A beaker contains a fluid of density ρ k g m 3 , specific heat S J k g o C and viscosity η . The…

A beaker contains a fluid of density ρkgm3 , specific heat SJkgoC and viscosity η . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area Q˙A by convection when beaker is put on a hot plate, a student proposes that it should depend on η , SΔθh and 1ρg when Δθ ( inoC ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for Q˙A is:
  1. SΔθhη
  2. ηSΔθh1ρ g
  3. SΔθηh1ρg
  4. SΔθηh

Solution

QA=ηxs∆θhy1ρgz . . . (1)

QA=MT-3,η=ML-1T-1

s∆θh=LT-2,1ρg=M-1L2T2

MT-3=MxL-xT-xLyT-2yM-2L2zT2z

MT-3=Mx-zL-x+y+2zT-x-2y+2z

So 1=x-z . . . (2)

-x+y+2z=0. . . (3)

-x-2y+2z=-3. . . (4)

from 2, 3, 4

x=1, y=1, z=0, from (1)

so QA=η s∆θh

Asked in: JEE Main 2015 (11 Apr Online)

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