A plane slab of 100 mm thickness generates heat. It is observed that the temperature drop between the centre and its surface to be 50°C . If the thickness is increased to 20 cm the temperature difference will be

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ESE Mechanical 2013 Official Paper - 1

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Answer 1

Concept:

Plane wall with uniform heat generation:

For one dimensional steady state condition

Here at x = -L, T = Tω ,x = L, T = Tω

Calculation:

Initial thickness = 2L₁ = 100 mm;

Final thickness = 2L₂ = 20 cm = 200 mm;

(T - T₁)_max = 50°C;

From the above relation,

Substituting the values of L₁ and L₂, we get

(T - T2)max = 4 × (T - T1)max

⇒ (T - T2)max = 200°C