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The temperature profile at a particular location on a surface is prescribed by the identity
(t s – t) / (t s – t infinity) = (1/2) (y/0.0075) + (3/2) (y/0.0075)
If thermal conductivity of air is stated to be 0.03 W/m K, determine the value of convective heat transfer coefficient
  • a)
    4 W/mK
  • b)
    5 W/mK
  • c)
    6 W/mK
  • d)
    7 W/mK
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The temperature profile at a particular location on a surface is presc...
h = – k/ (t s – t infinity) [d t/d y] y = 0.
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The temperature profile at a particular location on a surface is presc...

Given Data:
- Thermal conductivity of air = 0.03 W/m K
- Temperature profile equation: (ts - t) / (ts - tinfinity) = (1/2) (y/0.0075)^3 + (3/2) (y/0.0075)

Calculation:
- The convective heat transfer coefficient (h) can be calculated using the formula: h = k / (0.0075 * Bi)
- Bi = Biot number = h * L / k, where L is the characteristic length (0.0075 in this case)

Substitute the given temperature profile equation into the formula:
- ts = surface temperature
- tinfinity = ambient temperature
- y = distance from surface

- (ts - t) / (ts - tinfinity) = (1/2) (y/0.0075)^3 + (3/2) (y/0.0075)
- Bi = h * 0.0075 / 0.03
- h = 0.25 / Bi

Solving for h:
- Differentiate the temperature profile equation with respect to y
- Substitute y = 0 to find h

- h = 6 W/m^2K

Therefore, the convective heat transfer coefficient is 6 W/m^2K, which corresponds to option 'C'.
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The temperature profile at a particular location on a surface is prescribed by the identity(ts– t) / (ts– tinfinity) = (1/2) (y/0.0075)3+ (3/2) (y/0.0075)If thermal conductivity of air is stated to be 0.03 W/m K, determine the value of convective heat transfer coefficienta)4 W/m2Kb)5 W/m2Kc)6 W/m2Kd)7 W/m2KCorrect answer is option 'C'. Can you explain this answer?
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