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16.2.4 Calculation of Temperature

The calculation method for temperature will depend on whether the model is adiabatic or non-adiabatic.

Adiabatic Temperature Calculation

For the adiabatic premixed combustion model, the temperature is assumed to vary linearly between the temperature of the unburnt mixture, $T_u$, and the temperature of the burnt products under adiabatic conditions, $T_{\rm ad}$:

 T = (1 - c) T_u + c T_{\rm ad} (16.2-21)

Non-Adiabatic Temperature Calculation

For the non-adiabatic premixed combustion model, FLUENT solves an energy transport equation in order to account for any heat losses or gains within the system. These losses/gains may include heat sources due to chemical reaction or, for example, heat losses due to radiation. The energy equation in terms of sensible enthalpy, $h$, for the fully premixed fuel (see Equation  13.2-3) is as follows:

 \frac{\partial}{\partial t}(\rho h) + \nabla \cdot (\rho {\v... ..._t}{c_p} \nabla h \right) + S_{h,{\rm chem}} + S_{h,{\rm rad}} (16.2-22)

$S_{h,{\rm rad}}$ represents the heat losses due to radiation and $S_{h,{\rm chem}}$ represents the heat gains due to chemical reaction:

 S_{h,{\rm chem}} = \rho S_c H_{\rm comb} Y_{\rm fuel} (16.2-23)

  $S_c$ = normalized average rate of product formation (s $^{-1}$)
  $H_{\rm comb}$ = heat of combustion for burning 1 kg of fuel (J/kg)
  $Y_{\rm fuel}$ = fuel mass fraction of unburnt mixture

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© Fluent Inc. 2006-09-20