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# for an infinitely long fin, the efficiency of fin is given by

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### Mohammed

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## [Solved] Effectiveness of Infinitely long fin is given by (where, P

Explanation:  Fins: Fins are extended surfaces used to increase the heat transfer from a surface by increasing the effective surface area. The effective Home Heat Transfer Fins

## Question

Effectiveness of Infinitely long fin is given by

(where, P = Fin parameter, K = Fin thermal conductivity, h = Convective heat transfer coefficient, Ac = Fin cross-section area)

This question was previously asked in

MPPSC AE Mechanical 2021 Official Paper

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PhKAC PKh.AC P.Ach.K Ph.K.Ac

## Answer (Detailed Solution Below)

Option 2 : PKh.AC

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## Detailed Solution

Explanation: Fins:

Fins are extended surfaces used to increase the heat transfer from a surface by increasing the effective surface area.

The effectiveness ϵ of a fin is given by -

ϵ

ϵ=HeattransferratewithfinHeattransferratewithoutfin=kPhA

where k = thermal conductivity, P = perimeter of fin, h = heat transfer coefficient and A = cross-sectional area.

For large heat transfer, ϵ should be as high as possible. It can be increased by -

Materials of high thermal conductivity (k) like copper and aluminium.

Increasing the ratio of the perimeter to the cross-sectional area of the fin i.e. P/A which can be achieved by placing short, thin fins in closed spacing instead of thick fins.

Placing fins on the gas side which has a lower heat transfer coefficient (h).

hgas << hliquid and hnatural convection << hforced convection

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## More Fins Questions

Q1. Though fins are intended to cool the engine and prevent breakdowns, overcooling can cause a variety of issues. Which of the following statements is NOT true for this ?Q2. Primary function of fins is _________Q3. The provision of fins on a heat transfer surface can be made more effective by having ______ number of _____ fins.Q4. Statement(I): Fins are equally effective irrespective of whether they are on the hot-side or cold-side of the fluid. Statement (II): The temperature along the fins varies and hence the rate of heat transfer varies along the elements of fins.Q5. A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end of the fin is kept at a constant temperature tb. The fin loses heat by convection to the atmosphere which is at a temperature ta (ta < tb). Four options of temperature profiles are shown. Identify the correct option.Q6. Three fins of equal length and diameter but made of aluminium, brass and cast-iron are heated to 200° C at one end. If the fins dissipate heat to the surrounding air at 25°C the temperature at the free end will be least in case ofQ7. Fins are provided on heat transferring surface in order to increase:Q8. Insulated tip temperature of a rectangular longitudinal fin will be equal toQ9. An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of Q̇1 to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes Q̇2. The ratio Q̇2/Q̇1 isQ10. The purpose of providing fins on heat transfer surface is to increase

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## Heat Transfer Test

This set of Heat Transfer test focuses on “Fin Performance”. 1. The utility of fin in dissipating a given quantity of heat is generally assessed on the basic of how many parameters? a) 1 b) 2 c) 3 d) 4 2. A copper steel rod (k = 55 W/m degree) has been attached to a ... Read more ## Heat Transfer Questions and Answers – Fin Performance

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This set of Heat Transfer test focuses on “Fin Performance”.

1. The utility of fin in dissipating a given quantity of heat is generally assessed on the basic of how many parameters?

a) 1 b) 2 c) 3 d) 4 View Answer

2. A copper steel rod (k = 55 W/m degree) has been attached to a plane wall which is maintained at a temperature of 350 degree Celsius. The rod is 8 cm long and has the cross-section of an equilateral triangle with each side 5 mm. Determine the heat dissipation from the rod if it is exposed to a convection environment at 25 degree Celsius with unit surface conductance 100 W/m2 degree. Consider end surface loss to be negligible

a) 10.26 W b) 9.26 W c) 8.26 W d) 7.26 W View Answer

3. For an infinitely long fin, the efficiency of fin is given by

a) 1/ml b) 2/ml c) 3/ml d) 4/ml View Answer

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4. For a fin of finite length with an insulated end, the fin efficiency is given as

a) tan h (ml) b) tan (ml)/ml c) tan h (m)/ml d) tan h (ml)/ml View Answer

5. For an infinitely long fin, the effectiveness of fin is given as

a) (P k/h AC) b) (P k/h AC)3/2 c) (P k/h AC)1/2 d) (P k/h AC)2 View Answer

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6. For a straight rectangular fin of thickness δ and width b, choose the correct option

a) P/AC = 1/ δ b) P/AC = 2/ δ c) P/AC = 3/ δ d) P/AC = 4/ δ View Answer

7. “Effectiveness of fin is the ratio of the fin heat dissipation with fin to that of no fin”.

8. Three fins of equal length and diameter but made of aluminum, brass and cast iron is heated to 200 degree Celsius at one end. If the fins dissipate heat to the surrounding air at 25 degree Celsius, the temperature at the free end will be least in

a) Brass fin b) Cast iron fin c) Aluminum fin

d) Each fin will have the same temperature

9. Two long rods A and B of the same diameter have thermal conductivities k and 4k and have one of their end inserted into a furnace at 400 K. At 9.5 m away section from the furnace, the temperature of rod B is120 degree Celsius. So find out at what end from the furnace end, the same temperature would be reached in the rod A?

10. The figure shows a 5 cm diameter rod, 90 cm long, which is having its lower face grinded smooth. The remainder of the rod is exposed to 32 degree Celsius room air and a surface coefficient heat transfer equal to 6.8 W/m2 degree exists between the rod surface and the room air. The grinder dissipates mechanical energy at the rate of 35 W. If thermal conductivity of rod material is 41.5 W/m degree, find the temperature of the rod at the point where the grinding is taking place

a) 161.45 degree celsius

b) 151.45 degree celsius

c) 141.45 degree celsius

d) 131.45 degree celsius

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## For an infinitely long fin, the efficiency of fin is given by

For an infinitely long fin, the efficiency of fin is given by 1/ml 2/ml 3/ml 4/ml. Heat Transfer Objective type Questions and Answers.

## E-PolyLearning

E-PolyLearning Discussion Forum

Que. For an infinitely long fin, the efficiency of fin is given by

a. 1/ml b. 2/ml c. 3/ml d. 4/ml Correct Answer:1/ml

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Three rods, one made of silver (l = 420W/m K), second made of aluminum (k = 210W/m K) and the third made of iron (k = 70W/m K) are coated with a uniform layer of wax all around. The rods are placed vertically in a boiling water bath with 250 mm length of each rod projecting outside. If all the rods are having following dimensions i.e. diameter = 15 mm and length = 300 mm and have identical surface coefficient 12.5W/ m² K, work out the ratio of lengths up to which wax will melt on each rod

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Mohammed 8 day ago

Guys, does anyone know the answer?