Finding the convection of a node in a hot pipe

1. The problem statement, all variables and given/known data

I just completed a lab in class where we heated a copper pipe and measured the temperatures at 25 different locations. Each of these locations is called a node. The goal is to find the convection losses by using the First Law (q_c1 + q_c2 + q_c3 + q_c4 + q_rad + q_conv = dE_CV/dt).



Here is the temperature data for the 25 nodes:





Also, the ambient temperature is 22 °C.



Specifically I circled the nodes I would like to analyze - the node at 58.327 °C. So I assumed the system is in steady state and got:



q_c1 + q_c2 + q_c3 + q_c4 + q_rad + q_conv = 0



Conduction heat transfer: q = kA(T2-T1)/t

Convection heat transfer: q = hA(Tw-T∞)

Radiation heat transfer: q = σε(T2⁴-T1⁴)



Looking at the data, we see that the heat transfer by conduction is out of the middle node to the four surrounding nodes. Also, there is radiation out of that node as well. In other words both conduction and radiation is transferring out of the node.



By the First Law, this would imply that the heat transfer by convection is into the node. However, this does not make sense since the ambient temperature is lower than the node temperature so we should expect the heat to transfer out of the node.



Does anyone know what I am doing wrong?