A composite one-dimensional plane wall is of overall thickness 2L. Material A spans the domain − L ≤ x < 0 and experiences an exothermic chemical reaction leading to a uniform volumetric generation rate of q A . Material B spans the domain 0 ≤ x ≤ L and undergoes an endothermic chemical reaction corresponding to a uniform volumetric generation rate of q . B = − q . A . The surfaces at x = ± L are insulated. Sketch the steady-state temperature and heat flux distributions T ( x ) and respectively, over the domain − L ≤ x ≤ L for k A = k B , k A = 0.5 k B , and k A = 2 k B . Point out the important features of the distributions you have drawn. If q . B = − 2 q . A , can you sketch the steady-state temperature distribution?
A composite one-dimensional plane wall is of overall thickness 2L. Material A spans the domain − L ≤ x < 0 and experiences an exothermic chemical reaction leading to a uniform volumetric generation rate of q A . Material B spans the domain 0 ≤ x ≤ L and undergoes an endothermic chemical reaction corresponding to a uniform volumetric generation rate of q . B = − q . A . The surfaces at x = ± L are insulated. Sketch the steady-state temperature and heat flux distributions T ( x ) and respectively, over the domain − L ≤ x ≤ L for k A = k B , k A = 0.5 k B , and k A = 2 k B . Point out the important features of the distributions you have drawn. If q . B = − 2 q . A , can you sketch the steady-state temperature distribution?
A composite one-dimensional plane wall is of overall thickness 2L. Material A spans the domain
−
L
≤
x
<
0
and experiences an exothermic chemical reaction leading to a uniform volumetric generation rate of
q
A
.
Material B spans the domain
0
≤
x
≤
L
and undergoes an endothermic chemical reaction corresponding to a uniform volumetric generation rate of
q
.
B
=
−
q
.
A
. The surfaces at
x
=
±
L
are insulated. Sketch the steady-state temperature and heat flux distributions
T
(
x
)
and respectively, over the domain
−
L
≤
x
≤
L
for
k
A
=
k
B
,
k
A
=
0.5
k
B
,
and
k
A
=
2
k
B
.
Point out the important features of the distributions you have drawn. If
q
.
B
=
−
2
q
.
A
,
can you sketch the steady-state temperature distribution?
To maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during
transportation from a production field.
(1) Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating
material. The inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe (
ks = 40 W/m-K) has an inside diameter of Di, 1 = 150 mm and wall thickness t; = 20 mm while the outer
steel pipe has an inside diameter of D2 = 250 mm and wall thickness, = 1,. Determine the maximum
allowable crude oil temperature to ensure the polyurethane foam insulation (k, = 0.0425 W/m.K) between
the two pipes does not exceed its maximum service temperature of Tp, max = 70°C. The ocean water is at
Too, o
ho
T = -5°C and provides an external convection heat transfer coefficient of h = 500 W/m²K. The
convection coefficient associated with the flowing crude oil is h₁ = 450 W/m²K.
(2) It is proposed to enhance the performance of…
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Refrigeration and Air Conditioning Technology (Mi...Mechanical EngineeringISBN:9781305578296Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill JohnsonPublisher:Cengage Learning