How to model negative heat flux BC on water tubes in a furnace

a furnace is modeled using pdf gas combustion. In reality, water tubes run along the walls of the furnace carrying water. One may be inclined to not model the internal tube walls but assume the furnace wall to be the tube wall and apply a heat flux there. This is where the problem starts. Due to very high flux, a very large gradient is needed between the cells next to the wall and the wall faces resulting in negative temperatures at the wall. This is not realistic.
One way of accounting for energy extracted by water tubes is to create appropriate energy sink terms in cells next to the wall. This is done by creating a zone just next to the wall (about one cell layer thick) using the fluid zone. Total amount of energy extracted is the product of wall area and average wall heat flux. This energy divided by the volume of new fluid zone provides a constant volumetric energy sink term. This sink term can be applied to the new fluid volume via BC panel. The furnace wall can be changed to adiabatic. This will solve the problem of negative temperatures. Temperatures are realistic at the wall,

Applying the heat flux values obtained for water tube walls on the actual furnace wall is not realistic.

One should either include these tube walls in the analysis or
apply energy sink term to account for energy extraction.

Including the tube walls will be much closer to reality and one will be able to model flow around the tubes as well.

However, if source terms are to be used, a fluid volume is needed that can represent water tube volume and then a source term can be applied in that fluid volume.

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