Question

4. In the same experimental system as in question (3), the environment temperature was 25 C. However, a small isolated section has been measured and found to be T spotted from the base of the fin which does not exchange heat with the environment. What would be the length of the isolated part Z that would allow the agreement between both efficiency calculations methods described in question (3) 3. A single fin, made of stainless steel (304) is given in figure (17). The following data is provided: h 6 [W Im'K]. During and experiment the following data was found: Base temperature: T, 135' C and heat transfer rate of: q, 1.5 [W] The environment temperature is unknown. a. Consider environment temp. of T 25 C. Calculate the fin efficiency using the temperature difference between both ends of the fin. Calculate the fin efficiency using the given geometry (figure (17)) and h, k values. What is the correct environment temperature that allows agreement between both previous calculations? b. C. 1.5W T, 135 C 10(em 3 mm 20(mm Figure 17- Fin experimental system for question 3

Answer 1

h= 6 W = 135 c Given, - MS Ticknsst) Length L o.1 m width(ni)o.02. 0.003 m Actual Heaf fansfer kate efidenty fin Maximum Possible ta teams let Ra fe D.487 GY 48.7 hxAxT-T) 6x 4.6Cxi3 (135-25 )+axtxL) 02x.02)x2 x0) 2x0.003 0) totaf Sweface areg, = (Wxt) (2> Note Ac 4.66 X103 2 for stainless steel (s04) 14 K. 2x 6 6.g m /Kt 14x o.003 L + 0.1015 m 0. 0.003 Nno E ieny offin Is also given by tanh(te tan h 16.9x0. l0 16. 9 x 0-101S 5 4.6 0.546 fin

the cocec Envionment femp be det tan h CmLe) then mLc 0 546 1 6 x 4,66 x10. 98. 25 6 S dy. 36.74°c An effectve he ef tansfe his the Case d) m will be AS akea - 2 4.66 Nows 5.c6 0.0462]x hAS TT C135-5 O. 546 -0.046 Z 4,66 X10 3 -3 4.66 X10 = 4.1625XIO- O.046 Z 0.010 m Z