Steady two-dimensional heat conduction takes place in the

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Steady two-dimensional heat conduction takes place in the body shown in the figure below. The normal temperature gradients over surface P and Q can be considered to be uniform. The temperature gradient δT/δt at surface Q is equal to 10 K/m. Surfaces P and Q are maintained at constant temperatures as shown in the figure, while the remaining part of the boundary is insulated. The body has a constant thermal conductivity of 0.1 W/mK.
The values of δT and δT at surface P are
δy δx

1. δT = 20 K/m δT = 0 K/m
  δx δy
2. δT = 0 K/m δT = 10 K/m
  δx δy
3. δT = 10 K/m δT = 10 K/m
  δx δy
4. δT = 0 K/m δT = 20 K/m
  δx δy

Correct Option: D

Direction of heat flow is always normal to surface of constant temperature
So for surface P₁, dT/dx = 0
From energy conservation,
Heat rate at P = Heat rate at Q

0.1 × 1

= 0.1 × 2 ×

⇒	dT	= 20 K/m
	dy

The values of	δT	and	δT	at surface P are
	δy		δx

	δT	= 20 K/m	δT	= 0 K/m
	δx		δy

	δT	= 0 K/m	δT	= 10 K/m
	δx		δy

	δT	= 10 K/m	δT	= 10 K/m
	δx		δy