Fixed Cartesian grid based numerical model for solidification process of semi-transparent materials II: Reflection and refraction or transmission of the thermal radiation at the solid–liquid interface

Łapka, Piotr; Furmański, Piotr

doi:10.1016/j.ijheatmasstransfer.2012.03.077

Cited by 19 publications

(12 citation statements)

References 20 publications

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“…Therefore, distribution of spectral radiative intensity was given by the following radiative transfer equation [22][23][24][25]:…”

Section: Radiative Heat Transfermentioning

confidence: 99%

“…(6), (8)- (11) were given by the following relationships: In the above equations subscripts and superscripts: a, c, e, f, h, i, in, p, s, w, L and R denote the air, cooling water, surroundings, fabric, hot gases or source of thermal radiation, interface, incident, internal surface of the plate, external surface of the plate, clothing external surface, left and right side of the interface, respectively, while E b is the blackbody emissive power [22], h and h m -convective heat and mass transfer coefficients, respectively, n -refractive index, q -heat flux, r -hemispherical surface reflectivity [22,25,26] (for transparent interface r was found by averaging the Fresnel reflectivity over the hemisphere), respectively, t -hemispherical surface transmissivity and ε -surface emissivity.…”

Section: ð9þmentioning

confidence: 99%

“…(10) and (16a, 16b) emission and diffusive reflection and transmission of the incident radiation. For more details see [24][25][26]. Initial conditions for Eqs.…”

Section: ð9þmentioning

confidence: 99%

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Verification and validation of an advanced model of heat and mass transfer in the protective clothing

Łapka

Furmański

2018

Heat Mass Transfer

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The paper presents verification and validation of an advanced numerical model of heat and moisture transfer in the multi-layer protective clothing and in components of the experimental stand subjected to either high surroundings temperature or high radiative heat flux emitted by hot objects. The developed model included conductive-radiative heat transfer in the hygroscopic porous fabrics and air gaps as well as conductive heat transfer in components of the stand. Additionally, water vapour diffusion in the pores and air spaces as well as phase transition of the bound water in the fabric fibres (sorption and desorption) were accounted for. All optical phenomena at internal or external walls were modelled and the thermal radiation was treated in the rigorous way, i.e., semi-transparent absorbing, emitting and scattering fabrics with the non-grey properties were assumed. The air was treated as transparent. Complex energy and mass balances as well as optical conditions at internal or external interfaces were formulated in order to find values of temperatures, vapour densities and radiation intensities at these interfaces. The obtained highly non-linear coupled system of discrete equations was solved by the Finite Volume based in-house iterative algorithm. The developed model passed discretisation convergence tests and was successfully verified against the results obtained applying commercial software for simplified cases. Then validation was carried out using experimental measurements collected during exposure of the protective clothing to high radiative heat flux emitted by the IR lamp. Satisfactory agreement of simulated and measured temporal variation of temperature at external and internal surfaces of the multi-layer clothing was attained.

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“…Therefore, distribution of spectral radiative intensity was given by the following radiative transfer equation [22][23][24][25]:…”

Section: Radiative Heat Transfermentioning

confidence: 99%

Section: ð9þmentioning

confidence: 99%

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Verification and validation of an advanced model of heat and mass transfer in the protective clothing

Łapka

Furmański

2018

Heat Mass Transfer

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“…Fragments of boundaries of thus modified control volumes coincide with the SLI. More details are given in Section 4.1 and in [12][13][14][15].…”

Section: Front Tracking Proceduresmentioning

confidence: 99%

“…This allows using different macroscopic models of fluid flow resistance within distinct, thus recognized, dendritic zones. Similar approach of tracking the SLI during solidification of semi-transparent medium has been developed in [12][13][14][15] providing the possibility of analyzing the role of SLI optical properties on solidification of an optically functional material.…”

Section: Introductionmentioning

confidence: 99%