18 fins enhance the heat rate by 500% (with respect to heat rate with no fins) f
ID: 2995260 • Letter: 1
Question
18 fins enhance the heat rate by 500% (with respect to heat rate with no fins) for a surface with a base temperature of 500 C. The ambient is at 25 C, with heat transfer coefficient h=30 W/m^2*C, and h = 40 W/m^2*C for the base. The material is Aluminum. Design what should the width, length, thickness and spacing of the fins be to meet the 500% enhancement.
A) Use retanguluar fins, for a flat surface with a width of 1m and height of 2m. The fins are to be place parallel to the width.
B) Use annular fins, for cylindrical surface witha base radius of 0.5 inches and hieght of 12 inches.
Explanation / Answer
Tf = ( 500+25)/2 = 262.5 degree c. or 535.68
beta = 1/ Tf = 1/ 535.68 = 1.866
Prpperties at 262.5 degree c.
Pr = 0.68
V=41.17X10^-6 (m2/s)
K = 0.0421 W/mK
rayleigh no. can be found as
Ra = GrPr. = 9.8 (m/s2) (535.68 K)( 500-25 oC) (0.68)(4m3)/ 41.17X10^-6
Ra= 1.647X10^11
Nusselt No.
= 0.1X(Ra)^(!/3) = 548.19
heat transfer coefficient is
h = Nu K /L
L= NuK/h = 0.769 m
optimum spacing can be found from
h=1.31 K / S(optimum)
s (optimum) = 1.31K/h = 0.0083 m =1.83 mm
if we assume thickness = 1mm
width can be calculated as
no. of fins = Width / (S+t)
Width = no. of fins X (S+t)
Width = 51.09mm =0.051 m
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