(A) 13823 W/m
(B) 15487 W/m
(C) 17279 W/m
(D) 27646 W/m
GATE 2005
Answer: (B)
Consider the
flow of a gas with density 1 kg/m3, viscosity 1.5×10-5 kg/(m.s)
specific heat Cp = 846 J/kg.K and thermal conductivity k = 0.01665 W/m.K, in a
pipe of diameter D = 0.01 m and length L = 1 m and assume the viscosity does
not change with temperature. The Nusselt number for a pipe with (L/D) ratio
greater than 10 and Reynolds number greater than 20000 is given by
Nu = 0.026Re0.8Pr1/3
While
the Nusselt number for a laminar flow for Reynolds number less than 2100 and
(RePrD/L)<10 is
Nu =
1.86[Re.Pr(D/L)]1/3
If
the gas flows through the pipe with an average velocity of 0.1 m/s, the heat
transfer coefficient is
(A) 0.68 W/(m2.K)
(B) 1.14 W/(m2.K)
(C) 2.47 W/(m2.K)
(D) 24.7 W/(m2.K)
GATE 2005
Answer: (C)
A semi-infinite slab occupying the region x = 0 and x = ∞ is at an initial temperature T0. At time t = 0, the surface of the slab at x = 0 is brought into contact with a heat bath at a temperature TH. The temperature T(x,t) of the slab rises according to the equation
Where x is position and t is time. The heat flux at the surface x = 0 is proportional to
(A) t-1/2
(B) t1/2
(C) t
(D) t3/2
GATE
2005
Answer: (A)
A counter
current flow double pipe heat exchanger is used to heat water flowing at 1 kg/s
from 40°C to 80°C. Oil is used for heating and its temperature changes from
100°C to 70°C. The overall heat transfer coefficient is 300 W/m2C.
If it is replaced by a 1 – 2 shell and tube heat exchanger with counter current
flow configuration with water flowing in shell and oil flowing in tube, what is
the excess area required with respect to double pipe heat exchanger?
The
correction factor, Ft for LMTD based on the above double pipe heat
exchanger is 0.5. The heat transfer coefficient remains unchanged and the same
inlet and outlet conditions are maintained.
Cp, water = 4180 J/kg.°C, Cp, oil = 2000 J/kg.°C.
(A) 0 m2
(B) -20.15 m2
(C) 22.6 m2
(D) 9.09 m2
GATE 2005
Answer: (C)
Fluid flows in an annulus of inner diameter 0.8 m and outer diameter 1 m. Heat is transferred to the fluid from inner tube surface of the annulus. What is the equivalent diameter for heat transfer in m?
(A) 0.45
(B) 0.20
(C) 1.64
(D) 0.90
GATE 2005
Answer: (A)
Common statement for next two questions
A liquid of mass 7 kg and specific heat 4
KJ/kg.°C is contained in a cylindrical heater of diameter 0.15 m and height
0.40 m. The cylindrical surface of the heater is exposed to air at 25°C while
the end caps are insulated. So that heat transfer takes place only through the
cylindrical surface.
The thickness of the wall of the heater = 2
mm
The wall thermal conductivity = 10 W/(m.K)
The heat transfer coefficient in the liquid =
100 W/(m2.K)
The heat transfer coefficient in air = 10
W/(m2.K)
The liquid is initially maintained at a
temperature of 75°C. At time t = 0, the heater is switched off, and the
temperature of the liquid in the heater decreases due to heat loss across the
cylindrical surface.
What is the overall heat transfer coefficient in W/(m2.K)
(A) 1
(B) 4.04
(C) 9.07
(D) 10
GATE 2005
Answer: (C)
What is the time required for the temperature of the liquid to reduce to 50°C after the heater is switched off, assuming lumped system analysis is valid?
(A) 7.874×103 s
(B) 11.346×103 s
(C) 16.828×103 s
(D) 23.213×103 s
GATE 2005
Answer: (B)
A stagnant
liquid film of 0.4 mm thickness is held between two parallel plates. The top plate
is maintained at 40°C and the bottom plate is maintained at 30°C. If the
thermal conductivity of the liquid is 0.14 W/(m K), then the steady state heat
flux (in W/m2) assuming one dimensional heat transfer is
(A) 3.5
(B) 350
(C) 3500
(D) 7000
GATE 2006
Answer: (C)
An insulated
cylindrical pipe of 0.2 m diameter has a surface temperature of 45°C. It is
exposed to black body surroundings at 25°C. The emissivity and absorptivity of
the insulation surface are 0.96 and 0.93, respectively. The convective heat
transfer coefficient outside the insulation surface is 3.25 W/(m2
K). The Stefan-Boltzmann constant is 5.67 ×10–8 W/(m2 K4).
The surrounding fluid may be assumed to be transparent. Find the percentage
contribution from radiation to the total heat transfer rate to the surroundings.
(A) 30.9
(B) 50.0
(C) 57.6
(D) 68.4
GATE 2006
Answer: (D)
A process fluid
has to be cooled from 22°C to 2°C using brine in a 2-4 shell-and tube heat
exchanger shown below. The brine enters at –3°C and leaves at 7°C. The overall
heat transfer coefficient is 500 W/(m2 K). The design heat load is
30 kW. The brine flows on the tube side and the process fluid on the shell
side. The heat transfer area in m2 is
(A) 1.1
(B) 5.77
(C) 6.59
(D) 7.53
GATE
2006
Answer: (D)
Common statement
for next two questions
In film
condensation on a vertical plane surface the x directional velocity
distribution is given by
where
δ is the film thickness at any x.
The mass flow
rate of the condensate m(x) through any axial position x per unit width of the
plate is given by
Answer: (A)
Differentiate
m(x) with respect to δ to get the differential increase in condensate mass dm
with film thickness i.e., dm/dδ. Then obtain dm/dx assuming heat flux through
the film to be due to conduction based on a linear temperature profile between
the vapor and wall. Hence determine dδ/dx. Here μ1 is liquid viscosity,
kl is thermal conductivity, and λ is latent heat of condensation. Tv
is the vapor temperature and TW is the wall temperature
GATE 2006
Answer: (D)
For
the two long concentric cylinders with surface areas A1 and A2,
the view factor F22 is given by
(A) 0
GATE 2007
Answer: (C)
The composite
wall of an oven consists of three materials A, B and C. Under steady state
operating conditions, the outer surface temperature T
is 20⁰C,
the inner surface temperature Tsi is 600⁰C
and the oven air temperature is T∞=800⁰C.
For the following data
Thermal
conductivities kA = 20 W/(mK) and kC = 50 W/(mK),
thickness LA = 0.3 m, LB = 0.15 m and LC=0.15
m, inner-wall heat transfer coefficient h = 25 W/(m2K), The thermal
conductivity kB (W/(mK)) of the material B, is calculated as
(A) 35
GATE 2007
Answer: (B)
Water enters a
thin walled tube (L=1 m, D = 3 mm) at an inlet temperature of 97⁰C
and mass flow rate 0.015 kg/s. The tube wall is maintained at a constant
temperature of 27⁰C. Given the following
data for water
Density, ρ = 1000 kg/m3
Viscosity, µ = 489×10-6 Ns/m2
Specific heat Cp = 4184 j/kg/k
Inside
heat transfer coefficient h = 12978 W/(m2.K)
The outlet temperature of water in ⁰C is
(A) 28
(B) 37
(C) 62
(D) 96
GATE 2007
Answer: B
A hot fluid
entering a well-stirred vessel is cooled by feeding cold water through a jacket
around the vessel. Assume the jacket is well-mixed. For the following data,
Mass
flow rates of the hot fluid = 0.25 kg/s,
Mass
flow rate of cold water = 0.4 kg/s,
Specific
heats of oil = 6000 J/kg K
Specific
heat of cold water = 4184 J/kg K
The
inlet and exit temperature of the hot fluid is 150⁰C
and 100⁰C respectively.
Inlet
temperature of cold water = 20⁰C
The overall heat transfer coefficient is 500 W/m2K. The heat transfer area in m2, is
(A) 1.82
(B) 2.1
(C) 3
(D) 4.26
GATE 2007
Answer: (D)
Consider a
liquid stored in a container exposed to its saturated vapour at constant
temperature Tsat. The bottom surface of the container is maintained
at a constant temperature Ts<Tsat while its side walls
are insulated. The thermal conductivity k1 of the liquid, its latent
heat of vaporization λ and density ρ1 are known. Assuming a linear
temperature distribution in the liquid, the expression for the growth of the
liquid layer δ as a function of time t is given by
GATE
2007
Answer: (C)
The following
list of options P, Q, R and S are some of the important considerations in the
design of a shell and tube heat exchanger.
(P) Square pitch permits the use of more tubes in a
given shell diameter
(Q) The tube side clearance should not be less than
one fourth of the tube diameter
(R) Baffle spacing is not greater than the diameter
of the shell or less than one-fifth of the shell diameter
(S) The pressure drop on the tube side is less than
10 psi
Pick out the correct combination of ‘TRUE’ statements from the following:
(A) P, Q and R
(B) Q, R and S
(C) R, S and P
(D) P, Q, R and S
GATE 2007
Answer: (B)
The Grashof number is
(A) Thermal diffusivity/mass diffusivity
(B) Inertial force/surface tension force
(C) Sensible heat/latent heat
(D) Buoyancy force/viscous force
GATE
2007
Answer: (D)
The
temperature profile for heat transfer from one fluid to another separated by a
solid wall is
GATE
2008
Answer: (B)
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