Heat Transfer - Conduction
Homework Answers
dk/dx = a
heat flux is constant
d(kdT/dx) = 0
(dk/dx)(dT/dx) + kd^2T/dx^2 = 0
aT' + kT" = 0
there should be two boundary conditions to solve this differential equation
1 ) at x=0 T =T1
2)??
one more condtion has to be given
other wise we will get an expression with some unknown constant
aT' + kT" = 0
-a/(ax+b) dx = T"/T' dx
integrating on both sides
gradient dT/dx = C1/(ax+b)
T = C1/a ln(ax + b) + T1 - C1/a (ln b)
heat transfer
A wall is made from an inhomogeneous (nonuniform) material for which the thermal conductivity varies through the thickness according to k = ax +b, where a and b are constants. The heat flux, q” is known to be constant.a) Determine expressions for the temperature gradient and the temperature distribution if the surface at x= 0 is temperature T1. b) If the values are given as a = 50 , b= 200 , q” =1200 , T1= 500 K and 0...
PLEASE ANSWER a,b,c Heat Conduction Heat conduction occurs through any material, represented here by a rectangular...
PLEASE ANSWER a,b,c
Heat Conduction Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material is T2 on the left and T1 on the right, where T2 is greater than T1. The rate of heat transfer by conduction is directly proportional to the surface area A, the temperature difference T2 - T1, and the substance's conductivity k. The rate of heat transfer is inversely proportional to the...
Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or...
Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material is T2 on the left and T1 on the right, where T2 is greater than T1. The rate of heat transfer by conduction is directly proportional to the surface area A, the temperature difference T2 - T1, and the substance's conductivity k. The rate of heat transfer is inversely proportional to the thickness d. Q kA (T2-T)...
Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or...
Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material is T2 on the left and T1 on the right, where T2 is greater than T1. The rate of heat transfer by conduction is directly proportional to the surface area A, the temperature difference T2 - T1, and the substance's conductivity k. The rate of heat transfer is inversely proportional to the thickness d. Q kA (T2-T)...
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...
Question You are studying heat transfer through a spherical shell container with a thermal conductivity k....
Question You are studying heat transfer through a spherical shell container with a thermal conductivity k. The inner and outer radii are identified as a and b, respectively. The inside surface of the shell is exposed to a constant heat flux in the outward direction. The outside surface temperature of the container is measured at Note that only the variables values provided in the problem statement are known. Assume steady one-dimensional radial heat transfer a. Give the mathematical formulation of...
Problem 2 Heat Diffusion: A tall wall has a thickness of L = 400 mm and...
Problem 2 Heat Diffusion: A tall wall has a thickness of L = 400 mm and a thermal conductivity of 0.25 W/m-K. One side of the wall is maintained at Ts 80°C. The temperature in the wall varies as a function of position due to internal heat generation. The temperature variation is given as, goL2 where go 10 W/m3. Use this expression to answer the following questions. Assume that the wall temperature is at steady state. A) Find the temperature...
Problem 2: Consider a large plane slab of semi-thickness L = 0.3 m, thermal conductivity k...
Problem 2: Consider a large plane slab of semi-thickness L = 0.3 m, thermal conductivity k = 2.5 W/m K and surface area A = 20.0 m². Both sides of the slab is maintained at a constant wall temperature of 358°K while it is subjected to a uniform but constant heat flux of 950.0 W/m2 Evaluate the temperature distribution/profile within the wall. Calculate the heat flux and temperature at location x = 0.1m. Problem 3: Consider a 10.0 m long...
12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall...
12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall thickness L are held at constant values of T and T, respectively, where T, <To. The wall material has thermal conductivity that varies linearly according to k = k,(1 +BT), where k, and ß are constants. Draw a schematic of the system. Define and label a coordinate system. State assumptions and boundary conditions. b. Derive the governing differential equation for the heat transport and...
Consider steady-state conditions for one-dimensional conduction
Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 50 W/m·K and thickness L = 0.35 m, with no internal heat generation Determine the heat flux and the unknown quantity for each case and sketch the temperature distribution, indicating the direction of the heat flux.
PLEASE ANSWER a,b,c
Heat Conduction Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material is T2 on the left and T1 on the right, where T2 is greater than T1. The rate of heat transfer by conduction is directly proportional to the surface area A, the temperature difference T2 - T1, and the substance's conductivity k. The rate of heat transfer is inversely proportional to the...
Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material is T2 on the left and T1 on the right, where T2 is greater than T1. The rate of heat transfer by conduction is directly proportional to the surface area A, the temperature difference T2 - T1, and the substance's conductivity k. The rate of heat transfer is inversely proportional to the thickness d. Q kA (T2-T)...
Heat conduction occurs through any material, represented here by a rectangular bar, whether window glass or walrus blubber. The temperature of the material is T2 on the left and T1 on the right, where T2 is greater than T1. The rate of heat transfer by conduction is directly proportional to the surface area A, the temperature difference T2 - T1, and the substance's conductivity k. The rate of heat transfer is inversely proportional to the thickness d. Q kA (T2-T)...
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...
Question You are studying heat transfer through a spherical shell container with a thermal conductivity k. The inner and outer radii are identified as a and b, respectively. The inside surface of the shell is exposed to a constant heat flux in the outward direction. The outside surface temperature of the container is measured at Note that only the variables values provided in the problem statement are known. Assume steady one-dimensional radial heat transfer a. Give the mathematical formulation of...
Problem 2 Heat Diffusion: A tall wall has a thickness of L = 400 mm and a thermal conductivity of 0.25 W/m-K. One side of the wall is maintained at Ts 80°C. The temperature in the wall varies as a function of position due to internal heat generation. The temperature variation is given as, goL2 where go 10 W/m3. Use this expression to answer the following questions. Assume that the wall temperature is at steady state. A) Find the temperature...
Problem 2: Consider a large plane slab of semi-thickness L = 0.3 m, thermal conductivity k = 2.5 W/m K and surface area A = 20.0 m². Both sides of the slab is maintained at a constant wall temperature of 358°K while it is subjected to a uniform but constant heat flux of 950.0 W/m2 Evaluate the temperature distribution/profile within the wall. Calculate the heat flux and temperature at location x = 0.1m. Problem 3: Consider a 10.0 m long...
12. The temperature at the inner and outer surfaces of a hollow cylindrical pipe with wall thickness L are held at constant values of T and T, respectively, where T, <To. The wall material has thermal conductivity that varies linearly according to k = k,(1 +BT), where k, and ß are constants. Draw a schematic of the system. Define and label a coordinate system. State assumptions and boundary conditions. b. Derive the governing differential equation for the heat transport and...
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