A well machined steel plate of thickness L is kept such

A well machined steel plate of thickness L is kept such that the wall temperature are Th and Tc as seen in the figure below. A smooth copper plate of the same thickness L is now attached to the steel plate without any gap as indicated in the figure below. The temperature at the interface is T_t. The temperatures of the outer walls are still the same at T_h and T_c. The heat transfer rates are q₁ and q₂ per unit area in the two cases respectively in the direction shown. Which of the following statements is correct?

1. T_h > T_i > T_c and q₁ < q₂
2. T_h < T_i > T_c and q₁ = q₂
3. T_h = (T_i + T_c )/2 and q₁ > q₂
4. T_i < (T_h + T_c )/2 and q₁ > q₂

For caseI-:

Q₁ =	T_h - T_c
	R₁

where R₁ =	L
	K_SA

For Case-II:

Q₂ =	T_h - T_c
	R₂ + R₃

where R₂ =	L	and R₃ =	L
	K_sA		K_cuA

As R₂ + R₃ > R₁ at constant temperature difference in both cases.

Then q₁		or	Q₁		> q₂		or	Q₂
			A					A

For Case-II:
R₂ > R₃
∵ k_cu > k_s

Q₂ =	T_h - T₁
	R₂

or R₂ =	T_h - T₁
	Q₂

also Q₂ =	T_i - T_c
	R₃

or R₃ =	T_i - T_c
	Q₂

∴	T_h - T_i	>	T_i - T_c
	Q₂		Q₂

or T_h – T_i > T_i – T_c
or T_h + T_c > 2T_i

or T_i <	T_h + T_c
	2