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Consider a large plane wall of thickness L, thermal conductivity k and surface area A. The left surface of the wall is exposed to the ambient air at temperature T with a heat transfer coefficient of h while the right surface is insulated. The variation of temperature in the wall for steady state one-dimensional heat conduction with no heat generation is
  • a)
  • b)
  • c)
  • d)
    T(x) = T
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider a large plane wall of thickness L, thermal conductivity k an...
As the system is at steady state, therefore
Also
But surface x = ? is insulated
Also there is no internal heat generation,
therefore
Thus
I.e., hA(T = T0)
By heat conduction equation at any point in the slab
As internal heat generation is zero,
and
∴ c1 = 0
As T = T0 at x = 0
∴ T = 0 X x + c2 = T0 = T
i.e., T = T
i.e., The entire slab is at a uniform temperature equal to fluid temperature.
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Most Upvoted Answer
Consider a large plane wall of thickness L, thermal conductivity k an...
As the system is at steady state, therefore
Also
But surface x = ? is insulated
Also there is no internal heat generation,
therefore
Thus
I.e., hA(T = T0)
By heat conduction equation at any point in the slab
As internal heat generation is zero,
and
∴ c1 = 0
As T = T0 at x = 0
∴ T = 0 X x + c2 = T0 = T
i.e., T = T
i.e., The entire slab is at a uniform temperature equal to fluid temperature.
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Community Answer
Consider a large plane wall of thickness L, thermal conductivity k an...
As the system is at steady state, therefore
Also
But surface x = ? is insulated
Also there is no internal heat generation,
therefore
Thus
I.e., hA(T = T0)
By heat conduction equation at any point in the slab
As internal heat generation is zero,
and
∴ c1 = 0
As T = T0 at x = 0
∴ T = 0 X x + c2 = T0 = T
i.e., T = T
i.e., The entire slab is at a uniform temperature equal to fluid temperature.
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Consider a large plane wall of thickness L, thermal conductivity k and surface area A. The left surface of the wall is exposed to the ambient air at temperature T∞ with a heat transfer coefficient of h while the right surface is insulated. The variation of temperature in the wall for steady state one-dimensional heat conduction with no heat generation isa) b) c) d) T(x) = T∞Correct answer is option 'D'. Can you explain this answer?
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