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Experimental results indicate that the local heat transfer coefficient h g for flow over a flat plate with an extremely rough surface is approximated by the relation
x = a x -0.12
Where a is a constant coefficient and x is distance from the leading edge of the plate. What is the relation between this local heat transfer coefficient and the average heat transfer coefficient for a plate of length x? 
  • a)
    1.136 h x
  • b)
    2.136 h x
  • c)
    3.136 h x
  • d)
    4.136 h x
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Experimental results indicate that the local heat transfer coefficient...
Explanation: h = 1.136 a x -0.12 = 1.136 h x.
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Experimental results indicate that the local heat transfer coefficient...
Relation between local heat transfer coefficient and average heat transfer coefficient:
The relation between the local heat transfer coefficient hx and the average heat transfer coefficient hx_avg for a plate of length x can be determined by integrating the local heat transfer coefficient over the length of the plate.

Derivation:
Given that hx = a x^-0.12, we can integrate this expression over the length of the plate x to obtain the average heat transfer coefficient hx_avg.
∫hx dx = a ∫x^-0.12 dx
Integrating both sides, we get:
hx_avg = a * (x^0.88) / 0.88 + C
Where C is the constant of integration.
To simplify further, we can rewrite the expression as:
hx_avg = 1.136 * hx
Therefore, the relation between the average heat transfer coefficient and the local heat transfer coefficient for a plate of length x is hx_avg = 1.136 * hx.
Therefore, option 'A', 1.136 hx, is the correct answer.
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Experimental results indicate that the local heat transfer coefficient hgfor flow over a flat plate with an extremely rough surface is approximated by the relationhx= a x-0.12Where a is a constant coefficient and x is distance from the leading edge of the plate. What is the relation between this local heat transfer coefficient and the average heat transfer coefficient for a plate of length x?a)1.136 hxb)2.136 hxc)3.136 hxd)4.136 hxCorrect answer is option 'A'. Can you explain this answer?
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