solver windowOne Dimensional Heat Conduction in FinsHeat transfer analysis of heat conduction in straight fins of uniform cross-sectional area isincluded in heat transfer text books. The analysis results in formulas for temperaturedistribution, the rate of heat exchange with the surrounding environment, and the fin efficiency.Boundary conditions used in the analysis will influence the resulting equations. For example, foran infinitely long fin of a uniform cross-sectional area the temperature distribution and heattransfer are given by the following equations. T − T∞ θ= = e − mx To − T∞ (1) q = hPkA(T − To
principle. To do so let Brepresent entropy. The second law of thermodynamics states that entropy can be created withinthe control volume by dissipative processes such as friction. Entropy can cross the controlsurface by convection or without bulk motion as a consequence of heat. The terms of the generalbalance principle applied to entropy are the following. $ $ ? D $ ? / t s V © dA, $ ? / q © dA BCV ? Ð t s dV, B- Ð dV, Bc Ð r Bnc Ð (11) CV CV T CS CS T $ is the dissipation rate, T is the absolute temperature, and q isHere s is the entropy
-equilibrium equation of the link about its other end. E In the hypothetical sub-mechanism, Figure 3, this means that B j is determined from the moment-equilibrium equation of link i about H E E E E ÂM js h ? Ri · B j - Rgi · fi - qi ? Ri e jsi · B j e j - Rgi e jsi · fi e ji i - q i ? Ri B j sin*s j / s i + - Rgi f i sin*i i / s i + - q i ? 0 (15) Therefore Page 13.101.8
catastrophic or simply costly due to pump inefficiencies whenoperated outside of its intended operating range. Therefore, undergraduate mechanical engineersshould be well trained in this design or selection process through analytical and experimentalmethods learned in engineering science and experimental course work, respectively.In this light, to gain an understanding of the operation of the centrifugal pump4, first consider theenergy transfer of a pump by applying the steady state form of the energy equation as follows: Ç V2 Ç V2 Q% - W% s ? m% outlet Èh - - gz Ù / m% inlet Èh - - gz Ù (1) É 2 Ú
ecology and environmental biotechnology. Environmental Science & Technology 2006, 40,1096-1103.11. Hu, Z. Q., Chandran, K., Grasso, D., and Smets, B. F. Effect of nickel and cadmium speciation on nitrification inhibition. Environmental Science & Technology 2002, 36,3074-3078.12. Ellis, T. G., Barbeau, D. S., Smets, B. F., and Grady, L. C. P. Respirometric technique for determination of extant kinetic parameters describing biodegradation. Water Environment Research 1996, 68,917-926.13. Magbanua, B. S., Smets, B. F., Bowyer, R. L., Rodieck, A. G., Sanders, R. W., Sowers, W. W., Stolze, S. B., and Grady, C. P. L. Relative efficacy of intrinsic and extant parameters for modeling biodegradation of
Surface Temperature, T ( x, t ) − Ts x = erf (13) Ti − Ts 2 α ⋅t Constant Surface Heat Flux, α ⋅t 2 ⋅ q"0 π exp − x − q"0 ⋅x erfc x 2 T ( x, t ) − Ti = 4 ⋅α ⋅ t (14) k k 2 α ⋅t and
desired output to the required input.The desired output is the power produced to propel the aircraft and the required input isthe heating value of the fuel . WP ηP = . (11) Q in . . Qin = m HV fuel (12)Where HVfuel is the heating value of the fuelExperimental Results Figures 6-11 show sample of the output
with MathCAD basics from previous courses,which allowed a smooth transition to solving the specific problems encountered in controlsystems.Grading Scheme:100 points each for each of: homework (H), quizzes (Q), midterm exam (M), final exam (F), andproject (P) have been assigned for a total of 500 points. The grade distribution is shown in Table6. A statistical analysis similar to the one in Table 3 for “Course 1” is not given, due to the smallnumber of students in the course. Also, the project for this course is an individual effort. Eachstudent chooses their control system, and performs the modeling and analysis. However a shortpower point presentation is prepared and given in the final class session by each student andcomments are received
stability, ζ = 0, and the form of theclosed loop transfer function must be: Dg = ( s + a )( s 2 + ω n2 ) (3)The students can then expand equation (3) and equate it to the denominator of the closed loop Page 13.763.8transfer function they determined in the pre-lab (see Figure 5) to arrive at equation (4) below. β B 2 β (A 2 + K ce B) β K p K amp K q As 3 + as 2 + ωn2 s + ωn2 = s 3 + (4 K ce + )s + 4 s+4 (4) Vt M Vt M
. Appendix B: Sample Engineering Design Question. Q.1. Engineering Guesstimation. You are required to design a new cantilever arm to support the winch for a Coast Guard Helicopter. The arm is going to be made out of hollow aluminum or steel tube and a sketch of the arm installation (Fig.1) and cross section (Fig.2) are shown below. Cantilever Arm r2 A Winch A Helicopter Length L
(Q3a, Exm1(Q Student ID Hw1(1,2) a,Q1b) Score Hw2(1,2,3) Q3b) Hw3(1) Final (3) Score Lab1/2 Lab3/4 2a,b,c,d) Lab 5 Exm2(3) Score 6617 100 21 5 99 10 20 18 4 26 24 10 22 10 4 7814 95 25 5 72 25 20 20 4 24 27 20 30 0 4 7825 100 30 5 91 20 20 20 4 28 30 25 27 10 5 5267 87 25 4 0 13 20 20 3 0 30 9 30 10