Let

f = 2 n + t

Now I want to evaluate f given values for n and t. So what I've done is

Module[{n = 1, t = 5},
 f]
(*f*)

What I expected to get is 7, of course. But the output is just f.

However,

Module[{n = 1, t = 5},
 2 n + t]
(*7*)

returns a calculation.

Now I moved on to something more complicated. Let

u = a Sqrt[k^2 n1^2 - \[Beta]^2]

and

w = a Sqrt[\[Beta]^2 - k^2 n0^2]

I want to get the value of

 BesselJ[1, u]/(u BesselJ[0, u]) == -(BesselK[1, w]/(w BesselK[0, w]))]

for some values of n1, n2 and a, as a function of Beta and k (and then plot a ContourPlot).

The same trick does no calculation:

Module[{n1 = 1.4475, n2 = 1.4444, a = 5},
 Evaluate[BesselJ[1, u]/(u BesselJ[0, u])] == 
  Evaluate[-(BesselK[1, w]/(w BesselK[0, w]))]]

nor

Module[{n1 = 1.4475, n2 = 1.4444, a = 5},
 Evaluate[BesselJ[1, u]]/Evaluate[u BesselJ[0, u]] == 
  Evaluate[-(BesselK[1, w]/(w BesselK[0, w]))]]

or any other combination of wrapping Evaluate[] around the u and w.

Can I use Module at all for this kind of numerical substitution? Is Module the advised tool?

Of course, I can set n1, n2 and a to these numerical values, but I good bookkeeping in my code.

Thanks very much for your help!