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I have solved thermal energy balance equation during cold fluid injection into a semi-infinite model. I obtained the following solution in Laplace domain.

$$\bar T_D = \frac{r_D^vK_v(\sqrt[]s r_D)}{sK_v(\sqrt[]s)}$$

How can I obtain inverse Laplace transformation of this solution given $K_v$ is modified Bessel function of second kind and order $v$. $v $ is an integer number higher than zero.

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  • $\begingroup$ What is the specific function $K$? $\endgroup$
    – mattos
    Oct 3, 2019 at 18:41
  • $\begingroup$ Kv is Modified Bessel function of second kind and integer order v. @Mattos $\endgroup$
    – Refaat Galal
    Oct 3, 2019 at 18:42
  • $\begingroup$ Most likely you'll have to do the complex line integral definition of the ILT. $\endgroup$
    – Adrian Keister
    Oct 3, 2019 at 18:54
  • $\begingroup$ I hope anyone can help me obtain this inversion. I am sorry but as a petroleum engineer, my mathematical skills are not high.@AdrianKeister Keister $\endgroup$
    – Refaat Galal
    Oct 3, 2019 at 19:02
  • $\begingroup$ It seems someone has already tried something very similar here. $\endgroup$
    – mattos
    Oct 4, 2019 at 15:07

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