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# Multiple choice question for engineering

## Set 1

1. Assumptions made for calculation of logarithmic mean temperature difference are
(i) Constant overall heat transfer coefficient
(ii) The kinetic and potential energy changes are negligible
(iii) There is no conduction of heat along the tubes of heat exchanger
Identify the correct statements
a) 1, 2 and 3
b) 1 and 3
c) 1 and 2
d) 2 and 3

Answer: a [Reason:] These assumptions are made for simplicity. During heat exchange between two fluids, the temperature of the fluids change in the direction of flow and consequently there occurs a change in the thermal head causing the flow of heat.

2. A cold fluid (specific heat 2.95 k J/kg K) at 10 kg/min is to be heated from 25 degree Celsius to 55 degree Celsius in a heat exchanger. The task is accomplished by extracting heat from hot water (specific heat 4.186 k J /kg K) available at mass flow rate 5 kg/min and inlet temperature 85 degree Celsius. Identify the type of arrangement of the heat exchanger
a) Concentric tubes
b) Parallel flow
c) Counter flow
d) Shell and tubes

Answer: c [Reason:] m h c h (t h 1 – t h 2) = m c c c (t c 2 – t c 1).

3. In a food processing plant, a brine solution is heated from – 12 degree Celsius to – 65 degree Celsius in a double pipe parallel flow heat exchanger by water entering at 35 degree Celsius and leaving at 20.5 degree Celsius. Let the rate of flow is 9 kg/min. Estimate the area of heat exchanger for an overall heat transfer coefficient of 860 W/m2 K. For water c P = 4.186 * 10 3 J/kg K
a) 1. 293 m2
b) 0.293 m2
c) 7. 293 m2
d) 8. 293 m2

Answer: b [Reason:] Q = m c P d t = 9104.5 J/s. A = Q/ U α m.

4. Exhaust gases (c P = 1.12 k J/kg K) flowing through a tubular heat exchanger at the rate of 1200 kg/hr are cooled from 400 degree Celsius to 120 degree Celsius. This cooling is affected by water (c P = 4.18 k J/kg K) that enters the system at 10 degree Celsius at the rate of 1500 kg/hr. If the overall heat transfer coefficient is 500 k J/m2 hr degree, what heat exchanger area is required to handle the load for parallel flow arrangement?
a) 7.547 m2
b) 6.547 m2
c) 5.547 m2
d) 4.547 m2

Answer: d [Reason:] m h c h (t h 1 – t h 2) = m c c c (t c 2 – t c 1).

5. A steam condenser is transferring 250 k W of thermal energy at a condensing temperature of 65 degree Celsius. The cooling water enters the condenser at 20 degree Celsius with a flow rate of 7500 kg/hr. Calculate the log mean temperature difference
a) 28.25 degree Celsius
b) 29.25 degree Celsius
c) 30.25 degree Celsius
d) 31.25 degree Celsius

Answer: a [Reason:] Q = m c c c (t c 2 – t c 1) and log mean temperature difference = α 1 – α 2 / log (α 12).

6. Consider the above problem, find what error would be introduced if the arithmetic mean temperature difference is used rather than the log-mean temperature difference? Take overall heat transfer coefficient for the condenser surface as 1250 W/m2 K
a) 7.61%
b) 7.71%
c) 7.81%
d) 7.91%

Answer: d [Reason:] α = α 1 + α 2/2. Error = 7.08 – 6.52/7.08 = 7.91%.

7. For what value of end temperature difference ratio, is the arithmetic mean temperature difference 5% higher than the log-mean temperature difference?
a) 2.4
b) 2.3
c) 2.2
d) 2.1

Answer: c [Reason:] α 1/ α 2 = 2.2.

8. A company is heating a gas by passing it through a pipe with steam condensing on the outside. What percentage change in length would be needed if it is proposed to triple the heating capacity?
a) 200%
b) 400%
c) 600%
d) 800%

Answer: a [Reason:] Present capacity, Q 1 = U 1 A 1 α 1 and new capacity, Q 2 = U 2 A2 α 2. According to the given condition, U 2 A 2 α 2 = 3 U 1 A 1 α 1.

9. A steam condenser is transferring 250 k W of thermal energy at a condensing temperature of 65 degree Celsius. The cooling water enters the condenser at 20 degree Celsius with a flow rate of 7500 kg/hr. If overall heat transfer coefficient for the condenser surface is 1250 W/m2 K, what surface area is required to handle this load?
a) 4.08 m2
b) 5.08 m2
c) 6.08 m2
d) 7.08 m2

Answer: d [Reason:] Q = U A α m. So, A = 7.08 m2.

10. Exhaust gases (c P = 1.12 k J/kg K) flowing through a tubular heat exchanger at the rate of 1200 kg/hr are cooled from 400 degree Celsius to 120 degree Celsius. This cooling is affected by water (c P = 4.18 k J/kg K) that enters the system at 10 degree Celsius at the rate of 1500 kg/hr. If the overall heat transfer coefficient is 500 k J/m2 hr degree, what heat exchanger area is required to handle the load for counter flow arrangement?
a) 2.758 m2
b) 3.758 m2
c) 4.758 m2
d) 5.758 m2

Answer: b [Reason:] m h c h (t h 1 – t h 2) = m c c c (t c 2 – t c 1).

## Set 2

1. Which is a full size structure employed in the actual engineering design?
a) Proton
b) Prototype
c) Electron
d) Neutron

Answer: b [Reason:] The prototype operates under the actual working conditions.

2. Which term refers to the theory and art of predicting prototype conditions from model observations?
a) Nusselt number
b) Dimensional homogeneity
c) Thermal boundary layer
d) Similitude

Answer: d [Reason:] It prescribes the relationship between a full scale flow and a flow involving smaller but geometrically similar boundaries.

3. The results obtained from experiments on models can be applied to prototype only if a complete similarity exists between the model and prototype and for that the two systems may be
(i) Geometrically similar
(ii) Kinematically similar
(iii) Dynamically similar
Identify the correct statements
a) 1 and 2
b) 2 and 3
c) 1, 2 and 3
d) 1 and 3

Answer: c [Reason:] It should be geometrically, cinematically and dynamically similar.

4. Geometrically similarity prescribes that the ratio of the corresponding linear dimensions of the two systems are
a) Unity
b) Same
c) Never same
d) May be twice

Answer: b [Reason:] It refers to the similarity of shape and form.

5. Thermal similarity refers to the comparison of two systems made on the basis of their
a) Temperature
b) Specific heat
c) Heat flux
d) Length

Answer: d [Reason:] A similarity in thermal quantities is achieved when Prandtl number is same for both the fields.

6. The comparison of two systems made on the basic of their temperature, specific heat and heat flus is known as
a) Dynamic similarity
b) Kinematic similarity
c) Thermal similarity
d) Geometrical similarity

Answer: c [Reason:] It is known as thermal similarity.

7. The similarity of masses and forces of the corresponding particles of flow is known as
a) Kinematic similarity
b) Dynamic similarity
c) Geometrical similarity
d) Thermal similarity

Answer: b [Reason:] Systems are dynamically similar if the corresponding particles experience similar force.

8. The similarity of motion is known as
a) Thermal similarity
b) Dynamic similarity
c) Geometrical similarity
d) Kinematic similarity

Answer: d [Reason:] Both the systems undergo similar rates of change of motion.

9. The similarity of shape and form is known as
a) Geometrical similarity
b) Thermal similarity
c) Geometrical similarity
d) Kinematic similarity

Answer: a [Reason:] They may differ in size but are identical in shape.

10. A similarity in thermal quantities is achieved when
a) Nusselt number is same for both the fields
b) Nusselt number is different for both the fields
c) Prandtl number is same for both the fields
d) Prandtl number is different for both the fields

Answer: c [Reason:] A similarity in thermal quantities is achieved when Prandtl number is same for both the fields.

## Set 3

1. The literature of heat transfer generally recognizes distinct modes of heat transfer. How many modes are there?
a) One
b) Two
c) Three
d) Four

Answer: c [Reason:] There are three modes of heat transfer i.e. radiation, convection and conduction.

2. Consider system A at uniform temperature t and system B at another uniform temperature T (t > T). Let the two systems be brought into contact and be thermally insulated from their surroundings but not from each other. Energy will flow from system A to system B because of

a) Temperature difference
b) Energy difference
c) Mass difference
d) Volumetric difference

Answer: a [Reason:] Greater the temperature imbalance the higher would be the rate of energy transfer.

3. An oil cooler in a high performance engine has an outside surface area 0.12 m2 and a surface temperature of 65 degree Celsius. At any intermediate time air moves over the surface of the cooler at a temperature of 30 degree Celsius and gives rise to a surface coefficient equal to 45.4 W/ m 2 K. Find out the heat transfer rate?
a) 238.43 W
b) 190.68 W
c) 543.67 W
d) 675.98 W

Answer: b [Reason:] Q = (T2 – T1) A h = 0.12 (65-30) 45.4 = 190.68 W.

4. Unit of rate of heat transfer is
a) Joule
b) Newton
c) Pascal
d) Watt

Answer: d [Reason:] Unit of heat transfer is Joule but rate of heat transfer is joule per second i.e. watt.

5. Convective heat transfer coefficient doesn’t depend on
a) Surface area
b) Space
c) Time
d) Orientation of solid surface

Answer: a [Reason:] It is denoted by h and is dependent on space, time, geometry, orientation of solid surface.

6. The rate equation used to describe the mechanism of convection is called Newton’s law of cooling. So rate of heat flow by convection doesn’t depend on
a) Convective heat transfer coefficient
b) Surface area through which heat flows
c) Time
d) Temperature potential difference

Answer: c [Reason:] It is directly proportional to all of above except time.

7. How many types of convection process are there?
a) One
b) Three
c) Four
d) Two

Answer: b [Reason:] Forced, natural and mixed convection.

8. Thermal conductivity is maximum for which substance
a) Silver
b) Ice
c) Aluminum
d) Diamond

Answer: d [Reason:] Thermal conductivity of diamond is 2300 W/m K.

9. A radiator in a domestic heating system operates at a surface temperature of 60 degree Celsius. Calculate the heat flux at the surface of the radiator if it behaves as a black body
a) 697.2 W/m2
b) 786.9 W/m2
c) 324.7 W/m2
d) 592.1 W/m2

Answer: a [Reason:] As, q = Q/A = 5.67 * 10-8 (273+60)4 = 697.2.

10. Which of the following is an example of forced convection?
a) Chilling effect of cold wind on a warm body
b) Flow of water in condenser tubes
c) Cooling of billets in the atmosphere
d) Heat exchange on cold and warm pipes

Answer: b [Reason:] In forced convection the flow of fluid is caused by a pump, fan or by atmospheric winds.

## Set 4

1. Newton-Rikhman law is given by
a) Q = h A (t s – t f)
b) Q = 2 h A (t s – t f)
c) Q = 3 h A (t s – t f)
d) Q = 4 h A (t s – t f)

Answer: a [Reason:] Regardless of the particular nature, the appropriate rate equation for the convective heat transfer is prescribed by Newton’s law of cooling.

2. The value of film coefficient is dependent upon
(i) Boundary layer configuration
(ii) Geometry and orientation of the surface
(iii) Surface conditions
a) 1 and 2
b) 2 and 3
c) 1 and 2
d) 1, 2 and 3

Answer: d [Reason:] It depends upon surface conditions i.e. roughness and cleanliness, geometry and orientation of the surface i.e. plate, tube and cylinder placed vertically or horizontally.

3. The convection coefficients for boiling and condensation lie in the range
a) 5000-12500 W/m 2 K
b) 2500-100000 W/m 2 K
c) 2500-5000 W/m 2 K
d) 2500-12500 W/m 2 K

Answer: b [Reason:] Convection mechanisms involving phase changes lead to important field of boiling and condensatio.

4. Forced air flows over a convection heat exchanger in a room heater, resulting in a convective heat transfer coefficient 1.136 k W/m2 K. The surface temperature of heat exchanger may be considered constant at 65 degree Celsius, and the air is at 20 degree Celsius. Determine the heat exchanger surface area required for 8.8 k W of heating
a) 0.272 m2
b) 0.472 m2
c) 0.172 m2
d) 0.672 m2

Answer: c [Reason:] Q = h A (t s – t f). So. A = 0.172 m2.

5. A region of fluid motion near a plate in which temperature gradient exist is
a) Thermal boundary layer
b) Diathermia boundary layer
c) Turbulent flow
d) Laminar flow

Answer: a [Reason:] The fluid velocity decreases as it approaches the solid surface reaching to zero in the fluid layer immediately next to the surface. The thin layer of stagnated fluid is called thermal boundary layer.

6. Thermo-physical properties of the fluid are represented by
(i) Density
(ii) Viscosity
(iii) Specific heat
(iv) Thermal conductivity
Identify the correct option
a) 1 and 2
b) 1, 2, 3 and 4
c) 2, 3 and 4
d) 1, 2 and 3

Answer: b [Reason:] The value of film coefficient is dependent upon thermos-physical properties of he fluid i.e. density, viscosity, specific heat, coefficient of expansion and thermal conductivity.

7. A motor cycle cylinder consists of ten fins, each 150 mm outside diameter and 75 mm inside diameter. The average fin temperature is 500 degree Celsius and the surrounding air is at 20 degree Celsius temperature. Make calculations for the rate of heat dissipation from the cylinder fins by convection when motor cycle is stationary and convective coefficient is 6 W/m2 K
a) 432.2 W
b) 532.2 W
c) 632.2 W
d) 763.2 W

Explanation: A = 0.265 m2 and Q = (6) (0.265) (500 – 20) = 763.2 W.

8. Consider the above problem, make calculations for the rate of heat dissipation from the cylinder fins by convection when motor cycle is moving at 60 km/hr and convective coefficient is 75 W/m2 K
a) 9640 W
b) 9540 W
c) 9440 W
d) 9340 W

Answer: b [Reason:] A = 0.265 m2 and Q = (75) (0.265) (500 – 20) = 9540 W.

9. The temperature profile at a particular location on a surface is prescribed by the identity
(t s – t) / (t s – t infinity) = (1/2) (y/0.0075) 3 + (3/2) (y/0.0075)
If thermal conductivity of air is stated to be 0.03 W/m K, determine the value of convective heat transfer coefficient
a) 4 W/m2 K
b) 5 W/m2 K
c) 6 W/m2 K
d) 7 W/m2 K

Answer: c [Reason:] h = – k/ (t s – t infinity) [d t/d y] y = 0.

10. Air at 20 degree Celsius flows over a flat surface maintained at 80 degree Celsius. The local heat flow at a point was measured as 1250 W/m2 .Take thermal conductivity of air as 0.028 W/m K, calculate the temperature at a distance 0.5 mm from the surface
a) 57.682 degree celsius
b) 67.682 degree celsius
c) 77.682 degree celsius
d) 87.682 degree celsius

Answer: a [Reason:] Temperature at 0.5 mm from the surface is 80 + (d t/d y) y = 0 (0.0005) = 57.682 degree celsius.

## Set 5

1. Which quantity signifies the ratio of temperature gradient at the surface to a reference temperature gradient?
a) Reynolds number
b) Nusselt number
c) Fourier number
d) Stanton number

Explanation: It is given by h l/k.

2. The determination of value of Nusselt number or the convective film coefficient forms a basis for the computation of heat transfer by convection. Towards that end, following approaches have been suggested
(i) Non-dimensional analysis and experimental correlations
(ii) Hydrodynamic concept of velocity boundary layer
(iii) Reynolds similarity between the mechanism of fluid friction in the boundary layer and the transfer of heat by convection
Identify the correct one
a) 1, 2 and 3
b) 1 and 2
c) 2 and 3
d) 1 and 3

Answer: c [Reason:] It should be dimensional analysis and experimental correlations.

3. Nusselt number is given by
a) h l/k
b) 2 h l/k
c) 3 h l/k
d) 4 h l/k

Answer: a [Reason:] The length parameter l specifies the geometry of solid body.

4. The temperature profile at a particular location in a thermal boundary layer is prescribed by n expression of the form
t (y) = A- B y + C y 2
Where, A, B and Care constants. What is the value of heat transfer coefficient?
a) B k/ (t s – t infinity)
b) 2 B k/ (t s – t infinity)
c) 3 B k/ (t s – t infinity)
d) 4 B k/ (t s – t infinity)

Answer: a [Reason:] h = – k/ (t s – t infinity) [d t/d y] y = 0 and (d t/d y) y = 0 = – B.

5. The temperature profile at a particular location on a surface is prescribed by the identity
(t s – t) / (t s – t infinity) = sin (π y/0.015)
If thermal conductivity of air is stated to be 0.03 W/m K, determine the value of convective heat transfer coefficient
a) 6.48 W/m 2 K
b) 6.38 W/m 2 K
c) 6.28 W/m 2 K
d) 6.18 W/m 2 K

Answer: c [Reason:] h = – k/ (t s – t infinity) [d t/d y] y = 0. Therefore h = – k/ (t s – t infinity) [π (t s – t infinity)/0.015].

6. Air at 20 degree Celsius flows over a flat plate maintained at 75 degree Celsius. Measurements shows that temperature at a distance of 0.5 mm from the surface of plate is 50 degree Celsius. Presuming thermal conductivity of air is 0.0266 W/m K, estimate the value of local heat transfer coefficient
a) 23.18 W/m 2 K
b) 24.18 W/m 2 K
c) 25.18 W/m 2 K
d) 26.18 W/m 2 K

Explanation: h = – k/ (t s – t infinity) [d t/d y] y = 0 and d t/d y = – 50 * 10 3 degree Celsius/m.

7. Air at 20 degree Celsius flows over a flat surface maintained at 80 degree Celsius. Estimate the value of local heat transfer coefficient if the local heat flow at a point was measured as 1250 W/m2. Take thermal conductivity of air as 0.028 W/m K
a) 23.83 W/m 2 K
b) 22.83 W/m 2 K
c) 21.83 W/m 2 K
d) 20.83 W/m 2 K

Answer: d [Reason:] Q = h A (t s – t infinity).

8. Consider the above problem, calculate the temperature gradient at the surface
a) – 44636 degree Celsius/m
b) – 34636 degree Celsius/m
c) – 24636 degree Celsius/m
d) – 14636 degree Celsius/m

Answer: a [Reason:] (d t/d y) y = 0 = – h (t s – t infinity)/k.

9. At the interface of solid body, heat flows by conduction and is given by
a) A (t s – t infinity)
b) h A (t s – t infinity)
c) h (t s – t infinity)
d) h A