Question

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?

Answer 1

`K_B=2.49\ W/m.K`

Step-by-step explanation:

We know that

Thermal resistance due to conductivity

`R=(L)/(KA)`

Thermal resistance due to heat transfer coefficient

`R'=(L)/(KA)`

We know that heat transfer Q

Q=ΔT/Rth

By equating heat

`(600-22)/((L_A)/(AK_A)+(L_B)/(AK_B)+(L_C)/(AK_C))=(800-22)/((L_A)/(AK_A)+(L_B)/(AK_B)+(L_C)/(AK_C)+(1)/(Ah))`

`(600-22)/((0.35)/(30)+(0.25)/(K_B)+(0.25)/(65))=(800-22)/((0.35)/(30)+(0.25)/(K_B)+(0.25)/(65)+(1)/(25))`

Now by solving we get

`K_B=2.49\ W/m.K`