Air at 20 degree Celsius flows over a flat plate maintained at 75 degree Celsius. Measurements shows that temperature at a distance of 0.5 mm from the surface of plate is 50 degree Celsius. Presuming thermal conductivity of air is 0.0266 W/m K, estimate the value of local heat transfer coefficienta)23.18 W/m2Kb)24.18 W/m2Kc)25.18 W/m2Kd)26.18 W/m2KCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

To estimate the value of the local heat transfer coefficient, we can use the Newton's Law of Cooling, which states that the rate of heat transfer between a solid surface and a fluid is directly proportional to the temperature difference between them. Mathematically, it can be expressed as:

q = h * A * ΔT

Where:
q is the rate of heat transfer
h is the local heat transfer coefficient
A is the surface area in contact with the fluid
ΔT is the temperature difference between the surface and the fluid

In this case, we have:
ΔT = 75°C - 50°C = 25°C
A = 1 m² (assuming the surface area is 1 m² for simplicity)

We need to convert the temperature difference to Kelvin scale for consistent units:
ΔT = 25°C + 273.15 = 298.15 K

Now, we can rearrange the equation to solve for h:
h = q / (A * ΔT)

The rate of heat transfer (q) can be calculated using Fourier's Law of Heat Conduction:
q = k * A * (dT / dx)

Where:
k is the thermal conductivity of air
A is the cross-sectional area perpendicular to the direction of heat transfer
dT/dx is the temperature gradient across the distance x

In this case, the distance x is given as 0.5 mm, which is equivalent to 0.0005 m. The temperature gradient (dT/dx) can be calculated as:
dT/dx = (50°C - 20°C) / 0.0005 m = 60,000 K/m

Substituting these values into Fourier's Law of Heat Conduction:
q = 0.0266 W/mK * 1 m² * 60,000 K/m = 1,596 W

Now, we can substitute the calculated value of q into the equation for h:
h = 1,596 W / (1 m² * 298.15 K) = 5.36 W/m²K

Therefore, the estimated value of the local heat transfer coefficient is 5.36 W/m²K. None of the given options match this value, so there might be an error in the question or the answer choices provided.

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A 50 mm X 50 mm iron bar 0.4 m long is connected to the walls of two heated reservoirs, each at 120°C. The ambient air temperature is 35°C and the convective heat transfer coefficient is 17.4 W/m2-K. Calculate the rate of heat loss from the bar. The thermal conductivity of iron is 52W/m-K.

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