Question

If a roof is treated with a layer of thermal
insulation material, the internal heat gain is
reduced by 60%. The U-value of the roof slab
(without thermal insulation) is 3 W m2/°C.
Assuming a constant temperature difference
between indoor and outdoor, the U-value of the
thermal insulation layer in W m2 / °C is​

Answer 1

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Explanation:

We will start from the beginning with concept. U-value =

1

- value

R

Following is the basic equation of heat flow,

image is there

then,

Where,

qx is rate of heat flow

k = Thermal conductivity

A = surface area of the wall

dx = wall thickness

dT = temperature difference

R-value is inversely related to the thermal conductivity constant and is also related to thickness, thus :

So, the equation (1) becomes,

Let, R-value of thermal insulation material = R1

R-value of the roof

= R2 = 1- value = 1......(given)U3

R-value of combined set = R1 + 2

According to question,

∆Q

= A(Tf - Ti)

....(heat transfer rate when there is no insulation)

∆t R20.4 ×∆Q

= A(Tf - Ti)

....(heat transfer rate with insulation)

∆t R1 + 21

= R1 + 20.4 R21

= R1 + 20.4131

= 1.2R2

Now as per addition of thermal resistance, R1 + 2 = R1 + R21

= R1 + 1

⇒ R1 = 2