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Developing mathematical modeling of the heat and mass transfer in a planar micro-combustor with detailed reaction mechanisms

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Abstract

In this study, an analytical investigation of heat and mass transfer in a planar micro-combustor with considering the detailed reaction mechanisms for a methane/air mixture is presented. The primary objective is to propose practical solutions to manage both heat and mass transfer, which are critical problems in micro-combustors. The reactive mixture is divided into pre-flame, reaction, and post-flame zones. Then, the partial differential equations of energy and species are analytically solved in each zone with regard to the detailed reaction mechanisms and matching conditions. Moreover, to make a general investigation, appropriate non-dimensional physical parameters are proposed considering interactions between reactive mixture, solid structure, and ambient. As a result, proper correlations are proposed for the wall temperature distribution under different conditions that can be suitable for the relative numerical simulations. It is shown that a maximum decrease of 45% occurs for the gas temperature at the post-flame zone when flow Peclet number is reduced by 50%. Furthermore, by increasing the solid–fluid thermal diffusion ratio from 50 to 100 and 100 to 200, the CO conversion rate is decreased around 77% and 16%, respectively.

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Abbreviations

A :

Frequency factor, (cm3 mol−1 s−1)

\(A_{\text{m}}\) :

Matching condition coefficients

\(A_{\text{n}}\) :

Boundary condition coefficients

Bi:

Biot number

\(C_{\text{p}}\) :

Constant pressure specific heat, (J kg−1 K−1)

D s :

Mass diffusivity of species, (m2 s−1)

d :

Half of distance between parallel plates, (m)

E :

Activation energy, (J mol−1)

H :

Enthalpy of reaction, (J m−3)

h :

External heat transfer coefficient (W m−2  K−1)

IETR:

Internal–external thermal resistance

k :

Thermal conductivity, (W m−1 K−1)

Pe:

Flow Peclet number

Pem :

Mass Peclet number

R :

Global gas constant, (J mol−1 K−1)

SFTDR:

Solid–fluid thermal diffusion ratio

\(S_{\text{T}}\) :

Normalized source term of energy equation

T :

Temperature, (K)

T a :

Adiabatic flame temperature, (K)

\(t_{\text{w}}\) :

Wall thickness, (m)

U :

x-direction velocity, (m s−1)

X :

Normalized axial coordinate

x :

Axial coordinate, (m)

y :

Mole fraction

Z :

Normalized perpendicular coordinate

z :

Perpendicular coordinate, (m)

\(\alpha\) :

Thermal diffusivity, (m2 s−1)

\(\delta\) :

Normalized reaction zone thickness

\(\varepsilon\) :

Reaction zone thickness, (m)

\(\theta\) :

Normalized temperature

ξ :

Internal–external thermal resistance

\(\rho\) :

Density, (kg m−3)

\(\tau\) :

Solid–fluid thermal diffusion ratio

\(\omega_{\text{r}}\) :

Net rate of each reaction, (s−1)

\(\omega_{\text{s}}\) :

Net production rate of species, (s−1)

g :

Gas mixture

i :

Inlet

pre:

Pre-flame zone

post:

Post-flame zone

react:

Reaction zone

w :

Wall

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Acknowledgements

This work was supported by the Brain Pool Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019H1D3A2A01102198).

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Authors and Affiliations

  1. Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran

    Mostafa Pourali & Javad Abolfazli Esfahani

  2. Center of Excellence on Modelling and Control Systems (CEMCS), Ferdowsi University of Mashhad, Mashhad, Iran

    Javad Abolfazli Esfahani

  3. School of Mechanical Engineering, Pusan National University, Busan, 46241, Republic of Korea

    Javad Abolfazli Esfahani & Kyung Chun Kim

  4. Mechanical Engineering Department, University of Birjand, Birjand, Iran

    Sayyed Aboozar Fanaee

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  1. Mostafa Pourali
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Correspondence to Javad Abolfazli Esfahani.

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Appendix: Reaction mechanisms of GRI 3.0

Appendix: Reaction mechanisms of GRI 3.0

Tables 5–7 separately represent the elementary reactions for methane combustion from GRI-Mech 3.0 mechanism for CO species, CO2 species, and both CO and CO2 species, respectively.

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Pourali, M., Abolfazli Esfahani, J., Fanaee, S.A. et al. Developing mathematical modeling of the heat and mass transfer in a planar micro-combustor with detailed reaction mechanisms. J Therm Anal Calorim 143, 2679–2694 (2021). https://doi.org/10.1007/s10973-020-09623-w

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