ME 311 – Heat Transfer
Fall 2013
Homework 4
1) Consider the one-dimensional wall shown in the sketch which is initially at a uniform temperature
Ti and is suddenly subjected to the convection boundary condition with a fluid at T∞.
Insulation
Wall,
T(x,0)= Ti,
k, α
T∞, h
For a particular wall, case 1, the temperature at x=L1 after t1=100s is T1(L1,t1) = 340˚C. Another wall,
case 2 has different thickness and thermal conditions as shown below.
L α k Ti T∞ h
Case (m) (m2/s) (W/m∙K) (˚C) (˚C) (W/m2∙K)
1 0.15 14x10-6 30 250 350 150
2 0.40 27x10-6 24 125 18 45
How long will it take for the second wall to reach 28.7˚C at the position x=L2? Use as the basis for
analysis, the dimensionless functional dependence for the transient temperature distribution expressed
in Equation 5.38.
SOLUTION:
Assumptions: - One dimensional conduction
- Constant properties
The dimensionless functional dependence for the one-dimensional, transient temperature distribution,
Equation 5.38, is:
where
x* = x/L Bi = hL/k Fo = αt/L2
If the parameters x*, Bi, and θ* are the same for both walls, then Fo must be the same. Evaluate these
parameters:
This study source was downloaded by 100000899606070 from CourseHero.com on 02-18-2026 22:37:49 GMT -06:00
https://www.coursehero.com/file/11357368/me311-Hw4-Solution/
, This study source was downloaded by 100000899606070 from CourseHero.com on 02-18-2026 22:37:49 GMT -06:00
https://www.coursehero.com/file/11357368/me311-Hw4-Solution/
Fall 2013
Homework 4
1) Consider the one-dimensional wall shown in the sketch which is initially at a uniform temperature
Ti and is suddenly subjected to the convection boundary condition with a fluid at T∞.
Insulation
Wall,
T(x,0)= Ti,
k, α
T∞, h
For a particular wall, case 1, the temperature at x=L1 after t1=100s is T1(L1,t1) = 340˚C. Another wall,
case 2 has different thickness and thermal conditions as shown below.
L α k Ti T∞ h
Case (m) (m2/s) (W/m∙K) (˚C) (˚C) (W/m2∙K)
1 0.15 14x10-6 30 250 350 150
2 0.40 27x10-6 24 125 18 45
How long will it take for the second wall to reach 28.7˚C at the position x=L2? Use as the basis for
analysis, the dimensionless functional dependence for the transient temperature distribution expressed
in Equation 5.38.
SOLUTION:
Assumptions: - One dimensional conduction
- Constant properties
The dimensionless functional dependence for the one-dimensional, transient temperature distribution,
Equation 5.38, is:
where
x* = x/L Bi = hL/k Fo = αt/L2
If the parameters x*, Bi, and θ* are the same for both walls, then Fo must be the same. Evaluate these
parameters:
This study source was downloaded by 100000899606070 from CourseHero.com on 02-18-2026 22:37:49 GMT -06:00
https://www.coursehero.com/file/11357368/me311-Hw4-Solution/
, This study source was downloaded by 100000899606070 from CourseHero.com on 02-18-2026 22:37:49 GMT -06:00
https://www.coursehero.com/file/11357368/me311-Hw4-Solution/
