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For a laminar flow over a flat plate, the local heat transfer coefficient ‘hx’ varies as x-1/2, where x is the distance from the leading edge (x = 0) of the plate. The ratio of the average coefficient ‘ha’ between the leading edge and some location ‘A’ at x = x on the plate to the local heat transfer coefficient ‘hx’ at A is:
  • a)
    1
  • b)
    2
  • c)
    4
  • d)
    8
Correct answer is option 'B'. Can you explain this answer?
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Explanation:

Ratio Calculation:
- The average coefficient is given as ha = (1/x) ∫hx dx from 0 to x.
- Therefore, ha = (1/x) ∫x^(-1/2) dx from 0 to x.
- Solving the integral, we get ha = 2*x^1/2.

Local Coefficient Calculation:
- The local coefficient hx at location A is hx = x^(-1/2).

Ratio Calculation:
- To find the ratio of ha to hx at location A, we substitute x = A in ha and hx.
- Therefore, ha/hx = 2*A^1/2 / A^(-1/2) = 2*A^(1/2 + 1/2) = 2*√A = 2.

Therefore, the ratio of the average coefficient ha to the local coefficient hx at location A is 2, which corresponds to option 'B'.
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For a laminar flow over a flat plate, the local heat transfer coefficient ‘hx’ varies as x-1/2, where x is the distance from the leading edge (x = 0) of the plate. The ratio of the average coefficient ‘ha’ between the leading edge and some location ‘A’ at x = x on the plate to the local heat transfer coefficient ‘hx’ at A is:a)1b)2c)4d)8Correct answer is option 'B'. Can you explain this answer?
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