) Page 14.103.11 m Fin parameter, ? hP kA c (1/m) M ? hPkA c θ b (W) P Fin perimeter (m) q Heat transfer rate (W) Rt,f Fin resistance, ? θ b q f (K/W) t Fin thickness (m) T Temperature (ºC, K) x Distance along fin, measured from base (m) Greek Θ Temperature difference between fin and ambient temperature, ? T - T♣ (ºC, K) ε Fin effectiveness, ? q f hA c θ b η Fin efficiency, ? q f q max Subscripts b Base of fin c Cross-section, or corrected length f Fin L Condition at fin tip max Maximum possible ∞ Condition
stm,3 + Qin = m air h av,4 + m ∀,5h ∀,5 + Q out Page 11.1220.3 2 Figure 1 Handout on Property Definitions Air/Water Vapor Mixtures Basic DefinitionsMole Fraction (yi): This is the mole percent of component i in the mixture. number of moles of component 1 in the mixture N1 y1 = = total number of moles in the mixture N totwith ∑ yi = 1 iPartial Pressure (Pi): This is the apparent pressure
between work and heat is that work can always be converted completely to heat but that only a fraction of work can ever be transferred to heat. For that reason alone, we can argue that of the two forms, work is the “higher value” form of energy transfer. More on this with the second law introduction later. So taking B as Energy in our Reynolds Transport Equation we can write the First law of Thermodynamics so :- Q% / W% - (m% e) in / (m% e) out - E% gen ? E% CV First Law of Thermodynamics Net Energy accumulated in theDirect Energy
, temperature and electrical current and voltage in the PTAC experiments (left). Their results suggested a violation of the First Law of Thermodynamics (right). Page 11.963.6When the PTAC is considered as a control volume, the First Law of Thermodynamics can bewritten for the unit as P - Q% in / Q% out / KE% net ? 0 (2)where Q% is the rate that heat is taken into the PTAC from the air, Q% is the rate that heat is in outrejected from the PTAC, and KE% net represents the net change
operating practices during the testing phase.To successfully accomplish the task all students were introduced to the salient features of thepump experimental system and the associated components. The energy equation was employedto explain the dependency of the flow rate Q upon the pressure head (H) added by the pump. Inideal conditions this imbalance is the pressure difference (∆P) between the system inlet andoutlet. So that the pressure head obtained by a pump is directly dependent upon the power (P)supplied to the pump. Students were then explained how various combinations of the appropriatepump parameters such as flow rate (Q), head (H), Power (P), Speed (N - rpm), and the impellerdiameter (D) yield affinity laws3, 4. It was further shown how
students to show why enthalpy remains constant for a process involvingfluid flow in an expansion valve. They also had to show why the value of specific entropyincreases during the process. As a minimum, students had to state the logical assumptions thatthe process is a steady state, it involves no transfer of power, and kinetic energy and potentialenergy effects are negligible. They also had to show the following steps:dmcv = m& i − m& e or m& i = m& e = m& dtdEcv ⎛ V2 ⎞ ⎛ V2 ⎞ = Q& cv − W& cv + m& i ⎜ hi + i + gzi ⎟ − m& e ⎜ he + e + gz e ⎟ dt ⎜ 2 ⎟ ⎜ 2
flow of electric current. The flow is due to a driving potential: in heattransfer the driving potential is a temperature difference between two locations, while in the caseof electric current the voltage difference is the driving potential. The thermal resistance isobtained by employing this analogy and manipulating the heat transfer governing equations andcasting them in the form of Ohm’s law.For a plane thin wall with its two surfaces at constant, yet different, temperatures (Fig. 1), thesteady-state one-dimensional conduction heat transfer is given by Fourier’s law: T1 / T2 Q% ? k A (1
, not on the details of data acquisition. The laboratory exercise begins with warm-up problems on the rate form of the first law, andon possible choices of control volumes for the system. We found these warm-up problems to bevery helpful because qualitative reasoning is a new skill for students, and because (in ourapproach) the students have only recently been reintroduced to the first law of thermodynamics.See Appendix B, section 3.3. The first part of the blender exercise investigates the effect of varying the amount of waterin the blender. Qualitative analysis involves manipulating the rate form of the First Law ofthermodynamics dT ˙ ˙ mc = Q
responded in that category. Results are from Spring 2015 class.In both Spring of 2014 and 2015, the useful of the PLG sessions was very dependent on theindividual PLG leader. During both semesters, there was one PLG leader (PLGL1) whofollowed the exact procedure laid out in the methods section (15 minutes of Q&A, 45 minutes ofprepared exercise, 1 hour of work time). Additionally, each semester, the other PLG leader(PLGL2) did not follow the procedure and spent the majority of the time helping students withtheir assignments. PLGL1 had a small group of students who attended the sessions each week.These students were not struggling in the class, but actually using these sessions to enhance theiralready proficient level of understanding. PLGL2 had
undergraduate heat transfertextbooks is usually limited to fins of uniform cross-sectional area. For more complex finconfigurations, only efficiency charts are provided in most heat transfer textbooks1-15. Analysisfor fins of variable cross-sectional areas or annular fins results in more complex differentialequations. The solutions for temperature distribution involve complex functions such as Besselfunctions. The analyses for these types of fins are not typically fully covered in an introductoryheat transfer course. Instead the results are shown in the form of fin efficiency charts.The fin efficiency is defined as q act q act ϕf ? ? (1
) =0 x T (0, t ) = −q . (9) x 5Where k = 401 N/mK and q = 20 w. Initial condition is specified as that the temperature overthe rod T (x,0) = 290ok. The objective of the project is to build numerical models based on finite difference methodsfor predicting the changes of temperature along the rod with respect to time. The 7-inch-longrod is divided into n uniform segments, with nodes numbered from 0 on the left end to n on theright end. The first-order and second-order derivatives in the heat
, the flow area A2 of the nozzle exit, the density ρ of the fluid, and the volumetric flowrate Q of the fluid. (Why did we choose these parameters? Well, hindsight is great. Weactually performed the experiment and found that this choice of parameters was consistent withthe data.) Hence there are five parameters in the problem.The dimensional analysis technique 1, 2 will enable us to reduce the problem to one of only twodimensionless groups. These groups are determined via the Buckingham Pi method to be: andThis means that the dimensionless group is a function of .The following describes the determination of these pertinent dimensionless groups for thisproblem:We wish to determine how the
center of mass. Thisassumption can be later checked to see if it is valid.The cylinder is assumed to be at an initial temperature Ti and is then placed in still air at atemperature T∞. The coefficient of convection and surface area of the body are referred to as hand A, respectively. If the body is at a temperature T, then, the heat transfer Q due to convectionis given by Q = dU/dt = hA(T-Tinf) (2)where U is the total energy stored in the system. The temperature T obviously varies with time.The quantity Q can also be expressed in terms of the heat capacity C of the material. Indeed, bydefinition C is Q C
lab.The major tasks of the analysis are: 1. Identify symmetry (Alt B) to simplify analysis [analyze just the left or right half, starting from the top attachment]. 2. Add a dummy load (Q) at the location of maximum deflection [the lower left corner in Alt A and the middle of the lower span in Alt B]. 3. Use statics to determine the vertical reactions. 4. Identify one reaction as redundant (R) in Alt B [horizontal force on either side]. 5. Develop expressions for internal bending moments in all parts of the structure, as a function of the applied loads, dummy load, and redundant reaction load (Alt B): ALT A: pWL pWL
through the volumes worth of materialwritten on the subject in order to simplify the topic of entropy to something that is clear and easyto understand. To accomplish this, the paper contributes by (1) introducing examples ofspontaneous processes that most people should already understand, (2) providing a brief reviewof the general operations of heat engines and the Carnot cycle, (3) framing the Carnot cycle inrelation to entropy, (4) discussing non-ideal heat engines, (5) showing analogies to help thereader understand the significance of the ratio Q/T as a definition for entropy, (6) adding somebrief notes on entropy that are beyond the general scope of this paper, and (7) presentingbrainteasers designed to engage students in the classroom. We
or ft) (1) where f is the friction loss coefficient, L is the length of the pipe (m or ft), V is the velocity (m/s or ft2/s) and g is the gravitational acceleration (m/s2 or ft/s2). The velocity of water inside any section can be determined using continuity equation: Q = A.V (2) where Q is the volumetric flow rate in (gpm, lit/min, m3/s, or in3/min, or any units based on your system calculations) and A is the cross‐sectional of the pipe (Make sure you use consistent units for A and V to have the proper units for Q). The state of the flow is determined based on Reynold’s Number NR = V.D/𝜈 (3
assessed the normality of each student section’s data for each year. To do this, wecreated a quantile-quantile (Q-Q) plot for each student section, including both pre-test scores andlab quiz scores, resulting in a total of 8 plots. For simplicity, only one of the plots is shown inFigure 4, however, it is representative of the other plots obtained. Because this plot suggests alinear trend, we can infer that our data is approximately normally distributed, and thus, parametricstatistical tests, such as the t-test, are applicable in our subsequent analyses.Figure 4: A Q-Q plot from one student section assessing the normality of our data. The linearity ofthis plot suggests that the data follows an approximate normal distribution. Q-Q plots were
Page 15.356.11KK=A+A'-diag(diag(A))KK=KK.*area% apply boundary conditions for temperature T1=100 and T7=680K=KK;K(1,1)=1; K(1,2)=0;K(el_no+1,el_no)=0;K(el_no+1,el_no+1)=1;%apply nodal heat loadsheatload=zeros(el_no+1,1);heatload(1,1)=230; heatload(el_no+1,1)=50;%Solve for unknown nodal temperatures (t)t=inv(K)*heatload%find nodal heatq=zeros(el_no,1);for i = 1:el_no q(i)=area.*U(i).*(t(i+1)-t(i));end%q Page 15.356.12
injection water drained from thecylinder tended to overflow the FWT and that the temperature in the FWT of one of Smeaton’sengine was 134oF.methodologyThe general model that applies to a heat engine operating a pump is shown in Fig. 6. Figure 6 - Pumping Engine Efficiency Relationships Page 25.1357.8The notation convention used herein is that “dotted” terms indicate the time rate of the extensivevariable. The fuel energy rate ( E ) is the product of the mass flow rate of the fuel ( m ) and itsheating value (HV). The thermal power ( Q s ) supplied to the cylinder is the product of the massflow rate of the steam ( m stm
. Themanual robot control and lead-through programming session deals with manipulating varioussmall objects. The computer programming task (two week session) is to have the robot write aword (student’s name) on an 8 ½ by 11 inch sheet of paper. Students’ evaluation survey, collectedwith the lab reports at the end of lab sections, plays an important role of “closing the loop” instudents’ experiential learning process. Figure 1: Laboratory setup for the RV-M2 robot.Hardware Setup The robot system setup, shown in Fig.1, includes the RV-M2 robot arm, the teach pendant, thecontrol module, and a computer. The robot arm can be controlled manually by a teach pendant orprogrammatically by a Q-Basic program, which originally run on an
system. A central chiller facility is located in theopen area at the top of the figure (see Figure E2). Chilled fluid lines from the central chiller areto be run through access tunnels located 20 ft below grade level. Dowtherm QTM, a commonly-employed heat transfer fluid, is to be used. Properties of Dowtherm Q are available on the web.Cooling requirements are estimated as follows: Concourse tons( = 12,000 Btu/hr) K 1 750 2.0 2 500 4.50 3 750 2.0 4 500 4.50 500 4.50 (must be in parallel)The
. Welect. Bomb + - QB Fuse Wire Sample CMFor the process of igniting the fuse and the test sample, and the resulting rise in watertemperature, the 1st Law states that: E 2 − E 1 = Energy In − Energy outso that, ∆E = Welect. − Q B (1)Since
factors of 60s/min and 12 in/ft would be used in the actual numerical calculation.In those institutions with co-op programs, students may return to academic terms having beenexposed to shorthand equations, only to conclude that the “real world” has no patience withrigorous units treatments. One such example is the HVAC industry. A common expression forestimating the heat transfer rate in a system is q = cfm * 1.085 * T, where q is in units of Btu/h,cfm is ft3/min, and T is in units of F (in fact, 1.085 is often replaced with unity for “quick anddirty” results, leaving q = cfm * T). The constant, 1.085, necessarily has the units appropriatefor the equation to be dimensionally homogeneous. A student using this equation on a dailybasis – or a
resources k. Defines a market and market opportunities l. Engages in actions with the understanding that they have the potential to lead to both gains or lossesConnections m. Articulates the idea to diverse audiences n. Persuades why a discovery adds value from multiple perspectives (technological, societal, financial, environmental, etc.) o. Understands how elements of an ecosystem are connected p. Identifies and works with individuals with complementary skill sets, expertise, etc. q. Integrates/synthesizes different kinds of knowledgeThis framework is one of the few efforts to systematically map KEEN’s three C’s to specificstudent behavioral outcomes and it has been used in entrepreneurial mindset assessment effortsand/or validated by a few
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
coolingsystems? What is the purpose of finding the mass flow rate of the air in the house?”A: “Mass flow rate is used only in the calculating air exchanges between the house and theambient as it happens due to closing and opening of doors, leakage through the windows anddoors etc. and this is given as 0.4.”Q: “Shouldn't the heat input for solar radiation be higher in the summer than in the winter,considering we are closer to the sun in the summer time? Would you please elaborate on thismatter?”A: “Good question! In winter, the angle made by the sun is more oblique at the earth. (see linkfor a picture depicting this). Therefore, more of it may reach the house through the windows.However, there are other factors such as which direction the windows are
. T-High Q-High 3 kPa 10 © Pa 3 condenser 2 TH ( 273 - 25) © K TL ( 273 / 45) © K Ammonia W-in PL_NH3 100© kPa PH_R22 200© kPa 4 1 Heat Exchanger 3 2 kg mdotNH3 0.2© FT 10© K s R-22
the section on “MATLAB pdetool examples”. Theproblem statement and the differential equation is provided below. The boundary conditions mustbe designed by the student for both the exact/Galerkin MWR and the MATLAB pdetool drivensolution.Consider the unsteady 1-D heat equation for temperature u [in units of Kelvin]. du d2 u ρC −k 2 =Q+ h (uext − u) (3) dt dx Convective heat transferFor the following example values: ρ = 1.0 [kg/cubic m] , C = 1.0 [J/kg-K] andk = 1.0 [W/m-K] , with a heat source term Q = x [W/cubic m] and no convection heat transfer,with
i e e (1) dEcv V2 V2 Q cv W cv m i hi i gz i m e he e gz e (2) dt i 2 e 2 dS cv Qj mi si me s e cv (3) dt