Exam Prep - Heat Transfer

Question 1

Derive the Fourier formula

Answer 1

Fouriers Law:

Q = -kA (dt/dr)
Q = -k (2pirL) (dt/dr)
Q dr/r = -k (2piL) dt limits r2, r1, T2, T1
Q ln(r2/r1) = k (2piL)(T1 - T2) drop the minus
Q = [k (2piL)*(T1 - T2)] / ln(r2/r1)

maybe use U instead of k for the “general relation” and write that U = f (k, h , geometry)

Question 2

Finding the Q

Answer 2

Q = [k (2piL)*(T1 - T2)] / ln(r2/r1)

Plug input values, write that the convection and the radiation have been neglected.

Question 3

Finding the thickness of insulation

Answer 3

Q = [k (2*pi*L)*(T1 - T2)] / ln(r2/r1)  Layer 1
Q = [k (2*pi*L)*(T2 - T3)] / ln(r3/r2)  Layer 2

Qnew = % of Qold

T1-T3 = Qnew * Rtot

Plug in the numbers

ln(r3/r2) = some number

r3 = exp (some number) * r2

tins = r3-r2

Question 4

Finding the Q (if given heat convection has to be taken into account)

Answer 4

Q = h A (Tf - Tw)

Qtot = Qconduction + Qconvection