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A New Method to Calculate Incident Radiant Heat Flux by Using Plate Thermometer

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Abstract

Plate thermometer (PT) that consists of a thin metal plate and a layer of inorganic insulation material attached to the backside of the metal plate has been used to calculate the incident radiant heat flux by other researchers. However, the incident radiant heat flux is often underestimated using PT as the heat loss from the metal plate is not appropriately reflected in the calculation. Especially when PT is placed in low ambient temperature conditions or in a heating phase, the underestimation becomes more significant. Besides the heat loss effect, some PT properties such as surface emissivity and thermo-physical properties as well as errors of temperature measurements affect the accuracy of incident radiant heat flux calculations. In the current study, a new incident radiant heat flux calculation method is proposed to overcome the aforementioned inaccuracies. The temperature that a thermally thin metal element should ideally achieve with a perfectly insulated back surface is correlated with the actually measured surface temperature under known heat fluxes for calibration. From this correlation, a set of equations to calculate the incident radiant heat flux is derived for a mixed radiation/convection environment. For validation, the incident radiant heat fluxes calculated from the proposed method and measured from a commercially available Schmidt-Boelter type total heat flux gauge were compared and a good agreement was observed.

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Abbreviations

\(c_{p}\) :

Specific heat of Inconel 600 metal plate (kJ/kg K)

\(c_{ins}\) :

Specific heat of ceramic fiber insulation (kJ/kg K)

\(c_{met}\) :

Specific heat of metal plate (kJ/kg K)

C :

Thin skin calorimeter correction factor

\(C_{PT}\) :

Heat storage lumped heat capacity (J/m2 K)

\(d_{ins}\) :

Thickness of insulation (m)

\(d_{met}\) :

Thickness of metal plate (m)

\(h\) :

Convective heat transfer coefficient (W/m2 K)

\(h_{cont}\) :

Contact correction factor (W/m2 K)

\(k\) :

Thermal conductivity (W/m K)

\(K_{cond}\) :

Conduction correction factor (W/m2 K)

\(L\) :

Length (m)

\(\overline{Nu}\) :

Nusselt number

\(\Pr\) :

Prandtl number

\(\dot{q}^{\prime\prime}_{cond}\) :

Conduction loss (W/m2)

\(\dot{q}^{\prime\prime}_{cont}\) :

Contact heat loss (W/m2)

\(\dot{q}^{\prime\prime}_{conv}\) :

Convective heat flux (W/m2)

\(\dot{q}^{\prime\prime}_{HFG}\) :

Total heat flux of Schmidt-Boelter type total flux gauge (W/m2)

\(\dot{q}^{\prime\prime}_{inc}\) :

Incident heat flux (W/m2)

\(\dot{q}^{\prime\prime}_{{inc{\hbox{-}}rad}}\) :

Incident radiant heat flux (W/m2)

\(\dot{q}^{\prime\prime}_{{inc{\hbox{-}}rad{\hbox{-}}C/R}}\) :

Incident radiant heat flux in a mixed radiation/convection environment (W/m2)

\(\dot{q}^{\prime\prime}_{{inc{\hbox{-}}rad{\hbox{-}}R}}\) :

Incident radiant heat flux in a radiation-only environment (W/m2)

\(\dot{q}^{\prime\prime}_{loss}\) :

Heat loss flux (W/m2)

\(\dot{q}^{\prime\prime}_{{rad{\hbox{-}}in}}\) :

Radiant heat flux into PT (W/m2)

\(\dot{q}^{\prime\prime}_{{re{\hbox{-}}rad}}\) :

Re-radiation (W/m2)

\(\dot{q}^{\prime\prime}_{stored}\) :

Heat energy stored (W/m2)

\(Ra\) :

Rayleigh number

Re :

Reynolds number

\(T_{amb}\) :

Ambient temperature (K)

\(T_{AST}\) :

Adiabatic surface temperature (K)

\(T_{\infty }\) :

Ambient temperature (K)

\(T_{g}\) :

Gas temperature around PT (K)

\(T_{PT}\) :

Temperature of metal plate (K)

\(T_{s}\) :

Measured surface temperature of Inconel 600 metal plate (K)

\(T_{{s{\hbox{-}}ideal}}\) :

The surface temperature of Inconel 600 metal plate with a perfectly insulated back surface (K)

\(T_{0}\) :

Temperature of the first node of ceramic fiber board (K)

\(t\) :

Time (s)

\(\beta\) :

Portion of the insulation

\(\varepsilon_{HFG}\) :

Surface emissivity of Schmidt-Boelter type total heat flux gauge

\(\varepsilon_{PT}\) :

Surface emissivity of PT

\(\alpha_{disc}\) :

Absorptivity of the thin skin calorimeter metallic disc

\(\rho\) :

Density of Inconel 600 metal plate (kg/m3)

\(\rho_{ins}\) :

Density of insulation (kg/m3)

\(\rho_{met}\) :

Density of metal plate (kg/m3)

\(\sigma\) :

Stefan-Boltzmann constant (W/m2 K4)

\(\delta\) :

Thickness of Inconel 600 metal plate (m)

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Authors and Affiliations

  1. Jacobs Engineering, 1999 Bryan Street, Suite 1300, Dallas, TX, 75201, USA

    Qingtong Liu

  2. Fire Protection and Safety Engineering, Oklahoma State University, 543 Engineering North, Stillwater, OK, 74075, USA

    Haejun Park

  3. Artie McFerrin Department of Chemical Engineering, Jack E. Brown Chemical Engineering Building, 3122 TAMU, College Station, TX, 77843, USA

    Ruiqing Shen

  4. Fire Protection and Safety Engineering, Oklahoma State University, 501 Engineering North, Stillwater, OK, 74075, USA

    Lahiru Jayathunga-Mudiyanselage

Authors
  1. Qingtong Liu
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  2. Haejun Park
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  4. Lahiru Jayathunga-Mudiyanselage
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Correspondence to Haejun Park.

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Liu, Q., Park, H., Shen, R. et al. A New Method to Calculate Incident Radiant Heat Flux by Using Plate Thermometer. Fire Technol 57, 341–359 (2021). https://doi.org/10.1007/s10694-020-01006-9

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