Question

Problem 2 (30 Point) A copper tink concams hot waler which is maintained at 55 This hot water tank han an inier diameter of 40 cms and a height of 2 m The tank is seoeed in a small room whichs is imentained at 27 C The convective heae irssier coeffcients on the iside and cutside surfaces of the tank are 50 W/m K and 12 Wi K. rospectively, The tank ise placed inside another copper thank of inside diameter 46 em Both coppes tamks have extremely high thermal conductivity; thesefore, negligible thermal resestance (gligible wall thicksess) Foam insutaticn with k.03 WimK is aned to fill the space betwoes these two cotcentric tanks. The price of electricity is 50.08Wh, and the annual cost of water beating is $280 Neglecting the beat loss through the sop and bottom surfaces, determane the fractson of the hoe water energy cost that is due to the beat loss from the fank. Next, consider adding vn the outside of the tank a 3 em thick Giberglass (k-003S Wim K) insulation kit which costs $30 to install How leeg will it take for this additional insulation to pay lor itself? esse Devce Ai TTo s23y 26(416 W Cale 1 yeas cask Ecf 294 ero A:toy 3 h st freti of test t to lest T o31546

Answer 1

both the dem i Hiernen hos figh thermal Conducting and nyligible so Hit Anwil will be Tw s To Rinsulation Bin hosto Rretala I Rinsutine I hoto en 10:46 50 x(xx0.4 x 2) 2x Zx 0:03x2 123 Zx 0.us x 2 Where! Ring e n ( 10) 27 KL D: die of outer dark Da det of inner den 1- height = 2m Rotal = 0.0075193 K 55-27 e Rretel : 0.4075193 0 = 68.7084 Watt one year total Units in total Units: - 68.708 4 x 105 x 365 724 No . 601 8856 unit Суд h). Cost Correspuetig to No . c: 8856 x Oro 4 G 48.450 $ kWh

fraction of hot water energy cost that is best = 481150 - 0.17 1967 200 o 17:1962% less Now addig 3m thick insulation outside with le=0.035 to - Rinsulatio) fibergian 22KL Biyo en , 0340-46) Lene Do = 46+ (2x3) = 52cm Di = 46 cm 20. XX 0.035x2 Reso); = 0.2787531 ķ Now Rrotal) new a Rosal) ords Rios) 0.407s 193 +0.2787 53). Bloom) ve = 0.68627244 K Dnew- AT By Jw 0168823244 28 - 4018 W 0.68023244 :: Noto fatal Mi of Units in One year Nodena 40.8 x 10-34 365x24. = 357:40s Unib (kwh 1 New dotal Cost Correspondin to No) New C2 - 350.409 20:08 = 28.5927 8 Sovin in one year – G-C-48:150 - 28.5927 19:56 $ : tim required for saving of 30$ (instalatim time. 30 = 1.534 years u 560 days so Prices