tailieunhanh - fundamentals of heat and mass transfer solutions manual phần 3

ngành cơ khí, động cơ máy, nguyên lí hoạt động, hệ thống máy móc, cơ khí hóa, động cơ máy móc, chế tạo động cơ Nhớ rằng khả năng chịu nhiệt được định nghĩa là R t ≡ ΔT / q sau đó cho hình trụ rỗng, Rt = ln (ro / Giả sử k là hằng số, tỷ lệ nhiệt qr = 2π Lc (Ti -) ln (ro / ri). | PROBLEM KNOWN Dimensions and thermal conductivities of a heater and a finned sleeve. Convection conditions on the sleeve surface. FIND a Heat rate per unit length b Generation rate and centerline temperature of heater c Effect of fin parameters on heat rate. SCHEMATIC ASSUMPTIONS 1 Steady state 2 Constant properties 3 Negligible contact resistance between heater and sleeve 4 Uniform convection coefficient at outer surfaces of sleeve 5 Uniform heat generation 6 Negligible radiation. ANALYSIS a From the thermal circuit the desired heat rate is T T q As 1 R cond 2D Rt o T _T Rtot The two-dimensional conduction resistance may be estimated from Eq. and Case 6 of Table 1 S R cond 2D ln D _ ln 2n ks 2n 240W m K m K W The thermal resistance of the fin array is given by Eq. where no and At are given by Eqs. and and nf is given by Eq. . With Lc L t 2 m m 2h kst 1 2 m 1 and mLc c tanh mLc nf c f mLc At NAf Ab N 2L 1 4w - Nt NAf no 1 Tf 1 -nf 1 - _ o A t v f Rt o nohAt -1 m2 1 K W 300-50 C _ q 74 600W m m K W b Eq. may be used to determine ị if h is replaced by an overall coefficient based on the surface area of the heater. From Eq. PROBLEM Cont. UsA s UsnD Riot 1 K W 1 298W m K Us 298W m K 4750W m2 K q 4Us Ts -TL D 4 4750W m2 K 250 C m3 From Eq. the centerline temperature is T 0 qlD 2 2 Ts 238x i 0 m 2 300 C 315 C v 7 4kh s 4 400W m K c Subject to the prescribed constraints the following results have been obtained for parameter variations corresponding to 16 N 40 2 t 8 mm and 20 L 40 mm. N t mm L mm f q W m 16 4 20 74 400 16 8 20 77 000 28 4 20 107 900 32 3 20 115 200 40 2 20 127 800 40 2 40 151 300 Clearly there is little benefit to simply increasing t since there is no change in At and only a marginal increase in .