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# Multiple choice question for engineering

## Set 1

1. A 25 mm diameter egg roll (k = 1 W/m degree) is roasted with the help of microwave heating. For good quality roasting, it is desired that temperature at the center of roll is maintained at 100 degree Celsius when the surrounding temperature is 25 degree Celsius. What should be the heating capacity in W/m 3 of the microwave if the heat transfer coefficient on the surface of egg roll is 20 W/m2 degree?
a) 113.31 k W/m3
b) 213.31 k W/m3
c) 313.31 k W/m3
d) 413.31 k W/m3

Answer: b [Reason:] t max = t a + q g R/2h + q g R2/4k.

2. The constants of integration are to be determined from the relevant boundary conditions which are
(i) t = t w at r = R
(ii) q g (π L R2) = -k (2 π R L) (d t/d r)
(iii) Increasing temperature gradient
Choose the correct option?
a) Only 1
b) Only 2
c) 1 and 3
d) 1 and 2

Answer: d [Reason:] Temperature gradient must be constant.

3. A concrete column used in bridge construction is cylindrical in shape with a diameter of 1 meter. The column is completely poured in a short interval of time and the hydration of concrete results in the equivalent of a uniform source strength of 0.7 W/kg. Determine the temperature at the center of the cylinder at a time when the outside surface temperature is 75 degree Celsius. The column is sufficiently long so that temperature variation along its length may be neglected. For concrete
Average thermal conductivity = 0.95 W/m K
Average density = 2300 kg/m3
a) 190.92 degree Celsius
b) 180.92 degree Celsius
c) 170.92 degree Celsius
d) 160.92 degree Celsius

Answer: b [Reason:] t max = t w + q g R2/4k. We get, q g = 0.7 W/kg.

4. The temperature distribution profile for a solid cylinder is
a) Parabolic
b) Linear
c) Ellipse
d) Hyperbolic

Answer: a [Reason:] It must be parabolic for maximum heat conduction.

5. For a solid cylinder, maximum temperature difference occurring at the center of the rod is given by
a) t W – q g R2/4K
b) q g R2/4K
c) t W + q g R2/4K
d) t W + q g R2/4KL

Answer: c [Reason:] As temperature distribution profile is parabolic so on integrating between boundary conditions we get the result.

6. A slab of 12 cm thickness and generating heat uniformly at 10 6 W/m3 has thermal conductivity of 200 W/m degree. Both surfaces of the slab are maintained at 150 degree Celsius. Determine the heat flow rate at the quarter planes a) 30000 W/m2
b) 40000 W/m2
c) 50000 W/m2
d) 60000 W/m2

Answer: a [Reason:] q g (π R2 L) = (t w – t a) (2 π R L) h.

7. Consider a convective heat flow to water at 75 degree Celsius from a cylindrical nuclear reactor fuel rod of 50 mm diameter. The rate of heat generatioN is 50000000 W/m3 and convective heat transfer coefficient is I kW/m2 K. The outer surface temperature of the fuel element would be
a) 625 degree Celsius
b) 700 degree Celsius
c) 550 degree Celsius
d) 400 degree Celsius

Answer: b [Reason:] t w = t a + q g R/ 2h.

8. For a cylindrical rod with uniformly distributed heat sources, the thermal gradient at half the radius location will be
a) Four times
b) Twice
c) One fourth
d) One half

Answer: d [Reason:] t = t w + q g (R2 – r2)/4k. (d t /d r) r = R/2 = 1/2(d t/d r) r = R.

9. The maximum temperature for cylindrical coordinate occurring at r = 0 is
a) t max = t a +q g R/h + q g R2/4k
b) t max = t a +q g R/4h + q g R2/4k
c) t max = t a +q g R/2h + q g R2/4k
d) t max = t a +q g R/6h + q g R2/4k

Answer: c [Reason:] As, t = t a +q g R/6h + q g R2/4k (R2 –r2).

10. In case of solid cylinder of radius R, the temperature distribution is given as
a) t – t w/t max – t w = 1 – (r/R)2
b) t – t w/t max – t w = 1 – (r/R)
c) t – t w/t max – t w = 1 – (r/R)3
d) t – t w/t max – t w = 1 – (r/R)4
Where, t w is outer surface temperature and t max is along cylinder axis.

Answer: a [Reason:] As we know for a long cylinder of radius R, t = t w + q g (R2 – r2)/4k. On integrating this we get the answer.

## Set 2

1. In case of heat conduction through plane wall, which one of the following is not a correct assumption?
b) Three dimensional heat flow
c) Volumetric heat generation must be constant
d) K must be constant

Answer: b [Reason:] There should be two dimensional heat flow. The differential equation describing the temperature distribution can be set up by making an energy balance.

2. If Q X is heat generated in at distance ‘x’, then heat conducted out at a distance (x + d x) will be
a) Q X + 3d (Q X) d x /d x
b) 2Q X + d (Q X) d x /d x
c) d (Q X) d x /d x
d) Q X + d (Q X) d x /d x

Answer: d [Reason:] Q X + Q g = Q X + d X.

3. Notable example of uniform generation of heat within the conducting medium are
(i) Energy of a nuclear reactor
(ii) Liberation of energy due to some exothermic chemical reactions
(iii) Resistance heating in electrical appliances
Which of the statements made above are correct?
a) 1, 2 and 3
b) 1 and 2
c) 1 and 3
d) Only 2

Answer: a [Reason:] All the statements are correct with respect to plane wall heat conduction.

4. For a plane wall of thickness l with uniformly distributed heat generation q g per unit volume, the temperature t 0 at mid plane is given by
a) t 0 = q g l 2/2k +t w
b) t 0 = q g l 2/4k +t w
c) t 0 = q g l 2/8k +t w
d) t 0 = q g l 2/16k +t w

Answer: c [Reason:] t = q g /2k (l – x) x + t w. At mid plane i.e. x = l/2 we get t 0 = q g l 2/8k +t w.

5. The temperature drop in a plane wall with uniformly distributed heat generation can be decreased by reducing
a) Wall thickness
b) Heat generation rate
c) Thermal conductivity
d) Surface area

Answer: a [Reason:] On decreasing wall thickness, generally temperature drop decreases.

6. Consider a slab of thickness δ with one side (x = 0) insulated and other side (x = δ) maintained at constant temperature. The rate of uniform heat generation within the slab is q g W/m3. Presuming that the heat conduction is in steady state and one dimensional along x direction, the maximum temperature in the slab would occur at x equal
a) δ/2
b) Zero
c) δ/4
d) δ

Answer: b [Reason:] Maximum temperature occurs at the insulated face of the wall where x = 0.

7. There occurs heat conduction and internal heat generation at uniform rate within the conduction medium itself in the following cases
(i) Drying of concrete
(ii) Chemical processes
(iii) Fuel elements in a nuclear reaction
Choose the correct option
a) 1 only
b) 2 only
c) 1 and 3
d) 1, 2 and 3

Answer: d [Reason:] All are correct as there is heat conduction in all above cases. The rate of heat generation has to be controlled one, otherwise the resulting temperature growth might result in the failure of the medium.

8. The rear window of an automobile is made of thick glass i.e. AB = 5 mm and thermal conductivity is 0.8 W/m degree. To defrost this window, a thin transparent film type heating element has been fixed to its inner surface. For the conditions given below, determine the electric power that must be provided per unit area of window if a temperature 5 degree Celsius is maintained at its outer surface. Interior air temperature and the corresponding surface coefficient are 20 degree Celsius and 12 W/m2 degree. Surrounding air temperature and the corresponding surface coefficient are – 15 degree Celsius and 70 W/m2 degree. Electric heater provides uniform heat flux a) 232.5 /m2
b) 1232.5 /m2
c) 2232.5 /m2
d) 3232.5 /m2

Answer: b [Reason:] (t I – t f)/(1/h i + δ/k) + q g = h 0 (t s – t 0).

9. Suppose heat is conducted due to electrons
Where, i = I/A and p is the resistivity, then
a) q g = 2i2 p
b) q g = 3i2 p
c) q g = i2 p
d) q g = 4i2 p

Answer: c [Reason:] It should be i2 p. Here i is current density.

10. In case when both the surfaces of plane wall are at different temperature, we get an expression i.e.
T MAX – T W2 /T W1 – TW2 = (B + 1)2/4B
What is the value of B?
a) (q g) (δ)2/2k (T W1 – TW2)
b) (q g) (δ)3/3k (T W1 – TW2)
c) (q g) (δ)4/4k (T W1 – TW2)
d) (q g) (δ)5/5k (T W1 – TW2)

Answer: a [Reason:] T – T W2 /T W1 – TW2 = [1 – x/ δ] [B x/ δ +1].

## Set 3

1. Consider heat conduction through a solid sphere of radius R. There are certain assumptions
(i) Unsteady state conditions
(ii) One-dimensional radial conduction
(iii) Constant thermal conductivity
Identify the correct statements
a) 1 and 3
b) 2 and 3
c) 1, 2 and 3
d) 1 and 2

Answer: b [Reason:] Statement 1 should be steady state condition.

2. An 8 cm diameter orange, approximately spherical in shape, undergoes ripening process and generates 18000 k J/m3 hr of energy. If external surface of the orange is at 6.5 degree Celsius, find out the temperature at the center of the orange. Take thermal conductivity = 0.8 k J/ m hr degree for the orange material
a) 13.5 degree Celsius
b) 12.5 degree Celsius
c) 11.5 degree Celsius
d) 10.5 degree Celsius

Answer: b [Reason:] q g = 5000 W/m3, k = 0.222 W/m K and t = t W + q g R 2/6K = 12.5 degree Celsius.

3. Consider the above problem, calculate the heat flow from the outer surface of the orange
a) 4.82 k J/hr
b) 5.82 k J/hr
c) 6.82 k J/hr
d) 7.82 k J/hr

Answer: a [Reason:] Q = 4/3 (π R 3 q g) = 1.34 J/s.

4. What is the heat flow for steady state conduction for sphere?
a) 4 Q R + Q G = Q R + d R
b) 3 Q R + Q G = Q R + d R
c) 2 Q R + Q G = Q R + d R
d) Q R + Q G = Q R + d R
Where, Q R = Heat conducted in at radius R
Q G = Heat conducted in the element
Q R + d R = Heat conducted out at radius R + d R

Answer: d [Reason:] Q R + Q G = Q R + d (Q R) d R/d R.

5. The general solution for temperature distribution in case of solid sphere is
a) t = t W + q g (R 2 – r 2)/4 k
b) t = t W + q g (R 2 – r 2)/8 k
c) t = t W + q g (R 2 – r 2)/6 k
d) t = t W + q g (R 2 – r 2)/2 k

Answer: c [Reason:] The temperature distribution is parabolic.

6. A solid sphere of 8 cm radius has a uniform heat generation 0f 4000000 W/m3. The outside surface is exposed to a fluid at 150 degree Celsius with convective heat transfer coefficient of 750 W/m2 K. If thermal conductivity of the solid material is 30 W/m K, determine maximum temperature
a) 444.45 degree Celsius
b) 434.45 degree Celsius
c) 424.45 degree Celsius
d) 414.45 degree Celsius

Answer: b [Reason:] q g (4 π R3/3) = h 4 π R2 (t W – t a), t w = 292.22 degree Celsius T MAX = t w + q g R 2/6 k.

7. Consider the above problem, find the temperature at 5 cm radius
a) 348.9 degree Celsius
b) 358.9 degree Celsius
c) 368.9 degree Celsius
d) 378.9 degree Celsius

Answer: d [Reason:] t – t w/t MAX – t w = 1 – (r/R) ½.

8. Identify the correct boundary condition for hollow sphere with inside surface insulated
a) At r = r 1, the conduction region is perfectly insulated
b) At r = r 1, the conduction region is partially insulated
c) Heat flow is infinity
d) Heat flow is negative

Answer: a [Reason:] In this range, the conduction region must be perfectly insulated.

9. A hollow sphere (k = 30 W/m K) of inner radius 6 cm and outside radius 8 cm has a heat generation rate of 4000000 W/m3. The inside surface is insulated and heat is removed by convection over the outside surface by a fluid at 100 degree Celsius with surface conductance 300 W/m2 K. Make calculations for the temperature at the outside surfaces of the sphere
a) 105.6 degree Celsius
b) 205.6 degree Celsius
c) 305.6 degree Celsius
d) 405.6 degree Celsius

Answer: c [Reason:] q g 4 π (R 3 – r 3)/3 = h 0 4 π r 2 (t 2 – t a).

10. Consider the above problem, also calculate the temperature at the inside surfaces of the sphere
a) 138.3 degree Celsius
b) 327.8 degree Celsius
c) 254.7 degree Celsius
d) 984.9 degree Celsius

Answer: b [Reason:] t = t 2 + q g (R 2 – r 2)/6 k – q g r 3 (1/r – 1/R)/3 k.

## Set 4

1. Which one is having highest value of overall heat transfer coefficient?
a) Steam condensers
b) Feed water heaters
c) Alcohol condensers
d) Steam

Answer: b [Reason:] Overall heat transfer coefficient for feed water heaters is 8500 W/m2 K while that of steam, alcohol condensers and ammonia condensers are 5000 W/m2 K, 630 W/m2 K and 1400 W/m2 K.

2. What is the value of overall heat transfer coefficient for air to heavy tars and liquid?
a) As low as 45 W/m2 K
b) As low as 40 W/m2 K
c) As low as 35 W/m2 K
d) As low as 30 W/m2 K

Answer: a [Reason:] It is an incompressible fluid which has constant volume independent of pressure.

3. What is the value of overall heat transfer coefficient for air to low viscosity liquid?
a) As high as 900 W/m2 K
b) As high as 800 W/m2 K
c) As high as 700 W/m2 K
d) As high as 600 W/m2 K

Answer: d [Reason:] It is made up of tiny vibrating particles of matter which are held together by intermolecular bonding.

4. Which one is having lowest value of overall heat transfer coefficient?
a) Steam
b) Air condensers
c) Air to heavy tars
d) Ammonia condensers

Answer: c [Reason:] Overall heat transfer coefficient for air to heavy tars is 45 W/m2 K while that of steam, air condensers and ammonia condensers are 340 W/m2 K, 780 W/m2 K and 1400 W/m2 K.

5. What is the value of overall heat transfer coefficient for air condensers?
a) 350-780 W/m2 K
b) 250 -900 W/m2 K
c) 200-350 W/m2 K
d) 200-1950 W/m2 K

Answer: a [Reason:] It consists of an air coil which is used to remove heat from fluids.

6. Which one is having highest value of overall heat transfer coefficient?
a) Steam
b) Alcohol condensers
c) Air condensers
d) Air to various gases

Answer: c [Reason:] Overall heat transfer coefficient for air condensers is 780 W/m2 K while that of steam, alcohol condensers and air to various gases are 340 W/m2 K, 700 W/m2 K and 550 W/m2 K.

7. What is the value of overall heat transfer coefficient ammonia condensers?
a) 800-1400 W/m2 K
b) 200-750 W/m2 K
c) 250-2500 W/m2 K
d) 1500-1750 W/m2 K

Answer: a [Reason:] It is an electrical device that stores a vast amount of energy.

8. Which one is having lowest value of overall heat transfer coefficient?
a) Air condensers
b) Air to low viscosity liquids
c) Steam condensers
d) Feed water heaters

Answer: b [Reason:] Overall heat transfer coefficient for air condensers is 780 W/m2 K while that of steam condensers, air to low viscosity liquids and feed water heaters are 5000 W/m2 K, 600 W/m2 K and 8500 W/m2 K.

9. What is the value of overall heat transfer coefficient for steam condensers?
a) 200-9000 W/m2 K
b) 3000-5500 W/m2 K
c) 2000-9500 W/m2 K
d) 1500-5000 W/m2 K

Answer: d [Reason:] It is a rotating machine similar to a motor used to control power flow in electric power transmission.

10. Which one is having highest value of overall heat transfer coefficient?
a) Feed water heaters
b) Steam condensers
c) Alcohol condensers
d) Ammonia condensers

Answer: a [Reason:] Overall heat transfer coefficient for feed water heaters is 8500 W/m2 K while that of steam condensers, alcohol condensers and ammonia condensers are 5000 W/m2 K, 700 W/m2 K and 1400 W/m2 K.

## Set 5

1. The concept of hydrodynamic boundary layer was first suggested by
a) Isaac Newton
b) Ludwig Prandtl
c) Rodridge
d) Fourier

Answer: b [Reason:] It was suggested by Ludwig Prandtl in 1904. This is the thin layer where velocity changes continuously.

2. The free stream undisturbed flow has a uniform velocity U INFINITY in the
a) X-direction
b) Y-direction
c) Z-direction
d) Any direction

Answer: a [Reason:] It is in the x-direction only. Particles of fluid adhere to the plate surface as they approach it and the fluid is slowed down considerably.

3. The thin layer where velocity changes continuously is called
a) Differential layer
b) Thermal boundary layer
c) Hydrodynamic boundary layer
d) Velocity distribution layer

Answer: c [Reason:] In this layer the flow is rotational and shear stresses are present.

4. The conditions for flow beyond the boundary layer and its outer edge are
a) d u/d y = 0 and u = U 0
b) d u/d y = Infinity and u = U INFINITY
c) d u/d y = 1 and u = U 0
d) d u/d y = 0 and u = U INFINITY

Answer: d [Reason:] All the variation in fluid velocity is concentrated in a comparatively thin layer in immediate vicinity of the plate surface.

5. The pattern of flow in the boundary layer is judged by the
a) Reynolds number
b) Fourier number
c) Peclet number
d) Grashof number

Answer: a [Reason:] Re = U INFINITY x/v.

6. Consider the diagram given below and identify the correct option a) The velocity gradient is zero everywhere
b) The velocity profile changes at every instant of time
c) Boundary layers from the pipe walls meet the pipe anywhere
d) Thickness of the boundary layer is limited to the pipe radius

Answer: d [Reason:] Thickness of the boundary layer is limited to the pipe radius because of the flow being within a confined passage.

7. The transition from laminar to turbulent pattern of flow occurs at values of Reynolds number between
a) 1000-2000
b) 300000-500000
c) 500000-700000
d) 35750-45678

Answer: b [Reason:] It occurs at higher value. The pattern of flow in the boundary layer is judged by the Reynolds number, Re = U INFINITYY x/v.

8. The entrance length required for the flow to become fully-developed turbulent flow is dependent on
(i) Surface finish
(ii) Downstream conditions
(iii) Fluid properties
Identify the correct answer
a) 2 and 3
b) 1 and 3
c) 1, 2 and 3
d) 1 and 2

Answer: c [Reason:] It depend on surface finishing, various upstream and downstream conditions and various fluid properties.

9. What is the value of thickness of the boundary layer at leading edge of the plate?
a) 0.33
b) 1
c) 0.5
d) 0