# Numerical - Power transmitting capacity of gear box

Q.  A gear box having surface area of 0.30 m2 has overall heat transfer coefficient of 23 W/m2 oC,when a fan is mounted on worm shaft to circulate air on fins. What is the power transmitting capacity of a gear box based on thermal considerations, if temperature rise of lubricating oil is 50 oC? (Assume λ = 6o, Φn  = 22o & μ = 0.05)
- Published on 19 Oct 15

a. 1.023 kW
b. 1.006 kW
c. 1.227 kW
d. 2.000 kW

#### Discussion

• Sravanthi   -Posted on 01 Oct 15
Given: A = 0.30 m2 , C = 23 W/m2 oC, λ = 6o, Φn = 22o & μ = 0.05

• Rate of heat generation = (1 – η) Pi
• Rate of heat dissipation = CA Δt
• Rate of heat generation is equal to rate of heat dissipation

Therefore,

Power transmitting capacity is given by
(1 – η) Pi = CA Δt

Formula: 1) (1 – η) Pi = CA Δt
2) η = tan λ / tan ( Φv + λ)
3) Φv = tan-1 ( μ / cos Φn)

Substituting the given values we get,

1) Φv = tan-1 ( μ / cos Φn )
Φv = tan-1 ( 0.05 / cos 22)
Φv = 3.086

2) η = tan λ / tan ( Φv + λ)
η = tan 6 / tan ( 3.086 + 6)
η = 0.657

Substituting the values of η = 0.657 and Φv = 3.086

3) (1 – η) Pi = CA Δt
(1 - 0.657) Pi = 23 x 0.30 x 50

Therefore, Pi = 1.006 kW

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