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Doubt

A Slab consist of two parallel layers of diffrent matarials of same thickness thermal conductivities K and k . The equivalent themal conductivity of the slab ?

I REQUEST TO YOU PLEASE EXPLAIN EACH POINT SLAP ALSO EXPLAIN WHICH PRINCIPAL IS USING IN THIS QUES. AND WHY ?

Answer Explanation

The principal involved is simple. Thermal current will behave like electric current. So, if two slabs are connected in paralled, then equivalent thermal resistance will decrease and will be given by the formula :



So, assume first the area of each slab is A and  length is x.
So, the thermal resistances of each will be given by:

R1 = x/KA

R2 = x/kA

1/R1 = KA/x

1/R2 = kA/x

1/R1 + 1/R2 = KA/x + kA/x = (K+k)A/x = 1/R

Now, since the slabs are joined in parallel, the length of the equivalent slab will remain same but it will area will become twice.

So, 1/R = Keq2A/x = (K+k)A/x

or, 2 Keq = (K+k)

or, Keq = (K+k)/2.

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