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ABSTRACT
This article reports a study on simultaneous estimation of four parameters for combined-mode conduction and radiation heat transfer in a 2D rectangular porous matrix with a localized volumetric heat generation source. Air flows at uniform velocity through the conducting and radiating porous matrix. In the heat generation zone, and its downstream, the gas temperature is higher than that of the solid, and in the upstream the reverse situation occurs. This temperature difference between gas and the solid results in heat transfer by convection between the two phases, and the analysis thus requires consideration of separate energy equations for the two phases. The solid being involved radiatively, the volumetric radiative source term, in the form of the divergence of radiative heat flux, appears only in the solid-phase energy equation. The two equations are coupled through the convective heat transfer term. Four parameters—scattering albedo, emissivity, solid conductivity, and heat transfer coefficient—are simultaneously estimated based on the solid and gas temperature distributions, and convective and radiative heat fluxes at the outer surface of the porous matrix. In both direct and inverse approaches, the energy equations are solved using the finite volume method. For a test case, determining the genetic algorithm is much more time-consuming than the global search algorithm; in other cases, parameter estimations are done using the global search algorithm. Parameters are found to be estimated accurately.
Nomenclature
| A | = | surface area per unit volume of solid, |
| c | = | specific heat at constant pressure, |
| G | = | emissive power, |
| h | = | heat transfer coefficient, |
| I | = | radiation intensity, |
| J | = | objective function |
| k | = | thermal conductivity, |
| Lx | = | length in x direction, m |
| Ly | = | length in y direction, m |
| qR | = | radiative heat flux, |
| = | heat generation rate per unit volume, | |
| Sav | = | average source term, |
| T | = | temperature, K |
| u | = | velocity, |
| β | = | extinction coefficient, |
| δ | = | unit step function |
| ϵ | = | emissivity |
| η | = | dimensionless coordinate |
| θ | = | dimensionless temperature |
| ρ | = | density, |
| σ | = | Stefan–Boltzmann constant, |
| φ | = | porosity |
| ΨRad | = | nondimensional radiative heat flux |
| ΨConv | = | nondimensional convective heat flux |
| ω | = | scattering albedo |
| Subscripts | = | |
| e | = | exit |
| g | = | gas |
| i | = | inlet |
| s | = | solid |
| Superscripts | = | |
| * | = | nondimensional |
Nomenclature
| A | = | surface area per unit volume of solid, |
| c | = | specific heat at constant pressure, |
| G | = | emissive power, |
| h | = | heat transfer coefficient, |
| I | = | radiation intensity, |
| J | = | objective function |
| k | = | thermal conductivity, |
| Lx | = | length in x direction, m |
| Ly | = | length in y direction, m |
| qR | = | radiative heat flux, |
| = | heat generation rate per unit volume, | |
| Sav | = | average source term, |
| T | = | temperature, K |
| u | = | velocity, |
| β | = | extinction coefficient, |
| δ | = | unit step function |
| ϵ | = | emissivity |
| η | = | dimensionless coordinate |
| θ | = | dimensionless temperature |
| ρ | = | density, |
| σ | = | Stefan–Boltzmann constant, |
| φ | = | porosity |
| ΨRad | = | nondimensional radiative heat flux |
| ΨConv | = | nondimensional convective heat flux |
| ω | = | scattering albedo |
| Subscripts | = | |
| e | = | exit |
| g | = | gas |
| i | = | inlet |
| s | = | solid |
| Superscripts | = | |
| * | = | nondimensional |