MHB What Determines the Time Dependent Value of A[t] in Quasi-Static Approximations?

[mk747pe]

Hello,

I'm working on my bachelor's thesis, and I ran into a problem. In the text they say: "For hot
oil/watering jobs, U is typically large enough that f(t) is closer to a constant temperature than
constant flux boundary condition. In the quasi-static approximation,
these integrals are solved assuming that A[t] is a constant independent of time and then the
appropriate time dependent value of A[t] is plugged into the approximate solutions."

I don't understand how to do it. What will be that "appropriate time dependent value of A[t]"?View attachment 7574

I will be grateful for any advice,
Full text in the attachment,

Thanks in advance. Full text View attachment 7575

 

[I like Serena]

Hello,

I'm working on my bachelor's thesis, and I ran into a problem. In the text they say: "For hot
oil/watering jobs, U is typically large enough that f(t) is closer to a constant temperature than
constant flux boundary condition. In the quasi-static approximation,
these integrals are solved assuming that A[t] is a constant independent of time and then the
appropriate time dependent value of A[t] is plugged into the approximate solutions."

I don't understand how to do it. What will be that "appropriate time dependent value of A[t]"?

I will be grateful for any advice,
Full text in the attachment,

Thanks in advance. Full text

Hi mk747pe! Welcome to MHB! ;)

Your documents seem to be missing some context.
Anyway, my current interpretation is that we presumably have a fully known function A[t].
And we want to integrate something or solve some differential equation (that I can't seem to find) that includes A[t].
To do so, we assume A[t] to be constant to make it easier to integrate or solve the equation.
That is, we replace A[t] everywhere by A.
And when we have found the solution, we replace every occurrence of A again by A[t] for an approximate solution.

Btw, since this seems to be more about understanding what it all means than about actually integrating or solving a differential equation, I'm moving your thread to Other Advanced Topics.