Question

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t is proposed to air-cool the cylinders of a combustion chamber by joining an aluminum casing with annular fins (k 215 W/m-K) to the cylinder wall (k = 40 W/m-K). The air is at 320 K and the corresponding convection coefficient is 100 W/m-K. Although heațing t the inner surface is periodic, it is reasonable to assume steady-state conditions with a time-averaged heat flux of q = 1 x 10 W/m.Assuming negligible contact resistance between the wall and the casing, determine the wall inner temperature Ti, the interface temperature T1, and the fin base temperature Tb. Determine these temperatures if the interface contact resistance is R"= 10m2 -K/W. 2 mm, 8 = 2 mm, r Assume 90.0 mm, r= 99.0 mm, r= 105.0 mm, ra = 142.5 mm. Cylinder wall- Aluminum casing T T T h Physical Properties Mathematical Functions Step 1 Your Answer Correct Answer Determine the conduction resistance of cylinder wall, m K/W. R'=0.0003792 m-K/W Step 2 Your answer is correct. Determine the conduction resistance of aluminum base, m-K/W. R'w 0.0000435 57 m-K/W Attempts: 2 of 3 used Step 3 X Your answer is incorrect Determine the resistance of fins, m K/W R' m.K/W 0.00168 Attempts: 1 of 3 used Save for Later Check Answer Step 4 Neglecting the contact resistance determine the total resistance, m-K/W. R'tot = m-K/W Attempts: 0 of 3 used Save for Later Check Answer Step 5 Neglecting the contact resistance determine Ti, in K. Ti= К Attempts: 0 of 3 used Save for Later Check Answer Step 6 Neglecting the contact resistance determine T, in K. T = K Attempts: 0 of 3 used Save for Later Check Answer Step 7 Neglecting the contact resistance determi ne Th, in K Th=i K Attempts: 0 of 3 used Check Answer Save for Later Step 8 Including the contact resistance determine the total resistance, m-K/W. Rtotr m-K/W Attempts: 0 of 3 used Check Answer Save for Later Step 9 Including the contact resistance determine T, in K. Tit= K Attempts: 0 of 3 used Save for Later Check Answer Step 10 Including the contact resistance determine the temperature on the wall side of the wall/casing interface, T, in K. K T= Attempts: 0 of 3 used Save for Later Check Answer Step 11 Including the contact resistance determine the temperature on the casing side of the wall/casing interface, T, in K. T i K Attempts: 0 of 3 used Save for Later Check Answer Step 12 Including the contact resistance determine Th, in K. Тьст K i eTextbook and Media Attempts: 0 of 3 used Save for Later Check Answer

Answer 1

9 9omm; 1,*99mmj 12-(05mm ^o2 l4-2.5mm Conduction esis tanee of cylinde wall tepa) Ra,cn/] In/101 4 27T K 3.79x10' m Conduction oesistanee f 'Af basc:. '/2TT1K 435xl 27x 215 Resis-tance of fns: . aTO-142510- 14 S m E-ficlency of sloaght ins (Rectangula), ale, paaohc 3.19 bеok by Tncореa -=14-2.S+ 2/2* 14-3.5mm zo 14-35 m 2c Lca L+7/2:37.5 +1 * 38.5mm s o38-5 o.0395m 3 ml 4. 57 Resis tanee funfined suorface. R= Yh h00xo.S2TT0.logo0303 Rb Nlng tat nesterance: . Tb Rus M Rea .34-210mkw sfop ci) Rrto tal3.79xiot435xl5+ 9.34-2104 2s6x Jo3, step T *Aa+to^ 7lo2+320-39102 K, ep (vil: wit T7-VxR^367. / K. CamScann

itcontact esistance : Rb 10 R 10 2Tx99x03 m/w 3 1256x0 1416xlo m. step g 160円× K 56 54.8 x 4-16xio-+320 ^ 4-00 4-00,15653 x3.79*10T-z^8,6K. 56548×1、60子x10 =369.S9 K 3F6 36 1 56548 x 3sxl 369.59 Sep12) CS ISčanf CamScanner