Question on How energy equation is presented in Diff form

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thunderspeed
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Hi guys ,
I'm currently reading a book and I faced this with DEs:
In the 5 attached images you'll find the textbook paragraph I'm asking about .
I think I understood the first part under the title of : meaning of differential equation but I can't figure out how did he proceed with the same concept on applying it to the energy equation .

Please help . Thanks in advance .
 
Attachments
  • Textbook page titled 2.1 Governing Differential Equations, section 2.1-1 Meaning of a Differential Equation, with body text on conservation principles and specific properties and a footnote about temperature as a dependent variable.
    1.PNG
    17.5 KB · Views: 552
  • Textbook page explaining net efflux per unit volume: a control volume with flux Jx entering one face, flux leaving the opposite face, and the equation dJx/dx + dJy/dy + dJz/dz = div J (2.1).
    2.PNG
    27.5 KB · Views: 509
  • Diagram of a small rectangular box in 3D axes with inflow Jx entering the left face and outflow Jx + (∂Jx/∂x) dx leaving the right face, with edges labelled dx, dy and dz.
    3.PNG
    2.2 KB · Views: 498
  • Printed textbook page titled 2.1-3 The Energy Equation, showing the steady low-velocity energy equation div (rho u h) = div (k grad T) + S_h, labelled (2.5), with definitions of h, k, T and S_h.
    4.PNG
    13.6 KB · Views: 488
  • Printed textbook page with equations (2.6) to (2.10): c grad T = grad h; div (rho u h) = div((k/c) grad h) + Sh; h = cT; div (rho u T) = div((k/c) grad T) + Sh/c; and div (k grad T) + Sh = 0 for steady heat conduction.
    5.PNG
    18.1 KB · Views: 492

Discussion

Welcome to PF;
That's a lot of reading you want people to do on the off-chance they will understand your problem.
Which of the many paragraphs are you having trouble with?
What is it about the paragraph that is giving you trouble?
i.e. please let us know how you are thinking so we can best respond to your problem.
Alternatively, please attempt to express your problem as a specific question.