Transport Processes

Question 1

Formula for Conduction

Answer 1

Q/A = -kΔT/Δx

resistance = Δx/k

Question 2

Heat in Conduction

Answer 2

Qᴛ = Qᴀ = Qʙ = Qc

Question 3

Conduction in Hollow Cylinder

Answer 3

. - 2πkLΔT
Q= ———————
ln (r2/r1)

E5-7

Question 4

Conduction in Sphere

Answer 4

. - 4πkΔT
Q= ———————
1/r2 - 1/r1

E5-8

Question 5

Conduction in Sphere with more than 3 insulation

Uses the cylinder formula

Answer 5

. - 2πLΔT
Q= ——————————————-
1/kᴀ·ln(r₂/r₁) + 1/kʙ·ln(r₃/r₂)+…+

E5-8

Question 6

Conduction in Series

Answer 6

E5-9

Question 7

Formula for Convection

Answer 7

Q/A = -hΔT

resistance = 1/h

h = individual heat transfer coeff.

Question 8

Heat and Resistance in Convection

Answer 8

Qᴛ = Qᴀ + Qʙ + Qc
1/Rᴛ = 1/Rᴀ = 1/Rʙ = 1/Rc

Question 9

Combination in Series

Answer 9

Q/A = -ΔT/(1/U)
Q/A = -ΔT/ (Δx/k) + (1/h)

where 1/U = 1/k + 1/h

U = overall heat transfer coeff. (both resistance of conduction and convection)

Question 10

Conduction with Internal Heat Generation for Cylinder

Ex. Wire

Answer 10

. q̇r ²
To = ———- + Tw
4k
where:
q̇ = Q/V = I²R/ πr²L
r = radius
To = Center Temperature
Tw = Outside Temperature

Question 10

Conduction with Internal Heat Generation for a Flat Slab

Answer 10

. q̇x²
To = ———- + Tw
2k
where:
q̇ = Q/V
x = thickness
To = Center/Max Temperature
Tw = Surface Temperature

Question 11

Double Pipe Heat Exchanger

withour Ft

Answer 11

Q = UAΔTₗₘ

where:
Q = mCpΔT
-Qloss = Qgain
ΔTₗₘ = T1-T2/ln(T1/T2)
if not given: A = πDL (not cross-sectional)
1/U = 1/h,o + 1/h,cw; h=coeff.

Counter-current Flow
T1 ———-> T2
t2 <———- t1

Parallel Flow
T1 ———-> T2
t1 ———-> t2

Question 12

Heat Exchanger

with Ft

Answer 12

Q = UAΔTₗₘ · Ft
Q = UᵢAᵢΔTₗₘ = UₒAₒΔTₗₘ

where:
Q = mCpΔT
ΔTₗₘ = T1-T2/ln(T1/T2)
A = πDL
Ft = ? R = T₁ - T₂ / t₂ - t₁
S = t₂ - t₁ / T₁ - t₁

1-2 HE –> 1 shell and 2 tubes

Question 13

Heat Transfer Coefficient

Convection

Answer 13

Q/A = -hΔT

Use:
Re, Pr, and Nu formulas
**
T2-144 if Pr for air
T2-145 for k**