A30-cm-diameter, 4.8-m-high cylindrical column of a house made of concrete (k = 0.79 w/m·k, α = 5.94 × 10−7 m2/s, rho = 1600 kg/m3, and cp = 0.84 kj/kg·k) cooled to 14°c during a cold night is heated again during the day by being exposed to ambient air at an average temperature of 28°c with an average heat transfer coefficient of 14 w/m2·k. use analytical one-term approximation method (not the heisler charts). determine how long it will take for the column surface temperature to rise to 25°c. the time taken for the column surface temperature to rise to 25°c is

The time for the surface temperature to reach 25 ◦C is  3.24 hr

Explanation:

Assumptions

1. 1-D heat conduction

2. constant thermal properties

3. the heat transfer coefficient is constant & uniform over the surface.

Properties

k = 0.79 W/m · ◦C

α = 5.94 × 10−7 m^2/s

ρ = 1600 kg/m^3

Cp = 0.84 kJ/kg · ◦C

Step 1: Check the Biot number

As Bi > 0.1  hence lumped system analysis will not considered.

Check the Fourier number.

From Table 18-1

From Table 18-2, we can find

The Fourier number is determined as

solving τ

Since τ > 0.2, the one term approximation or the Heisler charts can be used.

The time for the surface temperature to reach 25 ◦C is

= 11674.24 s = 3.24 hours

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