Transport Processes in Materials Science

1
Transport Processes inMaterials Science
Engineering

• Notes on Text by
• D. R. Poirier and G. H. Geiger
• Background
• General Relations

2
Generalized Balances

• Amount of Yin - Amount of Yout Accumulation of
  Y
• Rate of Yin- Rate of Yout Rate of Accumulation
  of Y
• Where Y Mass, Momentum, Energy,
• Steady State Rate of Yin - Rate of Yin 0

3
Relate magnitude function y _at_ xDx in terms of
magnitude _at_ x
In the limit as

Dx
y
yxDx
Dy
yx
xDx
x
x
4
Relate value of function at xDx in terms of
value at x.
In the limit as

Dx
y
yxDx
Dy
yx
xDx
x
x
5
Relate value of f(x) at xDx in terms of f(x) at
x.
In the limit as

Dx
f(x)
f(x)xDx
Df(x)
f(x)x
xDx
x
x
6
Relate temperature temperature gradient at xDx
in terms of values at x.
Dx
T
x
x
Dx
7
Control Volume
x-plane
syy
y-plane
tyx
tyz
y
txy
Dy
tzy
sxx
txz
tzx

• x

szz
z
z-plane
Dz
Dx
8
Cylindrical Coordinates
Common Symmetry --- Axisymmetric (2-D)
Radial (1-D)
Axial (1-D)
Circumferential (1-D)
9
Spherical Coordinates
Common Symmetry --- Spherically Symmetric (1-D)
Y Y(r) Y Y(q,f)
10
Fundamental Dimensions Units

• Distance L m cm ft
• Mass M kg g lbm
• Time t s s s
• Temperature T K OC OF

11
Derived Dimensions Units

• Area L2 m2 cm2 ft2
• Volume L3 m3 cm3 ft3
• Velocity L/t m/s cm/s ft/s
• Acceleration L/t2 m/s2 cm/s2 ft/s2
• Density M/L3 kg/m3 g/m3 lb/ft3
• Force ML/t2 kg-m/s2 g-cm/s2 lbf
• Newton dyne
• Stress/Pressure M/Lt2 N/m2 dyne/cm 2
  lb/in2
• Pascal
• Momentum ML/t kg-m/s g-cm/s lb-ft/s
• Rate of ML/t2 N dyne lbf
• Momentum

12
Derived Dimensions Units

• Energy ML2/t2 N-m dyne-cm ft-lb
• Joule erg
• (calorie) (BTU)
• Power ML2/t3 Joule/s erg/s HP
• Watt
• Viscosity

13
Force rate of change in momentum

• For constant m

Per unit volume