From the following equation, assume that the cross-sectional area A is a constant. = (1/m) hc(T-Tfluid) Also assume that all other physical parameters k, h, A, C, L, Twall and T fluid are well known and assumed to be positive constants. (a) Based on these assumptions, the above ODE can be simplified to which of the follow? hc(T-Tfluid) Ока d²T dx2 (k.. dA dk dT + A. = dx dx dx hc(T-T fluid) dT ка = (hC(T-T fluid)) dx dx (k.. dA dk d²T + A. dx dx dx² hc(T-T fluid) d dx (kA) = (hC(TT fluid)) dx ат (b) Solve the ODE based on the following two boundary conditions. For simplicity, let a² T(x) = At x = 0, T = T wall At x = L, dT = 0. dx = Ch ка for when formulating your solution. (Use T, to represent T fluid and Tw to represent T wall in your response.) (c) Define a "dimensionless" variable @(x) = T(X) - Tfluid Twall - Tfluid ee Based on the T(x) solution, rewrite the solution in terms of (x) and the hyperbolic cosine function, where cosh(y) = Again, let a² = 2 8(x) = Ch for when formulating your solution. ка
From the following equation, assume that the cross-sectional area A is a constant. = (1/m) hc(T-Tfluid) Also assume that all other physical parameters k, h, A, C, L, Twall and T fluid are well known and assumed to be positive constants. (a) Based on these assumptions, the above ODE can be simplified to which of the follow? hc(T-Tfluid) Ока d²T dx2 (k.. dA dk dT + A. = dx dx dx hc(T-T fluid) dT ка = (hC(T-T fluid)) dx dx (k.. dA dk d²T + A. dx dx dx² hc(T-T fluid) d dx (kA) = (hC(TT fluid)) dx ат (b) Solve the ODE based on the following two boundary conditions. For simplicity, let a² T(x) = At x = 0, T = T wall At x = L, dT = 0. dx = Ch ка for when formulating your solution. (Use T, to represent T fluid and Tw to represent T wall in your response.) (c) Define a "dimensionless" variable @(x) = T(X) - Tfluid Twall - Tfluid ee Based on the T(x) solution, rewrite the solution in terms of (x) and the hyperbolic cosine function, where cosh(y) = Again, let a² = 2 8(x) = Ch for when formulating your solution. ка
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help with this problem described below and an explanation for the solution. (
Transcribed Image Text:From the following equation, assume that the cross-sectional area A is a constant.
= (1/m)
hc(T-Tfluid)
Also assume that all other physical parameters k, h, A, C, L, Twall and T fluid are well known and assumed to be positive constants.
(a) Based on these assumptions, the above ODE can be simplified to which of the follow?
hc(T-Tfluid)
Ока
d²T
dx2
(k..
dA
dk dT
+ A.
=
dx
dx dx
hc(T-T fluid)
dT
ка
=
(hC(T-T fluid)) dx
dx
(k..
dA
dk
d²T
+ A.
dx
dx dx²
hc(T-T fluid)
d
dx
(kA) = (hC(TT fluid))
dx
ат
(b) Solve the ODE based on the following two boundary conditions. For simplicity, let a²
T(x) =
At x = 0, T = T
wall
At x = L,
dT
= 0.
dx
=
Ch
ка
for when formulating your solution. (Use T, to represent T fluid and Tw to represent T
wall
in your response.)
(c) Define a "dimensionless" variable @(x) =
T(X) - Tfluid
Twall - Tfluid
ee
Based on the T(x) solution, rewrite the solution in terms of (x) and the hyperbolic cosine function, where cosh(y)
=
Again, let a²
=
2
8(x) =
Ch
for when formulating your solution.
ка
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