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4. In Figure 3 the half of the rod embedded in insulation generates heat which then...
A thin rod of radius r, length 3L, and thermal conductivity, k is divided into three...
A thin rod of radius r, length 3L, and thermal conductivity, k is divided into three regions, each of length L. Regions 1 and 2 are surrounded by a perfectly insulating wall, while Region 3 protrudes into ambient air well-insulated. Uniform heat generation, q, occus only in Region 1 Sketch the temperature prolile along the entire length of the rod. For each region, specify why the temperature prolile has the shape you have decided on. Also, specify the nature of...
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...
1) 2) 3) PROJECT #1 (2.5 Marks): The heat that is conducted through a body must...
1)
2)
3)
PROJECT #1 (2.5 Marks): The heat that is conducted through a body must frequently be removed by other heat transter processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width Z 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature 1. The conductivity of the aluminum...
The heat that is conducted through a body must frequently be removed by other heat transfer...
The heat that is conducted through a body must frequently be removed by other heat transfer processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature T. The conductivity of the aluminum fin (k) and coefficient of heat convection of...
A very long rod of 5-mm diameter and uniform thermal conductivity k = 25 W/m-K is subjected to a heat treatment process
A very long rod of 5-mm diameter and uniform thermal conductivity k = 25 W/m-K is subjected to a heat treatment process. The center, 30-mm-long portion of the rod within the induction heating coil experiences uniform volumetric heat generation of 7.5 x 106 W/m3. The unheated portions of the rod, which protrude from the heating coil on either side, experience convection with the ambient air at T∞ = 20 °C and h = 10 W/m2K. Assume that there is no convection...
The heat question and would like to have work solution. The answers are (c) 136.6 (d)...
The heat question and would like to have work solution. The
answers are (c) 136.6 (d) < 2%. thank you.
An long cylindrical vaccuum chamber shown in Figure 1, is used to anneal single titanium rods by maintaining their temperature at 800 °C for an extended period of time. Heat is introduced into the rods internally by induction. The insulation surrounding the chamber has a thicknesss of 50 mm and thermal conductivity of 0.1 W/m.K. The convective heat transfer coefficient...
Problems 4, 5 & 6 15) A heat-conducting rod, 0.90 m long and wrapped in insulation,...
Problems 4, 5 & 6
15) A heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum section that is 0.20 m long and a copper section that is 0.20m long. Both sections have a cross- sectional area of 0.00040 m2, The aluminum end and the copper end are maintained at temperatures of 30 C and 230 C respectively. The thermal conductivities of aluminum and copper are 205 W/m K (aluminum) and 385 W/m K (copper)....
blem 4 (20 pts) A square chip that is 12.7mm on a side has a maximum allowable chip operating temperature -75°C. To dissipate heat produced in the chip, a 4 x 4 array of copper (k-400 W/m.K) pin fins...
blem 4 (20 pts) A square chip that is 12.7mm on a side has a maximum allowable chip operating temperature -75°C. To dissipate heat produced in the chip, a 4 x 4 array of copper (k-400 W/m.K) pin fins is proposed to be etallurgically joined to the outer surface of the chip. The convection coefficient is h-250 W/m'K and ambient air mperature isTo-20°C. The pin fin dimeter is D,-1.5mm and length is L,-16mm. Assuming steady-state uniform chip temperature Te-75°C and...
Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state...
Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state conductive heat transfer through a metal rod and convection to the surrounding air, which are described by the following ordinary differential equation: T" – TQ2 = -a?T. T(x = 0) = 0 T(x = L) = 2 T is the temperature distribution in a rod, a = hP/kA, h is the heat transfer coefficient, P, A and L are the perimeter, the cross section...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg.K, and p=400 kg/m3. (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m?. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m².K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q'"...
A thin rod of radius r, length 3L, and thermal conductivity, k is divided into three regions, each of length L. Regions 1 and 2 are surrounded by a perfectly insulating wall, while Region 3 protrudes into ambient air well-insulated. Uniform heat generation, q, occus only in Region 1 Sketch the temperature prolile along the entire length of the rod. For each region, specify why the temperature prolile has the shape you have decided on. Also, specify the nature of...
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...
1)
2)
3)
PROJECT #1 (2.5 Marks): The heat that is conducted through a body must frequently be removed by other heat transter processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width Z 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature 1. The conductivity of the aluminum...
The heat that is conducted through a body must frequently be removed by other heat transfer processes. For example, the heat generated in an electronic device must be dissipated to the surroundings through convection by means of fins. Consider the one-dimensional aluminum fin (thickness t 3.0 mm, width 20 cm, length L) shown in Figure 1, that is exposed to a surrounding fluid at a temperature T. The conductivity of the aluminum fin (k) and coefficient of heat convection of...
The heat question and would like to have work solution. The
answers are (c) 136.6 (d) < 2%. thank you.
An long cylindrical vaccuum chamber shown in Figure 1, is used to anneal single titanium rods by maintaining their temperature at 800 °C for an extended period of time. Heat is introduced into the rods internally by induction. The insulation surrounding the chamber has a thicknesss of 50 mm and thermal conductivity of 0.1 W/m.K. The convective heat transfer coefficient...
Problems 4, 5 & 6
15) A heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum section that is 0.20 m long and a copper section that is 0.20m long. Both sections have a cross- sectional area of 0.00040 m2, The aluminum end and the copper end are maintained at temperatures of 30 C and 230 C respectively. The thermal conductivities of aluminum and copper are 205 W/m K (aluminum) and 385 W/m K (copper)....
blem 4 (20 pts) A square chip that is 12.7mm on a side has a maximum allowable chip operating temperature -75°C. To dissipate heat produced in the chip, a 4 x 4 array of copper (k-400 W/m.K) pin fins is proposed to be etallurgically joined to the outer surface of the chip. The convection coefficient is h-250 W/m'K and ambient air mperature isTo-20°C. The pin fin dimeter is D,-1.5mm and length is L,-16mm. Assuming steady-state uniform chip temperature Te-75°C and...
Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state conductive heat transfer through a metal rod and convection to the surrounding air, which are described by the following ordinary differential equation: T" – TQ2 = -a?T. T(x = 0) = 0 T(x = L) = 2 T is the temperature distribution in a rod, a = hP/kA, h is the heat transfer coefficient, P, A and L are the perimeter, the cross section...
2. A nuclear fuel rod with diameter of D=40 mm and length L=1m, has properties of k=1 W/mK, c=1600J/kg.K, and p=400 kg/m3. (a)Heat is generated uniformly in the rod with q'"' = 2 x 106 W/m?. The rod is first cooled in oil with constant temperature To= 400 K and average heat transfer coefficient h=50 W/m².K. Under steady state, determine the surface temperature of the rod Ts. (10 pts) (b)Now the heat generation in the rod is stopped, where q'"...
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