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Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as

The steady state temperature at the mid-location of the rod is given as TA . What will be the temperature at the same location, if the convective heat transfer coefficient increases to 2h?
  • a)
  • b)
    2TA
  • c)
    TA
  • d)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider a rod of uniform thermal conductivity whose one end (x = 0) i...

General heat conduction equation for plane wall 

For one dimensional heat conduction with steady state 

Integrate with respect to x

Again integrate 

C1 and C2 are the integration constant
Boundary conditions

At x = δ, T = TW
Apply first boundary equation 

At,

From, equation (A)
C1 = 0
(2) Second boundary condition 
At x = δ, T = Tw Put in equation (B)

Put the value of C1 and C2 in equation (B),

According to question 


At δ = x/2(at mid plane)

Equation (iii) shows the temperature distribution equation which is independent of heat transfer coefficient.
So there is no effect of heat transfer coefficient on temperature TA .
Hence, the correct option is (C).
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Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T∞ with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given asThe steady state temperature at the mid-location of the rod is given as TA . What will be the temperature at the same location, if the convective heat transfer coefficient increases to 2h?a)b)2TAc)TAd)Correct answer is option 'C'. Can you explain this answer?
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