Help with unstanding Energy Equation

siw

Hi,

I'm working through J D Andersons book CFD The Basics with Applications and I'm a bit confused with how he's putting together the energy equation.

The book states the energy equation (eq 2.59) is:

A = B + C where,

A - rate of change of energy inside fluid element. B - net flux of heat into element. C - rate of work done on element due to body and surface forces.

How does A = B + C equate? Because the units of A must be Joules per second as it's just dE/dt. The units of C must be the same as it's d(F * x)/dt with units [N m / s] = [J / s].

But with B the heat flux is [J / s m^2]. Which is not the same as [J / s] in A and C. If it was heat flow rate rather than heat flux then the units would match.

Am I missing something really simple. I'm working through the book and to me it does not work out. So I'd appreciate your help clarrifying this.

Thanks.