- #1
jcx3
- 1
- 0
A model of tank fluid temperature (fixed mass inside) based on the mixing of two streams, one hot and one cold, each with fixed temperature, the hot one a fixed flowrate and the cold one an oscillatory flowrate can be expressed as:
du/dt + [c1 + c2*(1+cos(t))]*u = c1
The solution can be solved easily with an integrating factor and written in terms of an integral. I am trying to derive an expression for the AMPLITUDE of the asymptotic oscillation of u(t)which comes down to reducing the integral:
Int[0,t] { exp[ - t' - k1*sin(k2*(t'-t)) ] } dt'
I saw a reference suggesting this could be expressed as a Bessel function, but I can't see how, and I'm having a very hard time finding ANY references to integrals of exponentials of trigonometric functions. ANY INSIGHT WOULD BE GREATLY APPRECIATED!
du/dt + [c1 + c2*(1+cos(t))]*u = c1
The solution can be solved easily with an integrating factor and written in terms of an integral. I am trying to derive an expression for the AMPLITUDE of the asymptotic oscillation of u(t)which comes down to reducing the integral:
Int[0,t] { exp[ - t' - k1*sin(k2*(t'-t)) ] } dt'
I saw a reference suggesting this could be expressed as a Bessel function, but I can't see how, and I'm having a very hard time finding ANY references to integrals of exponentials of trigonometric functions. ANY INSIGHT WOULD BE GREATLY APPRECIATED!