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Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107 W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.
Correct answer is '10'. Can you explain this answer?
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Heat is generated uniformly in a long solid cylindrical rod (diameter ...
Given that, heat is generated uniformly i.e.,
g = 4x107 W/m3Diameter at the rod (d) = 10 mm
Thermal conductivity of the rod (K) = 25 W/mK
W.K.T for steady state, with internal heat generation, the conduction equation will be,
The above equation will become
Most Upvoted Answer
Heat is generated uniformly in a long solid cylindrical rod (diameter ...
Problem Statement: Find the temperature difference between the center and surface of a solid cylindrical rod with a diameter of 10mm, given that the heat is generated uniformly at a rate of 4107W/m3 and the thermal conductivity of the rod material is 25W/m.K.
Solution:
To solve this problem, we will use the following formula:
Q = kA(T2-T1)/L
Where Q is the heat generated per unit length of the rod, k is the thermal conductivity of the material, A is the cross-sectional area of the rod, L is the length of the rod, T2 is the temperature at the center of the rod, and T1 is the temperature at the surface of the rod.
Step 1: Calculate the cross-sectional area of the rod.
Given:
Diameter of the rod = 10mm
Radius of the rod (r) = 5mm
The cross-sectional area of the rod is given by:
A = πr^2
A = 3.14 x (5 x 10^-3)^2
A = 7.85 x 10^-5 m^2
Step 2: Calculate the length of the rod.
The length of the rod is not given in the problem statement, so we cannot calculate it. However, we can assume a length for the rod and solve the problem. Let's assume the length of the rod to be 1m.
Step 3: Calculate the heat generated per unit length of the rod.
Given:
Heat generated uniformly = 4107 W/m^3
The heat generated per unit length of the rod is given by:
Q = heat generated per unit volume x volume of the rod per unit length
Q = 4107 x πr^2
Q = 4107 x 3.14 x (5 x 10^-3)^2
Q = 0.64 W/m
Step 4: Find the temperature difference between the center and surface of the rod.
Using the formula mentioned above and assuming the length of the rod to be 1m, we get:
Q = kA(T2-T1)/L
0.64 = 25 x 7.85 x 10^-5 (T2-T1)/1
(T2-T1) = 0.64 / (25 x 7.85 x 10^-5)
(T2-T1) = 10
Therefore, the temperature difference between the center and surface of the rod is 10°C.
Solution:
To solve this problem, we will use the following formula:
Q = kA(T2-T1)/L
Where Q is the heat generated per unit length of the rod, k is the thermal conductivity of the material, A is the cross-sectional area of the rod, L is the length of the rod, T2 is the temperature at the center of the rod, and T1 is the temperature at the surface of the rod.
Step 1: Calculate the cross-sectional area of the rod.
Given:
Diameter of the rod = 10mm
Radius of the rod (r) = 5mm
The cross-sectional area of the rod is given by:
A = πr^2
A = 3.14 x (5 x 10^-3)^2
A = 7.85 x 10^-5 m^2
Step 2: Calculate the length of the rod.
The length of the rod is not given in the problem statement, so we cannot calculate it. However, we can assume a length for the rod and solve the problem. Let's assume the length of the rod to be 1m.
Step 3: Calculate the heat generated per unit length of the rod.
Given:
Heat generated uniformly = 4107 W/m^3
The heat generated per unit length of the rod is given by:
Q = heat generated per unit volume x volume of the rod per unit length
Q = 4107 x πr^2
Q = 4107 x 3.14 x (5 x 10^-3)^2
Q = 0.64 W/m
Step 4: Find the temperature difference between the center and surface of the rod.
Using the formula mentioned above and assuming the length of the rod to be 1m, we get:
Q = kA(T2-T1)/L
0.64 = 25 x 7.85 x 10^-5 (T2-T1)/1
(T2-T1) = 0.64 / (25 x 7.85 x 10^-5)
(T2-T1) = 10
Therefore, the temperature difference between the center and surface of the rod is 10°C.
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Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.Correct answer is '10'. Can you explain this answer?
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Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.Correct answer is '10'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.Correct answer is '10'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.Correct answer is '10'. Can you explain this answer?.
Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.Correct answer is '10'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.Correct answer is '10'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.Correct answer is '10'. Can you explain this answer?.
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