Please clearly show the heat rate per unit wall depths for all 3 cases in both scenarios a and b. Consider a composite wall of overall height H = 20 mm and thickness L = 30 mm. Section A has thickness L₁ = 10 mm, andsections B and C each have height HB = 10 mm and thickness LB = 20 mm. The temperatures of the left and right faces of thecomposite wall are T₁ = 50°C and T₂ = 20°C, respectively.Consider the three cases shown below.T₁2A3·LA2.8L4.2BLBCCase kд(W/m-K) kg(W/m-K) kc(W/m.K)11.42.84.2HB1.4H4.21.4T₂2.8(a) If the top and bottom of the wall are insulated, determine the heat rate per unit wall depth for each of the three cases, in W/m,assuming that surfaces normal to the heat flow direction are isothermal.(b) If the top and bottom of the wall are insulated, determine the heat rate per unit wall depth for each of the three cases, in W/m,assuming that surfaces parallel to the heat flow direction are adiabatic.

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Please clearly show the heat rate per unit wall depths for all 3 cases in both scenarios a and b.

Consider a composite wall of overall height H = 20 mm and thickness L = 30 mm. Section A has thickness L₁ = 10 mm, and
sections B and C each have height HB = 10 mm and thickness LB = 20 mm. The temperatures of the left and right faces of the
composite wall are T₁ = 50°C and T₂ = 20°C, respectively.
Consider the three cases shown below.
T₁
2
A
3
·LA
2.8
L
4.2
B
LB
C
Case kд(W/m-K) kg(W/m-K) kc(W/m.K)
1
1.4
2.8
4.2
HB
1.4
H
4.2
1.4
T₂
2.8
(a) If the top and bottom of the wall are insulated, determine the heat rate per unit wall depth for each of the three cases, in W/m,
assuming that surfaces normal to the heat flow direction are isothermal.
(b) If the top and bottom of the wall are insulated, determine the heat rate per unit wall depth for each of the three cases, in W/m,
assuming that surfaces parallel to the heat flow direction are adiabatic.

Expert Solution

Step 1

From the given data:

The equivalent thermal resistance for the system for the case 1:

$\to R_{1} = R_{A} + \frac{R_{B} R_{C}}{R_{B} + R_{C}} = (\frac{L_{A}}{k_{A} H}) + \frac{(\frac{L_{B}}{k_{B} H_{B}}) (\frac{L_{C}}{k_{C} H_{C}})}{(\frac{L_{B}}{k_{B} H_{B}}) + (\frac{L_{C}}{k_{C} H_{C}})} = \frac{10}{1.4 * 20} + \frac{(\frac{20}{2.8 * 10}) (\frac{20}{4.2 * 10})}{(\frac{20}{2.8 * 10}) + (\frac{20}{4.2 * 10})} = 0.642 K / W$

So the heat transfer rate in case 1 :

$\to Q_{1} = \frac{(T_{1} - T_{2})}{R_{1}} = \frac{50 - 20}{0.642} = 46.67 W . . . . . . . . . . . . . . . . . . . a n s w e r$

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What would the heat rate per unit wall depth be for the second case in scenario b?

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