A very long solid cylindrical rod contains an internal source of uniform heat, per unit volume...
A very long solid cylindrical rod contains an internal source of
uniform heat, per unit volume f; and is
connected to a wall that is at the temperature T1, the
rod is exposed to a fluid with a convention coefficient h and
temperature T
.
It is requested:
a) Obtain the differential equation, which determines the
temperature distribution in stable state T(x) in the cylindrical
rod.
b) Solve the previous differential equation for the temperature
distribution.
c) Obtain an expression for heat transfer at the base of the
rod.
Homework Answers
Add Answer to:
A very long solid cylindrical rod contains an internal source of
uniform heat, per unit volume...
A long slender solid cylindrical rod made of copper is 2 cm in diameter. It is...
A long slender solid cylindrical rod made of copper is 2 cm in diameter. It is taken out of a liquid nitrogen bath at 77 K and exposed to a stream of warm air at a temperature of 50 C. Neglect internal temperature gradients find the time taken by the rod to heat up to a temperature of 10 C if the surface heat transfer coefficient is 20 W/m^2K. For copper, take k=330 W/mK and ?=95*10^-6 m^2/s.
A long solid rod of constant thermophysical properties and radius ro is initially at a uniform...
A long solid rod of constant thermophysical properties and radius ro is initially at a uniform temperature Tj. At time t = 0, the temperature of the peripheral surface at r=r, is changed to Tw and is subsequently maintained constant at this value for t> 0. (a) Show the governing equation with the boundary conditions. (b) Redefine the temperature for the homogeneous boundary conditions. (c) Show the separation of variables. (d) Show how to obtain the eigenvalues. (e) Obtain an...
A cylindrical fuel rod 50mm in diameter has a uniform internal heat generation of ??1̇ =...
A cylindrical fuel rod 50mm in diameter has a uniform internal heat generation of ??1̇ = 7*107 W/m3 . Under steady-state conditions, the temperature distribution is ??(??) = ?? + ????2, where T is in Celsius, ?? is in meters, ?? = 750°C, and ?? = -5.40*105 °C/m2 . The fuel rod properties are k=25 W/(m K), density= 1100 kg/m3 , and cp = 750 J/(kg K). (a) Determine the heat transferred (in Watts) at r=0 (centerline) and r=ro (outer...
A long cylindrical rod of diameter 100 mm with thermal conductivity of 0.5 W/mK experiences uniform...
A long cylindrical rod of diameter 100 mm with thermal conductivity of 0.5 W/mK experiences uniform volumetric heat generation of 5.0 x 10 W/m². The rod is encapsulated by a circular sleeve having an outer diameter of 400 mm and a thermal conductivity of 4 W/mK. The outer surface of the sleeve is exposed to cross flow of air at 27°C with a convection coefficient of 25 W/m2K (a) Find the temperature at the Interface between the rod and sleeve...
A long cylindrical rod of diameter 220 mm with thermal conductivity 0.5 W/m-K expe riences uniform...
A long cylindrical rod of diameter 220 mm with thermal conductivity 0.5 W/m-K expe riences uniform volumetric heat generation of 25,000 W/m3. The rod is encapsulated by a circular sleeve having 7 W/m K. The outer surface of the sleeve is exposed to cross flow of air at 25°C with a convection coefficient of 25 W/m2-K. Find the temperature at the interface between the rod and sleeve, and on the outer surface. an outer diameter of 410 mm and thermal...
3. The wall shown in the figure below has thickness L 0.25 m and uniform thermal...
3. The wall shown in the figure below has thickness L 0.25 m and uniform thermal conductivity k-1 W/mK. It is exposed to circulating fluid on the surface at x = L, where the temperature ofthe fluid is T-= 30°C and the convection coefficient is h = 4 W/m2.K. The surface at x = 0 is maintained at constant temperature T-20 °C. Assume ID heat flux, and that the system is at steady state a) b) Determine the temperature distribution...
Problem 3: In a molten-salt nuclear reactor, radioactive liquid is flowing through a cylindrical pipe of diameter D. Fi...
Problem 3: In a molten-salt nuclear reactor, radioactive liquid is flowing through a cylindrical pipe of diameter D. Fission in the liquid results in a uniform internal heat generation of à W/m3. The pipe wall also has a heater on it that can provide a uniform surface heating rate of q" W/m2. The radioactive liquid has a specific heat capacity of Cp J/kg-K, a mass flowrate of m kg/s, and an inlet temperature of Tm, Conduction in the fluid in...
QUESTION 1 (10 marks) a) Write the Newton's law of heat convection in fluid using convection heat transfer coef...
QUESTION 1 (10 marks) a) Write the Newton's law of heat convection in fluid using convection heat transfer coefficient, h (Wm2.K). Please explain the equation in terms of its driving force and resistancC (2 marks) (POUCOI/C2) b) Define the heat transfer rate, q,by inside and outside convection and wall conduction considering a stainless steel cylindrical pipe (inside radius, ri and outer radius, ) with fiberglass insulator (radius, s) in ą steady state condition as shown in Figure Q11 Steam with...
1. Heat is generated at a uniform steady rate in a long solid cylinder. The cylinder...
1. Heat is generated at a uniform steady rate in a long solid cylinder. The cylinder loses heat from its exposed surface to surroundings at constant temperature. Show that the radial temperature profile in the cylinder can be represented by the equation: T, = Twer - 9 4k where qy is the rate of heat generation per unit volume and Tur is the maximum temperature in the profile. [30%] In a long solid cylinder of 40mm diameter heat is generated...
! Required information An insulated heated rod with a uniform heat source can be modeled with...
! Required information An insulated heated rod with a uniform heat source can be modeled with the Poisson equation as given below. de = -f(x) Given: A heat source fx) = 25°C/m2 and the boundary conditions Tlx = 0) = 40 °C and Tlx = 10) = 200 °C Solve the ODE using the shooting method. (Round the final answer to the nearest integer.) The temperature distribution at x = 4 is K. Use the fourth-order RK method using a...
A long solid rod of constant thermophysical properties and radius ro is initially at a uniform temperature Tj. At time t = 0, the temperature of the peripheral surface at r=r, is changed to Tw and is subsequently maintained constant at this value for t> 0. (a) Show the governing equation with the boundary conditions. (b) Redefine the temperature for the homogeneous boundary conditions. (c) Show the separation of variables. (d) Show how to obtain the eigenvalues. (e) Obtain an...
A long cylindrical rod of diameter 100 mm with thermal conductivity of 0.5 W/mK experiences uniform volumetric heat generation of 5.0 x 10 W/m². The rod is encapsulated by a circular sleeve having an outer diameter of 400 mm and a thermal conductivity of 4 W/mK. The outer surface of the sleeve is exposed to cross flow of air at 27°C with a convection coefficient of 25 W/m2K (a) Find the temperature at the Interface between the rod and sleeve...
A long cylindrical rod of diameter 220 mm with thermal conductivity 0.5 W/m-K expe riences uniform volumetric heat generation of 25,000 W/m3. The rod is encapsulated by a circular sleeve having 7 W/m K. The outer surface of the sleeve is exposed to cross flow of air at 25°C with a convection coefficient of 25 W/m2-K. Find the temperature at the interface between the rod and sleeve, and on the outer surface. an outer diameter of 410 mm and thermal...
3. The wall shown in the figure below has thickness L 0.25 m and uniform thermal conductivity k-1 W/mK. It is exposed to circulating fluid on the surface at x = L, where the temperature ofthe fluid is T-= 30°C and the convection coefficient is h = 4 W/m2.K. The surface at x = 0 is maintained at constant temperature T-20 °C. Assume ID heat flux, and that the system is at steady state a) b) Determine the temperature distribution...
Problem 3: In a molten-salt nuclear reactor, radioactive liquid is flowing through a cylindrical pipe of diameter D. Fission in the liquid results in a uniform internal heat generation of à W/m3. The pipe wall also has a heater on it that can provide a uniform surface heating rate of q" W/m2. The radioactive liquid has a specific heat capacity of Cp J/kg-K, a mass flowrate of m kg/s, and an inlet temperature of Tm, Conduction in the fluid in...
QUESTION 1 (10 marks) a) Write the Newton's law of heat convection in fluid using convection heat transfer coefficient, h (Wm2.K). Please explain the equation in terms of its driving force and resistancC (2 marks) (POUCOI/C2) b) Define the heat transfer rate, q,by inside and outside convection and wall conduction considering a stainless steel cylindrical pipe (inside radius, ri and outer radius, ) with fiberglass insulator (radius, s) in ą steady state condition as shown in Figure Q11 Steam with...
1. Heat is generated at a uniform steady rate in a long solid cylinder. The cylinder loses heat from its exposed surface to surroundings at constant temperature. Show that the radial temperature profile in the cylinder can be represented by the equation: T, = Twer - 9 4k where qy is the rate of heat generation per unit volume and Tur is the maximum temperature in the profile. [30%] In a long solid cylinder of 40mm diameter heat is generated...
! Required information An insulated heated rod with a uniform heat source can be modeled with the Poisson equation as given below. de = -f(x) Given: A heat source fx) = 25°C/m2 and the boundary conditions Tlx = 0) = 40 °C and Tlx = 10) = 200 °C Solve the ODE using the shooting method. (Round the final answer to the nearest integer.) The temperature distribution at x = 4 is K. Use the fourth-order RK method using a...
Most questions answered within 3 hours.
-
Deacon Corporation has provided the following financial data
from its balance sheet and income statement:
Year...
asked 26 minutes ago -
List and discuss at least three variables from everyday life for
which you expect the variable ...
asked 25 minutes ago -
A high-pass filter consists of a 1.60 μF capacitor in series
with a 125 Ω resistor....
asked 27 minutes ago -
A newly developed artificial intelligence has trouble
distinguishing hand-written numbers from hand-written alphabets.
There are pictures...
asked 45 minutes ago -
The carbonate ion CO3 2- has multiple resonance structures.
a. Draw them and assign the hybridization...
asked 38 minutes ago -
In doing an allocation for a basket purchase
Use the individual costs and the total market...
asked 46 minutes ago -
what were the social political and economic causes and impacts of
the late 19th century urban...
asked 43 minutes ago -
if the magnitude of a velocity vector is 10m/s and it
makes an angle of 45...
asked 46 minutes ago -
Which amino acid has a basic R group?
A) tyrosine
B) Isoleucine
C) Glutamic Acid
D)...
asked 57 minutes ago -
Is there the need for the government to have hackers. Please
share your thoughts.
asked 1 hour ago -
Explain why you should not lose any LDH activity when you
centrifuge a crude sample at...
asked 1 hour ago -
An AA battery (object), standing on end, is placed to the left
of a diverging lens...
asked 1 hour ago