I have been asked to weld a track-way for a water cutting machine onto the outside of an un-cleaned storage tank. My client has asked for me to prove with calculations that the amount of heat we will b inputting on the outside of the tank shell will not be sufficient enough to make the product on the inside ignite or go bang.
The heat input at the end of the welding rod can be taken as 1500 degrees C and the tank shell is 15mm thick carbon steel. It is our intention to hold the track way on with 5-6mm tack welds spaced 0.5 metres apart.
Can anyone help me with how to go about this?

What is the material on the inside of the tank?

1500 degrees C is not a measure of heat.

It would depend on the amount of time that the outside temperature is held at 1500C and the cooling around the weld, both outside and inside the shell. If you can assume that the plate is flat around the weld then you'd have to do a 1D axisymmetric transient heat transfer calculation around the weld, assuming that the weld centre was at r=0 of a circular flat plate, with zero heat flux at some infinte point away. I'd think about bolting it on, just to be safe.

The manager

If the tank is steel, it would also be possible to use a magnetic track.  I know that they make them for automatic tank welders, and I'm pretty sure they make them for abrasive jet cutting as well.

The product on the inside of the tank is VGO (vacuum gas oil).

I have found a formula for heat input it is as follows, the figures after the variable identities are the parameters we are using.

H=60EI/1000S

H=heat input (kJ/in or kJ/mm)
E=arc voltage (20 volts)
I=current (80 amps)
S=travel speed (in/min or mm/min) (300mm)

I can not bolt the track-way on as this would mean drilling holes in the tank & at the moment there is no access to the inside as it  still has about a metre of residual product in it.

I will research the magnetic track-ways but would still like to know how to calculate my original question. Experience tells me that I could hold my hand against the inside of this plate without getting burnt but the client wants to see figures.

Much easier to do a simple test.

Get a chunk of the same thickness material and a length of track and weld.  Then measure the temperature on the back side.

I agree that a test would be much simpler. Unfortunately the client is insisting on calculations.

Those "tack welds" are very, very small.

I'd be more worried about the track staying in place.

A heavy (1/4 to 3/8) fillet weld on the outside of a 1/4 inch wall steel wall will burn the paint applied inside.   Tacks for the same material on the same thickness will discolor, but not burn, an (epoxy) paint layer inside.   

Have you looked at cleaning the outside of the tank where your cutter track will sit, then gluing the track on?  This way you will not have to worry about the heat transfer.
B.E.

The good engineer does not need to memorize every formula; he just needs to know where he can find them when he needs them.  Old professor