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# MCQs on Steady Flow of Heat Along a Rod

Which one is true regarding rectangular fin?

a) A _{C} = b δ and P = 2(b + δ)

b) A _{C} = 2 b δ and P = 2(b + δ)

c) A _{C} = 3 b δ and P = 2(b + δ)

d) A _{C} = 4 b δ and P = 2(b + δ)

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Answer: a

Explanation: For rectangle, A = (length) (breadth). Where, b = width and δ = thickness.

Analysis of heat flow from the finned surface is made with the following assumptions

(i) Uniform heat transfer coefficient, h over the entire fin surface

(ii) No heat generation within the fin generation

(iii) Homogenous material

Identify the correct option

a) i only

b) i and ii only

c) i, ii and iii

d) ii only

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Answer: c

Explanation: The knowledge of temperature distribution is necessary for their optimum design with regard to size and weight.

If heat conducted into the element at plane x is Q _{X }= – k A _{C} (d t/d x)_{ X}. Then heat conducted out of the element at plane (x + d x) is

a) – 2k A _{C} d/d x (t + d t/d x (d x))

b) – k A _{C} d/d x (t + d t/d x (d x))

c) – 3k A _{C} d/d x (t + d t/d x (d x))

d) – 4k A _{C} d/d x (t + d t/d x (d x))

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Answer: b

Explanation: Heat conducted out of the element is – [k A _{C} (d t/d x)_{ X + d x}].

A heating unit is made in the form of a vertical tube of 50 mm outside diameter and 1.2 m height. The tube is fitted with 20 steel fins of rectangular section with height 40 mm and thickness 2.5 mm. The temperature at the base of fin is 75 degree Celsius, the surrounding air temperature is 20 degree Celsius and the heat transfer coefficient between the fin as well as the tube surface and the surrounding air is 9.5 W/m^{2} K. If thermal conductivity of the fin material is 55 W/m K, find the amount of heat transferred from the tube without fin

a) 98.44 W

b) 88.44 W

c) 78.44 W

d) 68.44 W

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Answer: a

Explanation: Q = h A d t = h (π d _{0 }H) (t _{0 }– t _{INFINITY}).

The general solution of linear and homogenous differential equation (second form) is of the form

a) γ = C _{1 }e ^{2 m x} + C _{2 }e ^{– m x}

b) γ = C _{1 }e ^{3m x} + C _{2 }e ^{– m x}

c) γ = C _{1 }e ^{4 m x} + C _{2 }e ^{– m x}

d) γ = C _{1 }e ^{m x} + C _{2 }e ^{– m x}

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Answer: d

Explanation: It should contain m x and – m x term.

For steady flow of heat along a rod, the general equation is

d^{2}α/dx ^{2} – m ^{2 }α = 0

The value of constant m is

a) (h P/k A _{C})

b) (h P/k A _{C}) ^{3/2}

c) (h P/k A _{C}) ^{1/2}

d) (h P/k A _{C}) ^{2}

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Answer: c

Explanation: This provides a general form of the energy equation for one dimensional heat flow.

In convection from the tip, we introduced a factor known as

a) Fin length

b) Correction length

c) No fin length

d) Radial length

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Answer: b

Explanation: Just for simplicity we replace fin length by correction length.

Find the value of corrected length for rectangular fin?

Where, b is width and t is length of the fin

a) L _{C }= L + b t/2 (b + t)

b) L _{C }= L + b t/ (b + t)

c) L _{C }= L + 2 (b + t)

d) L _{C }= L + b t

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Answer: a

Explanation: For rectangle, area = t b.

Which one is true for the spine?

a) A _{C} = π d ^{2}/4 and P = 4 π d

b) A _{C} = π d ^{2}/4 and P = 3 π d

c) A _{C} = π d ^{2}/4 and P = π d

d) A _{C} = π d ^{2}/4 and P = 2 π d

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Answer: c

Explanation: A spine is a pin fin.

In convection from the tip what is the value of correction length?

a) L _{C} = A _{C}/P

b) L _{C} = L + A _{C}

c) L _{C} = L + P

d) L _{C} = L + A _{C}/P

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Answer: d

Explanation: It should contain all the three terms i.e. L, A and P.