In a Manipulate like this,
Manipulate[Plot[T, {r, 0, R}],
{{t, 15(*h*)*60*60}, 0, 24(*h*)*60*60},
{{s, 0.0225}, 0, 0.05}]
the s
and t
variables need to be part of the expression in the body of the Manipulate. What you have in the body, Plot[T, {r, 0, R}]
, is an expression, it's not a predefined procedure that Mathematica will reference. Mathematica needs to "remember" that expression so that it can recalculate it when s
or t
change, so it can't just automatically compute it (which, if it did, would presumably expose the s
and t
as you seem to expect). So, you change s
and Mathematica looks at Plot[T, {r, 0, R}]
and says, "nothing to do here", because it doesn't see any s
in that expression.
On a quick scan, I didn't even see where T
was defined, but whatever the expression is that uses s
and t
, that's the expression you want to plot.
Also, you mention that T depends on t
and s(t)
, but you set up the Manipulate with s
and t
as independent variables. I'm not sure what you expect to happen here. It seems to me that you should only need t
. Whatever the function s
is can be used in your definition of T
by just applying it to t
.