Need some help on this task.

This problem refers to the cooling of a sphere. Suppose that the sphere has radius a and V is its temperature. It cools by Newton's law conductivity k, constant ε and diffusion h square after the sphere has been put to cool by air at a temperature of 0◦C. It can be show that the temperature θ (r, t) at time t> 0 and r radius is: θ(r, t) = ∞X n=1 An r e −γ 2 nh 2 t sin γnr. Here yn has the positive root of the equation: γn cos γna − 1 a − ε k sin γna = 0 and An = 2γnV [γna − cos γna sin γna] a Z 0 r sin γnrdr. For an air-cooled steel sphere at 0 ◦ C, we assume that temperature page is V = 100 ◦ C and the radius is a = 0.30m. Corresponding constants are h square = 1.73 × 10(power of)-5 , ε = 20 and k = 60. Find the three lowest values of γna and use them to calculate A1, A2 and A3. Approximate temperature r = 0.25, for t = 10(power of)k seconds, k = 2, 3, 4, 5.

[Walter Roberson]

It would be appreciated if you could reformat this to be more readable.

I went to reformat it for you, but I couldn't make any sense of the source.

It appears that you have copy and pasted from an assignment.

What you have includes the characters control-S and control-T, neither of which have any defined printable representation in any ISO-8891 or unicode character set; Dingbats is about the only font that I can think of that has a glyph for those characters.

[Suciu Csaba]

I translated it from Romanian into English, but symbols like the amount or integral can not write. I will try to reformulet

[Suciu Csaba]

http://math.ubbcluj.ro/~tradu/subiecte/subiectefinal.pdf

this is the website where the task's are, this task is number 46.2

it will be more clearer

[Walter Roberson]

Transcribing:

theta(r,t) = Sum over n=1 to infinity of A[n]/r * exp(-gamma[nu]^2*h^2*t) * sin(gamma[nu]*r)

gamma[nu]*cos(gamma[nu]*a - (1/a - epsilon/k) * sin(gamma[nu]*a) = 0

A[n] = 2*gamma[nu]*V / (gamma[nu]*a - cos(gamma[nu]*a)*sin(gamma[nu]*a) * (integral over r = 0 to a of r * sin(gamma[nu]*r) dr)

Let V = 100 (degrees C)

Let a = 0.30 (meters)

Let h^2 = 1.73*10^(-5)

Let epsilon = 20

Let k = 60

(Sorry I don't have time to do a better job at the moment.)

[Suciu Csaba]

I will try the write the program, than post it, and you'll see if it's ok. Thank you verry much!;)

[Walter Roberson]

That sounds like a good idea, Suciu.

Answer 1

[Matt Fig]

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