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plane wall, 7.5 cm thick, generates heat internally at the rate of 105W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 120°C. The convection heat transfer coefficient between the wall and the environment is 750 W/m2K. If the thermal conductivity of the wall is 20 W/m K, calculate the maximum temperature in the wall.

Respuesta :

Answer:

T=120.04°C

Explanation:

Given that

L= 7.5 cm

q = 105 W/m³

T∞=120°C

h=750 W/m²K

K=20 W/mK

Here given that one side of the wall is insulated that is why the maximum temperature will be at the insulated surface.

The total heat transfer from the wall

Q= q A L

Q= 150 x 0.075 A

Q=7.875 A W

A=Area of wall

Now the total thermal resistance R

[tex]R=\dfrac{L}{KA}+\dfrac{1}{hA}[/tex]

[tex]R=\dfrac{0.075}{20A}+\dfrac{1}{750A}[/tex]

[tex]R=\dfrac{0.00508}{A}[/tex]

We also know that

[tex]Q=\dfrac{\Delta T}{R}[/tex]

Temperature at insulated side = T

[tex]7.875 A=\dfrac{T-120}{\dfrac{0.00508}{A}}[/tex]

[tex]7.875 =\dfrac{T-120}{0.00508}[/tex]

T=120.04°C

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