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A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.
Correct answer is '15.5'. Can you explain this answer?
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A plate shaped frozen food has a thickness of 20 mm, average thermal ...
Given data:
- Thickness of the frozen food (δ): 20 mm = 0.02 m
- Average thermal conductivity (k): 2.58 W/mK
- Density (ρ): 1080 kg/m3
- Specific heat (Cp): 3550 J/kgK
- Initial temperature of the food (T1): -20°C
- Temperature of the hot water (T2): 90°C
- Heat transfer coefficient (h): 25 W/m2K
- Final temperature of the food (T3): 30°C
Assumptions:
- 1D heat conduction through the thickness of the food
- Steady-state heat transfer
- Negligible internal heat generation
Formula:
The 1D heat conduction equation for steady-state conditions is given by:
q = (k * A * ΔT) / δ
where,
q = Heat transfer rate (W)
k = Thermal conductivity (W/mK)
A = Surface area perpendicular to heat flow (m2)
ΔT = Temperature difference (T2 - T1) (K)
δ = Thickness of the food (m)
Calculation:
Step 1: Calculate the surface area of the food
Since the food is plate-shaped, the surface area is given by:
A = 2 * L * W + L * δ
where,
L = Length of the food
W = Width of the food
As the shape and dimensions of the food are not provided, we will assume a rectangular shape with L = 1 m and W = 1 m.
A = 2 * 1 * 1 + 1 * 0.02
A = 2.02 m2
Step 2: Calculate the temperature difference
ΔT = T2 - T1
ΔT = 90 - (-20)
ΔT = 110°C
Step 3: Calculate the heat transfer rate
q = (k * A * ΔT) / δ
q = (2.58 * 2.02 * 110) / 0.02
q = 2839.4 W
Step 4: Calculate the mass of the food
The mass of the food can be calculated using the formula:
m = ρ * V
where,
ρ = Density (kg/m3)
V = Volume of the food (m3)
As the shape and dimensions of the food are not provided, we will assume a rectangular shape with L = 1 m, W = 1 m, and δ = 0.02 m.
V = L * W * δ
V = 1 * 1 * 0.02
V = 0.02 m3
m = 1080 * 0.02
m = 21.6 kg
Step 5: Calculate the energy required to heat the food from -20°C to 30°C
The energy required can be calculated using the formula:
Q = m * Cp * ΔT
where,
Cp = Specific heat (J/kgK)
ΔT = Temperature difference (T3 - T1) (K)
ΔT = 30 - (-20)
- Thickness of the frozen food (δ): 20 mm = 0.02 m
- Average thermal conductivity (k): 2.58 W/mK
- Density (ρ): 1080 kg/m3
- Specific heat (Cp): 3550 J/kgK
- Initial temperature of the food (T1): -20°C
- Temperature of the hot water (T2): 90°C
- Heat transfer coefficient (h): 25 W/m2K
- Final temperature of the food (T3): 30°C
Assumptions:
- 1D heat conduction through the thickness of the food
- Steady-state heat transfer
- Negligible internal heat generation
Formula:
The 1D heat conduction equation for steady-state conditions is given by:
q = (k * A * ΔT) / δ
where,
q = Heat transfer rate (W)
k = Thermal conductivity (W/mK)
A = Surface area perpendicular to heat flow (m2)
ΔT = Temperature difference (T2 - T1) (K)
δ = Thickness of the food (m)
Calculation:
Step 1: Calculate the surface area of the food
Since the food is plate-shaped, the surface area is given by:
A = 2 * L * W + L * δ
where,
L = Length of the food
W = Width of the food
As the shape and dimensions of the food are not provided, we will assume a rectangular shape with L = 1 m and W = 1 m.
A = 2 * 1 * 1 + 1 * 0.02
A = 2.02 m2
Step 2: Calculate the temperature difference
ΔT = T2 - T1
ΔT = 90 - (-20)
ΔT = 110°C
Step 3: Calculate the heat transfer rate
q = (k * A * ΔT) / δ
q = (2.58 * 2.02 * 110) / 0.02
q = 2839.4 W
Step 4: Calculate the mass of the food
The mass of the food can be calculated using the formula:
m = ρ * V
where,
ρ = Density (kg/m3)
V = Volume of the food (m3)
As the shape and dimensions of the food are not provided, we will assume a rectangular shape with L = 1 m, W = 1 m, and δ = 0.02 m.
V = L * W * δ
V = 1 * 1 * 0.02
V = 0.02 m3
m = 1080 * 0.02
m = 21.6 kg
Step 5: Calculate the energy required to heat the food from -20°C to 30°C
The energy required can be calculated using the formula:
Q = m * Cp * ΔT
where,
Cp = Specific heat (J/kgK)
ΔT = Temperature difference (T3 - T1) (K)
ΔT = 30 - (-20)
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A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.Correct answer is '15.5'. Can you explain this answer?
Question Description
A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.Correct answer is '15.5'. 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 A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.Correct answer is '15.5'. 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 A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.Correct answer is '15.5'. Can you explain this answer?.
A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.Correct answer is '15.5'. 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 A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.Correct answer is '15.5'. 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 A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.Correct answer is '15.5'. Can you explain this answer?.
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