radiation

[logistic_guy]

here is the question

In an industrial process, products of combustion at a temperature and pressure of $\displaystyle 2000$ K and $\displaystyle 1$ atm, respectively, flow through a long, $\displaystyle 0.25$-m diameter pipe whose inner surface is black. The combustion gas contains $\displaystyle CO_2$ and water vapor, each at a partial pressure of $\displaystyle 0.10$ atm. The gas may be assumed to have the thermophysical properties of atmospheric air and to be in fully developed flow with $\displaystyle \dot{m} = 0.25$ kg/s. The pipe is cooled by passing water in cross flow over its outer surface. The upstream velocity and temperature of the water are $\displaystyle 0.30$ m/s and $\displaystyle 300$ K, respectively.

(a) Determine the pipe wall temperature, $\displaystyle T_s$.
(b) Determine the heat flux, $\displaystyle q_{total}$.

Hint: Emission from the pipe wall may be neglected.


my attemv
i've to use the energy balance equation to solve this question (a)
$\displaystyle \epsilon_g \sigma T_g^4 + h_1(T_g - T_s) = h_2(T_s - T_{\infty})$
the pipe wall temperature is $\displaystyle T_s$

$\displaystyle \epsilon_g:$ emissivity of the gas
$\displaystyle \sigma:$ Stefan-Boltzmann constant
$\displaystyle T_g:$ temperature of the gas
$\displaystyle T_s:$ temperature of the surface
$\displaystyle T_{\infty}:$ temperature of the surroundings
$\displaystyle h_1:$ convective heat transfer coefficient related to the gas
$\displaystyle h_2:$ convective heat transfer coefficient related to the water

i understand the main two ingredients in the questions is carbon dioxide $\displaystyle CO_2$ and water $\displaystyle H_2O$
i think a lot of information is missing like the mean of the pipe length $\displaystyle L_c$ due to radiaion, not givenand there's no enough information to find it

i need this information to solve the emissivity of carbon dioxide $\displaystyle \epsilon_c$ and the emissivity of water $\displaystyle \epsilon_w$
which necessary to find $\displaystyle \epsilon_g$ also calculating $\displaystyle h_1$ and $\displaystyle h_2$ need a lot of information which is not given
for example what is Reylond's numbers $\displaystyle Re_1$ and $\displaystyle Re_2$?