If we’re going to talk about heat transfer, we’ve got to talk a little bit about thermodynamics. We’ll take it one law at a time.
The first law of thermodynamics just boils down to conservation of energy.
In a closed system, the total energy present remains constant. The only way the amount of energy present can change is if energy is put into the system or taken out. There are two ways to make energy cross system boundaries like this: either by heat transfer or by work done. So for a closed system, the total change in energy of the system is the net amount of heat put in minus the net amount of work out.
In addition to a closed system, this principle can also be applied to a control volume - that is, a defined region of space that mass can enter and leave. Mass entering will carry energy in with it, and mass leaving will carry energy out with it.
In the situation in which you are considering a control volume in the midst of a constant flow of incompressible fluid, you can consider the heat transfer occurring to be a function of the temperature difference between the fluid entering and the fluid exiting, the mass flow rate of the fluid (mass transferred per unit time), and the specific heat of the fluid, c, which is a physical property of the fluid - basically, how much energy you have to put into it to raise its temperature.
This is a simplified equation, and many situations involving fluid flow require consideration of additional factors, but for now it’ll work for us. We’ll get into the more complicated stuff later.
