Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Heat is to be transferred from water to air through an aluminum wall. It is prod

ID: 1717260 • Letter: H

Question

Heat is to be transferred from water to air through an aluminum wall. It is produce that rectangular fins 0.05 in. Thick and 1/4 in long and spaced 0.08 in a part be added to the aluminum surface to aid in transferring heat. The heat transfer coefficients on the air and water sides are 3 Btu/hr-ft2-T and 25C Btu/hr-ft2-T, respectively. Evaluate the percentage of increase in heat transfer if these files are added to (a) the air side, (b) the water side, or (c) both sides. What conclusions may be reached regarding this result?

Explanation / Answer

If the fin is insulated at the end then from the Data book and fin is fixed at the air side

Heat Transfer Q = Sq root of h x P x k x Acx(Tb -Ta )tanh(mL)

Where P = Perimeter h= heat transfer coefficient k = themal condutivity ,Ac Area of cross section

Tb = Temperature of the base of the fin

Talpha = surrounding temperature

P = 2 ( 0.05 +0.08)

= 0.26 in

Ac = Area of cross section= 0.05 x 0.08 = 0.004 in^2

m =sq root of h x P /k x Ac

= 3 x 0.26 / 124 x 0.004

= 1.572

Q = Sq root of (3 x 0.26 x 124 x 0.004 x (Tb-Ta ) tanh(mL)

mL = 1.572 x 0.25

= 0.393

Q = sq root of 0.3868)(Tb - Ta)tanh(0.393)

Assuming Tb = 80 Ta = 28 oC

Q = Sq root of (0.3868 ) (80 -28 ) tanh(0.393 )

= 0.621 x 52 x tanh (0.393)

= 7 .76 watts

When Fin is fixed in the Water side

Heat transfer Q = sq root of hxPxxkxAc (Tb -Ta )tanh(mL)

P = 2 ( 0.05 +0.08)

= 0.26 in

Ac = Area of cross section= 0.05 x 0.08 = 0.004 in^2

m =sq root of h x P /k x Ac

= 250 x 0.26 / 124 x 0.004

= 131.2

Q = Sq root of (250 x 0.26 x 124 x 0.004 x (Tb-Ta ) tanh(mL)

mL = 131.2 x 0.25

= 32.76

Q = sq root of 32.24)(Tb - Ta)tanh(32.76)

Assuming Tb = 80 Ta = 28 oC

Q = Sq root of (32.24 ) (80 -28 ) tanh(32.76 )

5.67 (52 ) (0.9809)

= 294 x 0.9809

Q = 289 W

when fin is fixed water side heat trasfer increased from 7.76 W to 289 W

If the both sides fins fixed then heat transfer still more = 296 W

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote