a constant electric current flows along a uniform wire with cross sectional radius "R" & heat conductivity coefficient "x" .a unit volume of wire generates a thermal power of "w". FIND the temperature distribution across the wire provided the steady- state temperature at the wire surface is equal to "T0"....................................................
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.......................................................please give a detailed soln. so that i may be able to understand where i hav mistaken
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1 Answers
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Hree,...
take a cyllinder of radius "r"
The heat generated inside it is given by pi.r2.w = dQ/dt
dQ/dt=-k.A.dT/dx
A=2pi.r.d
pi.r2.d.w =-x.2pi.r.d.dT/dr
so .. dT/dr=wr/2x
T=-wr2/4x + C
C is found by putting T=T0 at x=R
T= T0 + w/4x(R2 - r2)