Fundamentals of Momentum, Heat, and Mass Transfer
Fundamentals of Momentum, Heat, and Mass Transfer
6th Edition
ISBN: 9781118947463
Author: James Welty, Gregory L. Rorrer, David G. Foster
Publisher: WILEY
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Chapter 7, Problem 7.12P
Interpretation Introduction

Interpretation:

The percentage increase in heat transferred from the bearing is to be determined if the speed of shaft is doubled in the previous linked question.

Concept introduction:

By the 1st law of thermodynamics, the amount of heat removed is equal to the work done at the constant temperature of operation as Internal energy is zero here.

The work done is given by,

  W=τ×A×v........(1)

In the above formulae, the notations used are,

W is the work done

  τ is the Shear stress

A is the area of the shaft

v is the velocity of the shaft

The above notations also have individual formulae,

  τ=μdvdy.......(2)v=ωr.......(3)A=2πrL.......(4)

In the above formulae, the notations used are,

  μistheviscosityofoilωistherotatingspeedofshaftristheradiusoftheshaftListhelengthofshaft

In terms width gap, equation (2) can be written as,

  τ=μdvdy=μωrt.......(5)t=D2 -D12........(6)

D1 is the diameter of the shaft and D2 is the diameter of the bearing.

t is the gap width

The percentage increase in heat is given by,

  %increase=(Q2 -Q1Q1)×100.......(7)

Q1 is the heat transfer at original conditions

Q2is the heat transfer when shaft speed is doubled

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