Calculating surface temperature of pipe 1

[Wales_eng2019]

Good evening,

I have a question which I am struggling to find an adequate answer for and wondering if you could point me in the right direction.

I have attached a photo to demonstrate what I am trying to explain.

The photo shows a heat source (approx. 1000-1200 degrees C) going underneath a tower where there are a number of 316L St/St pipework roughly 1.5-2m above this heat source. I am looking to find an equation that I could use to give a answer to the pipes temperature on the surface reaches over a given period of time through exposure to this heat source at a given distance away. The pipe is considered to be empty for a period of time until water is released and enters through these sections of pipe.

Thank you.

 

[georgeverghese]

Looks like you could get direct flame impingement on to this pipe from the slag pot.

 

[chicopee]

There is one statement that is bothering me which you stated "... The pipe is considered to be empty for a period of time until water is released and enters through these sections of pipe." I am interpreting that statement that water is introduced after the pipes were heated and that is troubling because if the pipes become red hot and consequently deform than water will cool the pipes which will remain in the deformation state.
You obviously have to modes of heat transfer being convection and radiation. Based on the picture that you provided, I suspect that the amount of heat absorbed is about 60% of the heat input. You need a heat transfer equation that consider the combined modes of heat transfer mentioned above. Such equations can be found in heat transfer text books or in mechanical engineering handbooks such as Kent"Power" or Mark. Perry chemical engineering hanbbook may also dwell in that topic. Research is the key in solving your problem so be careful in that selection as you want an equation of combined heat transfer for cylindrical surfaces (tubes in your case); also select an appropriate coefficient of convective heat transfer of the products of combustion heating the external surfaces of the tubes or pipes before water is introduced (if I am interpreting your OP correctly); for the pipe surface emissivity needed for the radiation part of the equation use the black body value. Once all required values are provided for the combined equation for the two modes of heat transfers, than a trial and error approach must be used to solve the surface temperature of the pipes.