The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA = 30 W/m·K and kC = 65 W/m·K, and known thickness, LA = 0.35 m and LC = 0.25 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB = 0.25 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature (on outer surface of material C) of Ts,o = 22◦C, an inner surface temperature (on inner surface of material A) of Ts,i = 600◦C, and an oven temperature of T[infinity] = 800◦C. If the inside convection coefficient h = 25 W/m2 ·K, what is the value of kB?

Respuesta :

Answer:

[tex]K_B=2.49\ W/m.K[/tex]

Explanation:

We know that

Thermal resistance due to conductivity

[tex]R=\dfrac{L}{KA}[/tex]

Thermal resistance due to heat transfer coefficient

[tex]R'=\dfrac{L}{KA}[/tex]

We know that heat transfer Q

Q=ΔT/Rth

By equating heat

[tex]\dfrac{600-22}{\dfrac{L_A}{AK_A}+\dfrac{L_B}{AK_B}+\dfrac{L_C}{AK_C}}=\dfrac{800-22}{\dfrac{L_A}{AK_A}+\dfrac{L_B}{AK_B}+\dfrac{L_C}{AK_C}+\dfrac{1}{Ah}}[/tex]

[tex]\dfrac{600-22}{\dfrac{0.35}{30}+\dfrac{0.25}{K_B}+\dfrac{0.25}{65}}=\dfrac{800-22}{\dfrac{0.35}{30}+\dfrac{0.25}{K_B}+\dfrac{0.25}{65}+\dfrac{1}{25}}[/tex]

Now by solving we get

[tex]K_B=2.49\ W/m.K[/tex]

Ver imagen Netta00
Q&A Education