimensional
References
Backus G (1988) Hard and soft prior bounds in geophysical inverse problems. Geophys J 94:249–261
Özisik MN, Orlande HRB (2000) Inverse Heat Transfer Fundamentals and Applications. Taylor & Francis, New York
Osman AM, Beck JV (1990) Investigation of transient heat transfer coefficients in quenching experiments. ASME J Heat Transf 112:843–848
Saggio-Woyanski J, Scott C (1992) Processing of porous ceramics. Am Ceram Soc Bull 71:1674–1682
Kakati S, Mahanta P, Kakoty S (2007) Performance analysis of pressurized kerosene stove with porous medium inserts. J Sci Ind Res 66:565–569
Prosuntsov PV, Barinov DY (2021) Analysis of combined radiation-conductive heat transfer during destruction of porous carbon-ceramic matrix composite material of thermal protection. In: AIP conference proceedings, Vol 2318, 020024
Mishra VK, Mishra SC, Basu DN (2015) Combined mode conduction and radiation heat transfer in a porous medium and estimation of optical properties of the porous matrix. Numerical Heat Transfer (A) 67(10):1119–1135
Chopade RP, Agnihotri E, Singh AK, Kumar A, Uppaluri R, Mishra SC, Mahanta P (2011) Application of a particle swarm algorithm for parameter retrieval in a transient conduction-radiation problem. Numerical Heat Transfer (A) 59(9):672–692
Sans M, Schick V, Parent G, Farges O (2020) Experimental characterization of the coupled conductive and radiative heat transfer in ceramic foams with a flash method at high temperature. Int J Heat and Mass Transf 148:119077
Anand K, Bhardwaj A, Chaudhuri S, Mishra VK (2022) Self-organizing map network for the decision making in combined mode conduction-radiation heat transfer in porous medium. Arab J Sci Eng
Mishra VK, Dasgupta U, Patra S, Pal R, Anand K (2022) A dynamic two-level artificial neural network for estimation of parameters in combined mode conduction-radiation heat transfer in porous medium: an application to handle huge dataset with noise. Heat Transfer 51:1306–1335
Song FQ, Wen ZD, Wang ZY, Liu EYXL (2019) Numerical study and optimization of a porous burner with annular heat recirculation. Appl Therm Eng. https://doi.org/10.1016/j.applthermaleng.2019.113741
Jambunathan K, Hartle S, Ashforth-Frost S, Fontama VN (1996) Evaluating convective heat transfer coefficients using neural networks. Int J Heat Mass Transf 39:2329–2332
Sablani SS (2001) A neural network approach for non-iterative calculation of heat transfer coefficient in fluid-particle systems. Chem Eng Process 40:363–369
Mishra VK, Chaudhuri S (2021) Implementation of stochastic optimization method-assisted radial basis neural network for transport phenomenon in non-newtonian third-grade fluids: assessment of five optimization tools. Arab J Sci Eng 46:11797–11818
Mishra VK, Chaudhuri S (2021) Genetic algorithm-assisted artificial neural network for retrieval of a parameter in a third grade fluid flow through two parallel and heated plates. Heat Transfer 50:2090–2128
Tong T, Sathe S (1991) Heat transfer characteristics of porous radiant burners. J Heat Transf 113:423–428
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Acharya, S., Mishra, V.K., Patel, J.K., Gupta, G., Sah, M.K., Shah, P. (2023). Retrieval of Parameter in Combined Mode Conduction–Radiation Problem in Porous Ceramic Matrix by Artificial Neural Network . In: Revankar, S., Muduli, K., Sahu, D. (eds) Recent Advances in Thermofluids and Manufacturing Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-4388-1_25
Download citation
DOI: https://doi.org/10.1007/978-981-19-4388-1_25
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-4387-4
Online ISBN: 978-981-19-4388-1
eBook Packages: EngineeringEngineering (R0)