Heat

A constant electric current flows along a uniform wire with cross-sectional radius ‘R’ and heat conductivity coefficient ‘K’. A unit volume of the wire generates a thermal power ‘W’. Find the temperature distribution across the wire provided the steady-state temperature at the wire surface is equal to T.

16 comments:

  1. AmitMarch 11, 2011 at 9:17 PM

    temp= T-WR^2/2K(ln[r/R])
    r=radius vector from center

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  2. AnonymousMarch 12, 2011 at 12:08 AM

    yup same

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  3. AnujMarch 12, 2011 at 8:12 PM

    and wrong too.

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  4. AmitMarch 12, 2011 at 9:00 PM

    bhaiya, any hints then.

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  5. shouryaMarch 13, 2011 at 3:17 PM

    is it T-W(R^2-r^2)/4K.

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  6. Sambhav GuptaMarch 13, 2011 at 11:44 PM

    a soln to this, please!

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  7. AmitMarch 13, 2011 at 11:50 PM

    sambhav,
    maine dH/dt ko W likha hai and RHS is 2piK(@-T)....
    But, what I think shourya has done is write dH/dt as (W/R^2)x^2 and then have done the integral. I couldn't understand the reason that why he has divided the power as function of distance, wont it be the same???

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  8. AnujMarch 14, 2011 at 9:54 AM

    In this problem, H is not a constant, but a function of 'r'. So, you should consider an element of negligible thickness i.e. a thin shell of radius 'r'.

    Assume the temperature difference across this shell to be dT, and the 'H' to be constant i.e. H(r).

    You can write H(r) in terms of dT and dr easily.

    But H(r) is quite simple itself, isn't it?? ;)

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  9. Sambhav GuptaMarch 14, 2011 at 10:35 AM

    H(r) he to samajh nhi aaya :P

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  10. shouryaMarch 14, 2011 at 12:29 PM

    i thought that if we consider a thin shell rad(r),
    then h(r) would depend on the current flowing inside this shell. so h(r) is not constt.

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  11. shouryaMarch 14, 2011 at 12:30 PM

    This comment has been removed by the author.

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  12. AnujMarch 14, 2011 at 1:25 PM

    the shell of thickness 'dr' radiates negligible power. 'H' thru the shell is the total power radiated by the spherical volume enclosed by the shell.

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  13. ShivankerMarch 14, 2011 at 11:50 PM

    gettin the same as Shourya..
    T(r) = T-W(R^2-r^2)/4K
    plz confirm bhaiya..

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  14. AnujMarch 17, 2011 at 3:27 PM

    thats right.

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  15. AmitMarch 17, 2011 at 4:49 PM

    bhaiya, please confirm the reason for varying power. Is it that heat is also being generated inside the wire but, as steady state is there so, it must transfer all the heat forward on the surface.

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  16. ShivankerMarch 17, 2011 at 11:11 PM

    @Amit: Heat is being generated inside the wire ONLY.. Read the question again yaar..

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