1
GATE ME 2024
+1
-0.33

A plane, solid slab of thickness L, shown in the figure, has thermal conductivity k that varies with the spatial coordinate x as k = A + Bx, where A and B are positive constants (A > 0, B > 0). The slab walls are maintained at fixed temperatures of T(x = 0) = 0 and T(x = L) = T0 > 0. The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?

A
B
C
D
2
GATE ME 2016 Set 1
+1
-0.3
A plastic sleeve of outer radius $${r_0} = 1\,\,mm$$ covers a wire (radius $$r = 0.5$$ $$mm$$) carrying electric current. Thermal conductivity of the plastic is $$0.15\,\,W/m$$-$$K$$. The heat transfer coefficient on the outer surface of the sleeve exposed to air is $$25$$ $$W/{m^2}$$-$$K$$. Due to the addition of the plastic cover, the heat transfer from the wire to the ambient will
A
increases
B
remain the same
C
decreases
D
be zero
3
GATE ME 2016 Set 2
+1
-0.3
A hollow cylinder has length $$L,$$ inner radius $${{r_1}}$$, outer radius $${{r_2}}$$, and thermal conductivity $$k.$$ The thermal resistance of the cylinder for radial conduction is
A
$${{ln\left( {{r_2}/{r_1}} \right)} \over {2\pi kL}}$$
B
$${{ln\left( {{r_1}/{r_2}} \right)} \over {2\pi kL}}$$
C
$${{2\pi kL} \over {ln\left( {{r_2}/{r_1}} \right)}}$$
D
$${{2\pi kL} \over {ln\left( {{r_1}/{r_2}} \right)}}$$
4
GATE ME 2016 Set 3
Numerical
+1
-0
Steady one-dimensional heat conduction takes place across the faces $$1$$ and $$3$$ of a composite slab consisting of slabs $$A$$ and $$B$$ in perfect contact as shown in the figure, where $${k_A},\,\,{k_B}$$ denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature $${T_2}$$ $$\left( {in\,{\,^ \circ }C\left. \, \right)} \right.$$ is ______________.