Project ForgeConsider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as T1 at x=0 and T2 at x increasing, where T2>T1. The conductivity of the wall is given by k=k0+bT, where k0 and b are positive constants, and T is temperature. As x increases, the temperature gradient (dT/dx) will
- Aremain constant
- Bbe zero
- Cincrease
- decrease
Explanation
With no heat generation, the steady-state heat flux q=−k(dT/dx) must be constant along x (energy conservation). Since T increases monotonically from T1 to T2 as x increases, and b>0, the conductivity k=k0+bT increases along x. For q=−k(dT/dx) to stay constant while k increases, |dT/dx| must decrease correspondingly — the temperature gradient decreases as x increases.
Source: GATE ME 2013 (Booklet Code A) (2013)
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