The wall (thickness L) of a furnace, with inside temperature 800° C, is comprised of brick material [thermal conductivity = 0.02 W m-1 K-!)]. Given that the wall thickness is 12 cm, the atmospheric temperature is 0° C, the density and heat capacity of the brick material are 1.9 gm cm-³ and 6.0 J kg- K-l respectively, estimate the temperature profile within the brick wall after 2 hours. Solve the partial differential equation ƏT ƏT = pc subject to the initial condition T(x,0) = 800 sin 2L and boundary conditions at the inner (x = L) and outer (x = 0) walls of T = 0 at x = 0 and ƏT at x = L Find the temperature profile at T = 7200 seconds = 2 hours.
The wall (thickness L) of a furnace, with inside temperature 800° C, is comprised of brick material [thermal conductivity = 0.02 W m-1 K-!)]. Given that the wall thickness is 12 cm, the atmospheric temperature is 0° C, the density and heat capacity of the brick material are 1.9 gm cm-³ and 6.0 J kg- K-l respectively, estimate the temperature profile within the brick wall after 2 hours. Solve the partial differential equation ƏT ƏT = pc subject to the initial condition T(x,0) = 800 sin 2L and boundary conditions at the inner (x = L) and outer (x = 0) walls of T = 0 at x = 0 and ƏT at x = L Find the temperature profile at T = 7200 seconds = 2 hours.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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![The wall (thickness L) of a furnace, with inside temperature 800° C, is comprised of brick material
[thermal conductivity = 0.02 W m-1 K-1)]. Given that the wall thickness is 12 cm, the atmospheric
temperature is 0° C, the density and heat capacity of the brick material are 1.9 gm cm-3 and
6.0 J kg- K- respectively, estimate the temperature profile within the brick wall after 2 hours.
Solve the partial differential equation
ƏT
k
ƏT
= pc,
Ət
subject to the initial condition
TI
T(x,0) = 800 sin
2L
and boundary conditions at the inner (x = L) and outer (x = 0) walls of
T = 0
at
x = 0
and
ƏT
at
x = L
Find the temperature profile at T = 7200 seconds = 2 hours.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5eeb8363-e847-4f83-88cd-dc248860c018%2F1549de78-0c7b-46de-b99c-25ebd6468209%2Ftd8and9_processed.png&w=3840&q=75)
Transcribed Image Text:The wall (thickness L) of a furnace, with inside temperature 800° C, is comprised of brick material
[thermal conductivity = 0.02 W m-1 K-1)]. Given that the wall thickness is 12 cm, the atmospheric
temperature is 0° C, the density and heat capacity of the brick material are 1.9 gm cm-3 and
6.0 J kg- K- respectively, estimate the temperature profile within the brick wall after 2 hours.
Solve the partial differential equation
ƏT
k
ƏT
= pc,
Ət
subject to the initial condition
TI
T(x,0) = 800 sin
2L
and boundary conditions at the inner (x = L) and outer (x = 0) walls of
T = 0
at
x = 0
and
ƏT
at
x = L
Find the temperature profile at T = 7200 seconds = 2 hours.
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