Question

Qtotal QtopQbottom +Qrad 0.2217(Ts 20) 0.1108 (Ts - 20) +3.2659 x 10-9(Ts 273°K)4 - (17 273° K)4| 20W 46.8°C

Hi there, can someone please explain to me how to get ride of the power of 4 to solve for Ts in this question. No calculators with solving functions are allowed in our exams.

cheers

Answer 1

We can't solve this equation explicitly as it is a 4th order equation. A Numerical method like Newton-Raphson's method will serve well

Let

f (x)0.2217 (x 20)+0.1108 (x 20)+3.2659-10-) (((273)4 - (17 20 273)4))

So

f(x)0.22170.1108 3.2659 10-) ((4 (z 273)3-4 (17 273))

Newton-Raphson's iteration is

f(n f'(n n+1 n

So we get the following table of iterates:

n	x_n	f(x_n)	f'(x_n)
0	10	-25.4758	0.6286
1	50.5285	2.8327	0.7748
2	46.8728	0.0272	0.76
3	46.83709	0.0000025	0.76

Thus, we have the approximate root as
T 46.83709
for which
f(r) 2.5 x 10

$\blacksquare$

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