Question

In a slab under steady state conduction if the thermal conductivity increases along the thickness, the temperature gradient along the direction will become

Answer 1

In steady state conduction with thermal conductivity given by k=k ₂ (1+β) ... Will be the same as flow depends on the thickness only 13. ... The temperature will drop at a faster rate along the length b.

Answer 2

In a slab under steady-state conduction, if the thermal conductivity increases along with the thickness, the temperature gradient along with the direction decreases.

• During steady-state conditions, the rate of heat flow remains constant i.e. dQ / dt = Constant
• The formula for heat conduction across a conductor = dQ / dt

         = k A (d∅/ dl)

(Here, k = thermal conductivity, A = area of cross-section, ∅ = temperature, and l is the length)

• Since dQ / dt and A are constant in the given question, on cross multiplying we get k ∝ dl / d∅ or k is inversely proportional to the temperature gradient.
• So as K increases along with the thickness of the conductor, the temperature gradient decreases.