please help to solve this question, upvote will be given. formula is listed below
Posted: Mon May 09, 2022 9:55 am
please help to solve this question, upvote will be given. formula is listed below
Consider a steel pipeline (p = 7800 kg/m”, (p = 430 J/kg.K, k = 70 W/m.K, a = 19 x 10-6 m²/s) that is 1 m in diameter and has a wall thickness of 30 mm. The pipe is heavily insulated on the outside, and before the initiation of flow, the walls of the pipe are at a uniform temperature of -10 °C. With the initiation of flow, hot oil at 70 °C is pumped through the pipe, creating a convective condition corresponding to h=600 W/m²K at the inner surface of the pipe. In this question, it is assumed that the pipe wall can be approximated as plane wall, since thickness is much less than diameter. (a) What are the appropriate Biot and Fourier numbers 10 min after the initiation of flow? (6 marks) (b) At t=10 min, what is the temperature of the exterior pipe surface covered by the insulation? (9 marks) (c) What is the heat flux q" (W/m?) to the pipe from the oil at 1=10 min? (10 marks)
7(x, 0) = Ti = -10 °C TIL,
7(0, 0) To = 70 °C h = 600 W/m2K Insulation Steel 1 1 1 Oil L = 30 mm Appendix Q2.1: Possible required equations for your consideration hL, Bi k Fo= at L? k α = pcp Ꮎ = = = ө T-T. 0 Ti-T.
00 0* = C, exp (-5F0) cos ($,**) n=1 0* = G exp(-${F0) cos ($1x*) Where 4 sin in C,= 25, + sin (257) Stan Sn = Bi and
Appendix Q2.II Coefficients used in the one-term approximation to the series solutions for transient one-dimensional conduction. Br 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.20 0.25 0.30 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 է Ո Plane Wall 51 (rad) с 0.0998 1.0017 0.1410 1.0033 0.1723 1.0049 0.1987 1.0066 0.2218 1.0082 0.2425 1.0098 0.2615 1.0114 0.2791 1.0130 0.2956 1.0145 0.3111 1.0161 0.3779 1.0237 0.4328 1.0311 0.4801 1.0382 0.5218 1.0450 0.5932 1.0580 0.6533 1.0701 0.7051 1.0814 0.7506 1.0919 0.7910 1.1016 0.8274 1.1107 0.8603 1.1191 1.0769 1.1785 1.1925 1.2102 1.2646 1.2287 1 212 1 27 Infinite Cylinder 51 (rad) с 0.1412 1.0025 0.1995 1.0050 0.2440 1.0075 0.2814 1.0099 0.3143 1.0124 0.3438 1.0148 0.3709 1.0173 0.3960 1.0197 0.4195 1.0222 0.4417 1.0246 0.5376 1.0365 0.6170 1.0483 0.6856 1.0598 0.7465 1.0712 0.8516 1.0932 0.9408 1.1143 1.0184 1.1345 1.0873 1.1539 1.1490 1.1724 1.2048 1.1902 1.2558 1.2071 1.5994 1.3384 1.7887 1.4191 1.9081 1.4698 Sphere $1 (rad) G C 0.1730 1.0030 0.2445 1.0060 0.2991 1.0090 0.3450 1.0120 0.3854 1.0149 0.4217 1.0179 0.4551 1.0209 0.4860 1.0239 0.5150 1.0268 0.5423 1.0298 0.6609 1.0445 0.7593 1.0592 0.8447 1.0737 0.9208 1.0880 1.0528 1.1164 1.1656 1.1441 1.2644 1.1713 1.3525 1.1978 1.4320 1.2236 1.5044 1.2488 1.5708 1.2732 2.0288 1.4793 2.2889 1.6227 2.4556 1.7202 TURU no 5704 1 7870
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7(x, 0) = Ti = -10 °C TIL,
7(0, 0) To = 70 °C h = 600 W/m2K Insulation Steel 1 1 1 Oil L = 30 mm Appendix Q2.1: Possible required equations for your consideration hL, Bi k Fo= at L? k α = pcp Ꮎ = = = ө T-T. 0 Ti-T. 00 0* = C, exp (-5F0) cos ($,**) n=1 0* = G exp(-${F0) cos ($1x*) Where 4 sin in C,= 25, + sin (257) Stan Sn = Bi and
Appendix Q2.II Coefficients used in the one-term approximation to the series solutions for transient one-dimensional conduction. Br 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.15 0.20 0.25 0.30 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 է Ո Plane Wall 51 (rad) с 0.0998 1.0017 0.1410 1.0033 0.1723 1.0049 0.1987 1.0066 0.2218 1.0082 0.2425 1.0098 0.2615 1.0114 0.2791 1.0130 0.2956 1.0145 0.3111 1.0161 0.3779 1.0237 0.4328 1.0311 0.4801 1.0382 0.5218 1.0450 0.5932 1.0580 0.6533 1.0701 0.7051 1.0814 0.7506 1.0919 0.7910 1.1016 0.8274 1.1107 0.8603 1.1191 1.0769 1.1785 1.1925 1.2102 1.2646 1.2287 1 212 1 27 Infinite Cylinder 51 (rad) с 0.1412 1.0025 0.1995 1.0050 0.2440 1.0075 0.2814 1.0099 0.3143 1.0124 0.3438 1.0148 0.3709 1.0173 0.3960 1.0197 0.4195 1.0222 0.4417 1.0246 0.5376 1.0365 0.6170 1.0483 0.6856 1.0598 0.7465 1.0712 0.8516 1.0932 0.9408 1.1143 1.0184 1.1345 1.0873 1.1539 1.1490 1.1724 1.2048 1.1902 1.2558 1.2071 1.5994 1.3384 1.7887 1.4191 1.9081 1.4698 Sphere $1 (rad) G C 0.1730 1.0030 0.2445 1.0060 0.2991 1.0090 0.3450 1.0120 0.3854 1.0149 0.4217 1.0179 0.4551 1.0209 0.4860 1.0239 0.5150 1.0268 0.5423 1.0298 0.6609 1.0445 0.7593 1.0592 0.8447 1.0737 0.9208 1.0880 1.0528 1.1164 1.1656 1.1441 1.2644 1.1713 1.3525 1.1978 1.4320 1.2236 1.5044 1.2488 1.5708 1.2732 2.0288 1.4793 2.2889 1.6227 2.4556 1.7202 TURU no 5704 1 7870