Linear Differential Equation (Energy Balance)

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Professor, I am not sure if I understood the energy balance explanation. Steps used were:
1. General energy balance: dh/dt = m_in*h_in + m_out*h_out + Q + W
2. Assumptions: No mass in nor out in thermocouple and Q input is divided by convection and radiation. No work identified.
3. Energy balance expression: dh/dt = q_conv + q_radiation

Am I correct?

rodrigostevensgacitua
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Thank you for your effort Professor, could you explain the Tg equation please ?

karimmanseri