An analytical solution for the temperature distribution in 2D laminar reacting flow between closely spaced parallel plates is derived as part of a larger effort to develop a nonintrusive technique for measuring gas temperature distributions in millimeter and submillimeter scale channel flows. The results show that the exact solution, a Fourier series, which is a function of the Peclet number, is approximated by second and fourth order polynomial fits to an R2 value of almost unity for both fits. The slopes of the temperature near the wall (heat fluxes) are captured to within 20% of the exact solution using a second order polynomial and to within 2% of the exact solution using a fourth order polynomial. The fits are used in a nonintrusive Fourier transform infrared spectroscopy technique and enable one to infer the temperature distribution along an absorbing gas column from the measured absorption spectrum. The technique is demonstrated in a silicon-walled microcombustor.

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