Miscellaneous
What is the equation to find the hmass of H20 diffusing into an air filled hollow fiber (cyl) ? (laminar flow)
Sh= (hmass*D) / (DH2o,air)
hmass= (Sh* Dab)/D
What is the equation for Heat Transfer via Conduction
Qcond= h * As * (Ts-Tinf)
Write the symbolic equivalents to
Nu=
Kinematic Viscosity=
Re number (length based)=
Nu= (hL/kfluid)
kinV= mu/rho
Re= VL/KinV
What is the most basic equation for Qdot for a heat exchanger, define each term.
Q=U*As*deltaTLM
Overall heat transfer coeff * Surface area * Log mean temp diff.
What did sydney major in at her highschool?
Dance
What is the q boil equation for nucleate boiling?
= muL* hfg * [(g(pl-pv)/ sigma)] ^ 1/2 *
[(Cpl(Ts-Tsat)/(Csf * hfg *Prl ^n)] ^3
What is the Fourier-Biot EQ for a cylindrical coordinate system where k is constant and there is only radial movement? NOT at steady state, and there is e generation. ( Heat Balance Equation)
1/r (d/dr)(kr* dT/dr) + egen/k = (1/alpha)(dT/dt)
What is the deltaT log mean equation for flow through a tube with a constant T surface?
DeltaTlm= [(Ts-Te) - (Ts-Ti)] / [ln ((Ts-Te)/(Ts-Ti))]
Sketch graphically/ physically the difference between Double pipe parallel flow and counter flow. (Temp and position on graph).
Which is more desired for HeatX design? Why?
Label
axis, deltaT1 and deltaT2, hot and cold streams.
Sydney has the answer I can't put pictures in.
Counter flow, The log mean temperature difference is smaller. DeltaT1 and DeltaT2 are more similar in value.
What will Sydney be working on during her internship this summer?
Biofuels, Bioenergy, Renewable Diesel, Biodiesel, Heat exchanger Design
What are the fin efficiency equations for both adiabatic and infinite assumptions?
N inf= sqrt(hPKA) * (Tb-Tinf) / h P L (Tb-Tinf) =
(1/mL)
N ad =
sqrt(hPKA)*(Tb-Tinf) *tanh(mL)/(hPL (Tb- Tinf))
= (tanh(mL)/mL)
If there is a fluid(a) flowing through a boundary (a window) to an adjacent fluid(b) on the other side, what are potentially useful boundary conditions to solve for the heat balance? ( also draw a picture of the set up)
qconv=qcond @ x=0
so
h1(Tinf-T1)=-k(dT/dx) @ x=0
Liquid water is flowing through a tube at a velocity of 0.5 m/s, at 100 C. What is the thermal entry length for a tube with a Diameter of 0.1 cm.
Hint: You will need Handout 4 for appropriate properties.
Properties at T=100 C
rho= 957.9 mu=0.282*10^-3 Pr=1.75
Re= (957.9)(0.5)(0.001)/(0.282*10^-3)= 1698
Laminar
Lh= 0.05*1698*0.001= 0.0849 m
Lt= Lh*Pr= 0.149 m
What is the NTU value for (single pass cross flow Heat X mixed cmax)
Handout 11
Ch= 8.7 * 2742
Cc=4.05 * 1964
Tce= 70
Tci= 10
Thi=110
Ch= 23855.4
Cc= 7954.2
c= 7954.2/23855.4= 0.333
E= Cc/Cmin * (60/100)= 0.6
NTU= -ln(1+(ln(1-Ec)/c)= 1.106
What is Sydney's favorite scent?
Acceptable answers:
balsam
Christmas tree
Pine
Woods
Sydney Is going to draw a picture on the board.
Draw the resistance network for this image.
Write out the Rtotal equation
Write out general forms of Rconv and Rcond
Sydney Has the answer lol she will write it
Rtotal= R1 + R2 + (1/R1 + 1/R4)^-1 + R5
Rconv= 1/hAs
Rcond= L/KAs
Write both the infinite fin, and adiabatic fin Theta equations.
What are the keywords for each assumption in problem statements?
Infinite: Long, infinitely long, The temperature at the tip of the fin is equal to T surroundings)
theta=
(T(x)-Tinf)/(Tb-Tinf)= exp(-mx)
Adiabatic: Adiabatic, the heat rate at the tip of the fin =0.
theta=
(T(x)-Tinf)/(Tb-Tinf)= ((cosh(m(L-x))/(cosh(mL))
List What Type of Convection each of these scenarios includes, and the appropriate Nu number equation.
100 pts each
1. A fan blowing over a flat plate. (laminar)
2. Air flow over a vertical printed circuit board. (Do not calc Ra*)
3. Flow of oil in a pipeline under a lake. (Developing Flow with Pr>5)
4. Air Flow perpendicular to in line tubes in a Tube Bank. NL=7, Pr= 20, Re= 2,000
1. External Forced Nu=0.664*(Re,L)^0.5*(Pr)^0.33
2. Natural Nu=
[(48/(Ra* x (S/L))+ (2.51/(Ra* x (S/L)^0.4)]^-0.5
3. Internal Forced Nu=
3.66+ [((0.065 (D/L)*Re*Pr)/
(1+0.04((D/L)*Re*Pr)^(2/3)]
4. External Forced Nu=
(0.96)*
(0.27)*(Re)^0.63*(Pr)^0.36* (Pr/Prs)^0.25
Solve for the As to maintain 70 C in a double pipe counterflow Heat X. (There IS fouling, table 11-2 for help)
Thin= 250
Tcin= 30
Tcout=70
hi= 1250
ho= 850
mdot= 3.47
Cp= 4181
(units cancel don't worry)
Q=U*As*deltaTLM=m*Cp*(Tcout-Tcin)
As= m*Cp*(Tcout-Tcin)/ (U*deltaTLM)
U= 1/hi + 1/ho + R fouling
U= (1/1250+1/850+1.5*10^-4)= 470.26
deltaTLM=
[(250-70)- (180-30)] / [(ln(180/150)] = 164.5
As= (3.47)(4181)(70-30) / (470.26*164.5) = 7.5
What TV show was Sydney in a commercial for?
Powerpuff Girls
If I am standing in a room How much heat am I radiating out if...
Tsurface= 30 C
As room= 1.4 m^2 (I'm very tiny)
E=0.95
Tsurr= 10 C
sigma= 5.67*10^-8
Qrad= E sigma As (Ts^4-Tsurr^4)
151.9
Set up the heat balance equation for a cylindrical electrical wire covered in a ceramic coating. There will be two equations, one for the wire and one for the coating. Do not solve. Your answer should be in terms of Tw(r), Tc(r), r, d/dr, dT/dr, and egen/kw.
For 100 extra points list the boundary conditions needed to solve. There are 4 each worth 25 points.
Ceramic: 1/r (d/dr) (r*dTc/dr)= 0
Wire: d/dr (r* dTw/dr) = (-egen/Kw)* r
Boundary Conditions
@ r=0 dTw/dr=0
@ r= r1 Tw=Tc
@ r=r1 qc=qw
@r = r2 Tc=Tsurrounding
SYMBOLICALLY solve to find the most accurate Nu, f, and T inner surface temperature of a smooth pipe wrapped with electrical tape. (Uniform Heating across tube surface)
*Assume fully developed Turbulent flow with an Re=8,000
Re= DV/ kinV
Nu=
((f/8)(Re-1000) Pr )/
(1 + 12.7(f/8)^0.5(Pr^(2/3) -1))
f= 0.79*ln(Re)-1.64)^-2
h=Nu*k/D
Q=h*As*(Tsin-Tout)
Tsin = Tout+ Q/(H*As)
Derive the 1/Ui and 1/Uo equation for a cylinder from
Q= UiAideltaTlm = UoAodeltaTlm
(1/UiAi)=
(1/hiAi)+ (ln(Do/Di)/2piKL) + (1/hoAo) =
(1/Uo/Ao)
(1/Ui ) = (1/hi)+ (2piDiLln(Do/Di)/ 2piKL) + (2piDiL/ho(2piDoL)
(1/Ui)= (1/hi)+(Di Ln (Do/Di)/ k) + (Di/hoDo)
1/Uo= (Do/hiDi) + (Doln(Do/Di)/K) + (1/ho)
How many siblings does sydney have?
17! (yes) (really)