## GATE ME solved Questions on Conduction (Heat Transfer)

**Question #1**

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} (in °C) is __________

**[GATE 2016 Set 2, 1 mark]**

**Question #2**

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)$\large \ln \frac{(r_{2}/r_{1})}{2\Pi kL}$

(b)$\large \ln \frac{(r_{1}/r_{2})}{2\Pi kL}$

(c)$\large \ln \frac{2\pi kL}{r_{2}/r_{1}}$

(d)$\large \ln \frac{2\pi kL}{r_{1}/r_{2}}$

**[GATE 2016 Set 2, 1 mark]**

**Question #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) increase

(B) remain the same

(C) decrease

(D) be zero

**[GATE 2016 Set 1, 1 mark]**

**Question #4**

If a foam insulation is added to a 4 cm outer diameter pipe as shown in the figure, the critical radius of insulation (in cm) is _____________

**[GATE 2015 Set 2,1 mark]**

critical radius of insulation will be,

$r_{c}=\frac{k_{foam}}{h_{o}}$

$r_{c}=\frac{0.1}{2}=0.05m=5cm$ ….(Answer)

**Question #5**

As the temperature increases, the thermal conductivity of a gas

(A) increases

(B) decreases

(C) remains constant

(D) increases up to a certain temperature and then decreases

**[GATE 2014 Set 4, 1 mark]**

**Question #6**

Consider a long cylindrical tube of inner and outer radii, r_{i} and r_{o}, respectively, length, L and thermal conductivity, k. Its inner and outer surfaces are maintained at T_{i} and T_{o} , respectively( T_{i} > T_{o} ). Assuming one-dimensional steady state heat conduction in the radial direction, the thermal resistance in the wall of the tube is

(a)$\large \frac{1}{2\pi kL}\ln\frac{r_{i}}{r_{o}}$

(b)$\large \frac{1}{2\pi r_{i}k}$

(c)$\large \frac{1}{2\pi kL}\ln\frac{r_{o}}{r_{i}}$

(d)$\large \frac{1}{4\pi kL}\ln\frac{r_{o}}{r_{i}}$

**[GATE 2014 Set 3, 1 mark]**

**Question #7**

10 mm diameter electrical conductor is covered by an insulation of 2 mm thickness. The conductivity of the insulation is 0.08 W/m-K and the convection coefficient at the insulation surface is 10 W/m^{2}-K. Addition of further insulation of the same material will

(A) increase heat loss continuously

(B) decrease heat loss continuously

(C) increase heat loss to a maximum and then decrease heat loss

(D) decrease heat loss to a minimum and then increase heat loss

**[GATE 2015 Set 1, 2 marks]**

**Question #8**

A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of 4×10^{7} W/m ^{3} . The rod is cooled by a liquid (convective heat transfer coefficient 1000 W/m^{2} K) at 25 °C. At steady state, the surface temperature (in K) of the rod is

(A) 308

(B) 398

(C) 418

(D) 448

**[GATE 2015 Set 2, 2 marks]**

**Question #9**

A brick wall (k=0.9 W/mK) of thickness 0.18 m separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is −5°C and the room needs to be maintained at 27°C. The heat transfer coefficient associated with outside air is 20 w/m^{2}k.

Neglecting the convective resistance of the air inside the room, the heat loss, in (W/m^{2}) is

(A) 88 (B) 110 (C) 128 (D) 160

**[GATE 2015 Set 3, 2 marks]**

**Question #10**

A material P of thickness 1 mm is sandwiched between two steel slabs, as shown in the figure below. A heat flux 10 kW/m2 is supplied to one of the steel slabs as shown. The boundary temperatures of the slabs are indicated in the figure. Assume thermal conductivity of this steel is 10 W/m.K. Considering one-dimensional steady state heat conduction for the configuration, the thermal conductivity (k, in W/m.K) of material P is _______

**[GATE 2014 Set 2, 2 marks]**

**Question #11**

Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness (l). The conductivity of one section is k and that of the other is 2k. The left face of the wall is at 600 K and the right face is at 300 K

The interface temperature Ti (in K) of the composite wall is _______

**[GATE 2014 Set 2, 2 marks]**

**Question #12**

A plane wall has a thermal conductivity of 1.15 W/m.K. If the inner surface is at 1100°C and the outer surface is at 350°C, then the design thickness (in meter) of the wall to maintain a steady heat flux of 2500 W/m^{2} should be _______

**[GATE 2014 Set 4. 2 marks]**

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