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I have a function:

u[r_] := 1/2*(uj + u∞) - 
  1/2*(uj - u∞)*Tanh[1/4*Rθ*(r/R - R/r)]

Where:

uj = 1;
u∞ = 0;
R = 1;

I want to plot:

Plot[(u[r/R] - u∞)/(uj - u∞), {r, 0, 3}, 
 PlotRange -> All]

But for three different values of parameters Rθ, some like that:

Plot[(u[r/R] - u∞)/(uj - u∞), {r, 0, 3}, 
 PlotRange -> All] /.{Rθ->10,Rθ->5,Rθ->2.5}

How to do that?

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  • 1
    $\begingroup$ It is better to write your function such that the parameters are also arguments to your function: u[uj_, u∞_, R_, Rθ_, r_] := 1/2*(uj + u∞) - 1/2*(uj - u∞)*Tanh[1/4*Rθ*(r/R - R/r)] $\endgroup$ – J. M.'s ennui♦ Feb 27 '19 at 0:34
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Plot[Evaluate[(u[r/R] - u∞)/(uj - u∞) /. {{Rθ -> 10}, {Rθ ->  5}, {Rθ -> 2.5}}], {r, 0, 3}, 
 PlotRange -> All]

enter image description here

Also:

Plot[Evaluate[Table[(u[r/R] - u∞)/(uj - u∞), {Rθ, {10, 5, 2.5}}]], {r, 0, 3}, 
   PlotRange -> All]

same picture

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Here is another way to get the desired result as pointed out in the comment,

uj = 1; u\[Infinity] = 0; R = 1;

u[r_, R\[Theta]_] :=  1/2*(uj + u\[Infinity]) - 
  1/2*(uj - u\[Infinity])*Tanh[1/4*R\[Theta]*(r/R - R/r)]

Plot[Evaluate[u[r, #] & /@ {10, 5, 2.5}], {r, 0, 3}]
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