. A long 10-cm-diameter steam pipe whose external surface temperature is 110oC passes through some open area that is not protected against the winds. Determine the rate of heat loss from the pipe per unit of its length when the air is at 1 atm pressure and 10oC and the wind is blowing across the pipe at a velocity of 8 m/s. Use the following relation to calculate the Nusselt number.

Explanation:

Let consider that pipe is a horizontal cylinder. The Nusselt number is equal to:

, for .

Where is the Rayleigh number associated with the cylinder.

The Rayleigh number is:

By assuming that air behaves ideally, the coefficient of volume expansion is:

The cinematic and dynamic viscosities, thermal conductivity and isobaric specific heat of air at 10 °C and 1 atm are:

The Prandtl number is:

Likewise, the Rayleigh number is:

Finally, the Nusselt number is:

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .