I have the following problem and hope you can help me. I have the setup as shown in the drawing. A pipe that is flowed through, and in the middle of it another pipe, but at the end of this branch is a sensor. Initially the fluid would flow, with a temperature of 25°C. If my thought is correct, the pipe with the sensor (if there is a drain valve) would fill with the liquid and then rest, because there would be no more flow, since it has nowhere to flow.
Now the liquid is slowly heated (heating to about 350°C) and continues to flow the same way. How would the temperature in the branch change? This would have to be still relatively cold at the sensor, since no exchange of the liquid takes place, since no flow is present in the branch, or do I have there a mistake in my thought?
How would you calculate the heat exchange between the flowing and standing medium? Because there is heat exchange only there, which would then have to be "up" through the entire
water column. Can we calculate this in a simplified way as forced convection on a plane wall and assume the fluid portion in the branch as a plane wall?
I hope the problem is apparent, because I would need to calculate the length of the branch so that a certain temperature at the sensor is not exceeded.
Thanks a lot!