Question

Standards for firewalls may be based on their thermal response to a prescribed radiant heat flux. Consider a 0.25-m-thick concrete wall ( 2300 kg/m^3, 880 J/kg·K, 1.4 W/m·K), which is at an initial temperature of 25°C and irradiated at one surface by lamps that provide a uniform heat flux of 0.75·104 W/m^2. The absorptivity of the surface to the irradiation is 1.0. If building code requirements dictate that the temperatures of the irradiated and back surfaces must not exceed 325°C and 25°C, respectively, after 30 min of heating, will the requirements be met?

Answer 1

Answer:

yes requirement will be met

Explanation:

considering temperature distribution through following relation

$T(x,t) = T_1 + \frac{2q_o"\frac{(\alpha t)^0.5}{\pi}{k} exp (\frac{-x^2}{4\alpha t} - \frac{q_o" x}{k} erfc (\frac{x}{2\sqrt{\alpha t}}$

where $\alpha =\frac{1.4}{2300\times 880} = 6.92\times 10^{-7} m^2/s$

$t = 30\times 60 = 1800 sec$

Q = HEAT FLUX  = 0.75 \times 10^4 W/m^2

$T( 0, 30) =   25 + \frac{2(.75\times 10^4)[\frac{(6.92\times 10^{-7} \times 1800}{\pi}]^{0.5}}{1.4} exp (\frac{-0^2}{4(6.92\times 10^{-7} \times 1800)} - \frac{(0.7\times 10^{4} 0}{k} erfc(0)$

T(0,30 min) = 25 + 213.34 = 238.34 degree C

CALCULATE THE TEMPERATURE AT X = 0.25 M

$T(0.25, 30)  = 25 + 213.34 [exp (\frac{0.25^2}{4\times 6.92\times 10^{-7} \times 1800})] - \frac{0.75\times 10^4(0.25)}{1.4} erfc(\frac{0.25}{2\sqrt{6.92\times 10^{-7} \times 1800}})$

$T(0.25,30 min) = 25 + 213.34(3.56\times 10^{-4}) - 1339.28 (.00000054765)$

T(0.25,30 min) = = 25.00 degree celcius

since both surface have temperature lower than allowable therefore code requirement be met