A metal bar has a cross section of A mm². The length of the bar is B m. The bar is heated from one of its ends using the heating rate of C W. Simultaneously, the other end of the bar is maintained at a constant temperature T = D °C. Determine the temperature distribution within the metal bar. The thermal conductivity of the metal bar is E [W/(m°C)]. Determine the temperature distribution using analytical calculations or computer software (Excel, Matlab). Draw a graph showing the temperature distribution as a function of distance x from the heated end of the bar According to the Fourier's Law the heat flux density [W/m²] as a function of distance equals q(x) = -k (x). Now the heat quantity Q [W] flowing through the bar becomes Q = qA = −kA¹ dT(x) dx dx Above, k is thermal conductivity [kW/(m°C)] A is the surface are of cross section [m²]
A metal bar has a cross section of A mm². The length of the bar is B m. The bar is heated from one of its ends using the heating rate of C W. Simultaneously, the other end of the bar is maintained at a constant temperature T = D °C. Determine the temperature distribution within the metal bar. The thermal conductivity of the metal bar is E [W/(m°C)]. Determine the temperature distribution using analytical calculations or computer software (Excel, Matlab). Draw a graph showing the temperature distribution as a function of distance x from the heated end of the bar According to the Fourier's Law the heat flux density [W/m²] as a function of distance equals q(x) = -k (x). Now the heat quantity Q [W] flowing through the bar becomes Q = qA = −kA¹ dT(x) dx dx Above, k is thermal conductivity [kW/(m°C)] A is the surface are of cross section [m²]
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.3P: 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of...
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![Project Theme 4: Insulated bar
A metal bar has a cross section of A mm². The length of the bar is B m. The bar is heated from one of
its ends using the heating rate of C W. Simultaneously, the other end of the bar is maintained at a
constant temperature T = D °C. Determine the temperature distribution within the metal bar. The
thermal conductivity of the metal bar is E [W/(m°C)]. Determine the temperature distribution using
analytical calculations or computer software (Excel, Matlab). Draw a graph showing the temperature
distribution as a function of distance x from the heated end of the bar
According to the Fourier's Law the heat flux density [W/m²] as a function of distance equals q(x) =
dT (x)
-kat (x)
Now the heat quantity Q [W] flowing through the bar becomes Q =qA = -kA
dx
dx
k is thermal conductivity [kW/(m°C)]
A is the surface are of cross section [m²]
Above,
Heat
Supply,
kW
x = 0m
Area, mm²
Insulation
-Temperature, T(x)
Heat flow
Constant point at
x = Bm
T =D °C
x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b49e7f7-2c5c-46e7-9733-06586610151a%2F9f0e9dde-0b9e-4790-8c37-0c67c209210e%2F155w8pk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Project Theme 4: Insulated bar
A metal bar has a cross section of A mm². The length of the bar is B m. The bar is heated from one of
its ends using the heating rate of C W. Simultaneously, the other end of the bar is maintained at a
constant temperature T = D °C. Determine the temperature distribution within the metal bar. The
thermal conductivity of the metal bar is E [W/(m°C)]. Determine the temperature distribution using
analytical calculations or computer software (Excel, Matlab). Draw a graph showing the temperature
distribution as a function of distance x from the heated end of the bar
According to the Fourier's Law the heat flux density [W/m²] as a function of distance equals q(x) =
dT (x)
-kat (x)
Now the heat quantity Q [W] flowing through the bar becomes Q =qA = -kA
dx
dx
k is thermal conductivity [kW/(m°C)]
A is the surface are of cross section [m²]
Above,
Heat
Supply,
kW
x = 0m
Area, mm²
Insulation
-Temperature, T(x)
Heat flow
Constant point at
x = Bm
T =D °C
x
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