ASSIGNMENT 1 STEADY STATE HEAT · PDF fileASSIGNMENT – 1 STEADY STATE HEAT CONDUCTION...

HEAT TRANSFER (2151909)

B.E. Semester – V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1

ASSIGNMENT – 1 STEADY STATE HEAT CONDUCTION

Theory

1. Derive general heat conduction equation in Cartesian co-ordinates. Also deduce the

equation for (i) steady state conduction (ii) No heat sources (iii) No heat source and

steady state condition (iv) one dimensional heat conduction equation without heat

generation under steady state.

(May-2011, May-2012, Winter-2012, Winter-2014)

2. Derive equation of heat transfer by conduction through composite wall.

(Winter-2014)

3. Write general heat conduction equation for non-homogeneous material, self-heat

generating and unsteady three-dimensional heat flow in cylindrical co- ordinates.

Name and state the unit of each variable. Step 1. Reduces above equation to one

dimensional Step 2. Reduces step 1 equation for steady and without heat generation

Step 3. Reduces step 2 equation for homogeneous and isotropic material Step 4.

Reduces step 3 equation to r(dt/dr) = constant. (Summer-2013, Winter-2013)

4. Derive equation of heat transfer by conduction through a multi layer cylindrical

wall. (Winter-2014)

5. Derive the one dimensional radial steady state heat conduction through hollow

cylinder without heat generation. Also obtain the expression of logarithmic mean

are for hollow cylinder. (May-2012)

6. Explain the following terms (Dec-2011)

I. Radiation

II. Thermal resistance

III. Thermal diffusivity

IV. Thermal conductivity

7. Derive general heat conduction equation in spherical co-ordinate. (Dec-2011)

8. Explain thermal Contact resistance. How contact pressure effects thermal contact

resistance? (Summer-2015)

9. What do you understand by critical radius of insulation? Draw rough sketch

showing variation in heat transfer with respect to radius of insulation. Derive the

equation for critical radius of insulation for cylinder.

(May-2012, Summer-2013, Summer-2014, Summer-2015)

Examples

1. A furnace wall comprises three layers: 13.5 cm thick inside layer of fire brick, 7.5 cm

thick middle layer of insulating brick and 11.5 cm thick outside layer of red brick.

The furnace operates at and it is anticipated that the outside of this composite

wall can be maintained at by the circulation of air. Assuming close bonding of



layers at their interfaces, find the rate of heat loss from the furnace and the wall

interface temperature. The wall measures and the data on thermal

conductivities are: (D.S. Kumar, Example 3.15)

Fire brick ⁄ Insulating brick ⁄

Red brick ⁄

2. The composite wall of an oven consists of three materials, two of them are of known

thermal conductivity, ⁄ and ⁄ and known thickness

and . the third material B, which is sandwiched between

material A and B is of known thickness, , but of unknown thermal

conductivity .

Under steady state operating conditions, the measurement reveals an outer surface

temperature of material C is and inner surface of A is and oven air

temperature is . The inside convection co-efficient is 25 ⁄ . What is the

value of ? (Mahesh Rathod, Example 3.4)

3. Hot gases at flow past the upper surface of the blade of a gas turbine and the

lower surface is cooled by air bled off the compressor. The convective heat transfer

coefficients at the upper and lower surfaces are estimated to be 2830 and 1415

⁄ respectively. The blade material has a thermal conductivity of

⁄ . If metallurgical considerations limit the blade temperature at

, workout the temperature of the cooling air. Consider the blade as a flat plate

0.115 cm thick and presume that steady state conditions have been reached. (D.S.

Kumar, Example 3.31)

4. The interior of a refrigerator has inside dimensions 60 cm X 45 cm base area and

120 cm high. The composite wall is made of two 3 mm mild steel sheets

( ⁄ ) with 6 cm of glass wool ( ⁄ )

insulation sandwiched between them. The average values of convective heat

transfer coefficients at the interior and exterior wall are 40.8 and 52.3

⁄ respectively. (D.S. Kumar, Example 3.38)

I. Calculate the individual resistance of this composite wall and the resistances

at the surfaces, and the overall conductance.

II. Draw the thermal circuit



III. For the air temperature inside the refrigerator at and outside of ,

determine the rate at which heat must be removed from the refrigerator.

Also, calculate the temperature on the outer surface of the metal sheet.

5. An exterior wall of a house may be approximated by 10 cm layer of common brick

( ⁄ ) followed by 4 cm layer of gypsum plaster

( ⁄ ) What thickness of loosely packed rock wool insulation

( ⁄ ) should be added to reduce the heat loss or gain through the

wall by 75%?(D.S. Kumar, Example 3.12)

6. A wall 30 cm thick of size 5 m X 3 m made of red brick ( ⁄ ). it is

covered on both sides by the layer of plaster 2 cm thick ( ⁄ ). The wall

has a window of size 1 m X 2 m. The window door is made of glass, 12 mm thick

having thermal conductivity ⁄ . Estimate the rate of heat flow through the

wall. Inner and outer surface temperature are and 4 respectively. (Mahesh

Rathod, Example 3.16)

7. A composite wall for thermal insulation has a rectangular section 2 m X 0.5 m and is

made from timber 15 cm thick, cork board 30 cm thick and steel plate 5 cm thick.

The temperature at the outside faces of timber and steel are and

respectively. How the heat transfer rate would be affected if aluminium rods of 4 cm

diameter were inserted through each square metre of the composite wall. Neglect

the effect of bolt heads and all lateral heat transfers.

The thermal conductivities are: timber ⁄ , cork ⁄ , steel

⁄ and aluminium ⁄ . (D.S. Kumar, Example 3.25)

8. A square plate heater (size: 15 cm X 15 cm) is inserted between two slabs. Slab A is 2

cm thick ( ⁄ ) and slab B is 1 cm thick ( ⁄ ). The outside heat

transfer coefficient on both sides of A and B are 200 and 50 ⁄ , respectively.

The temperature of surrounding air is 25 . If the rating of the heater is 1 kW, find:

i. Maximum temperature in the system

ii. Outer surface temperature of two slabs. (Mahesh Rathod, Example 3.12)

9. The hot combustion gases at flow through a hollow cylindrical pipe of 10 cm

inner diameter and 12 cm outer diameter. The pipe is located in a space at and

the thermal conductivity of the pipe material is ⁄ . Neglecting surface heat

transfer coefficients, calculate the heat loss through the pipe per unit length and the



temperature at a point halfway between the inner and outer surface. (D.S. Kumar,

Example 3.47)

10. An insulation steam pipe of 16 cm diameter is covered with 4 cm thick layer of

insulation ( ⁄ ) and carries process steam. Determine the

percentage change in the rate of heat loss if an extra 2 cm thick layer of lagging

( ⁄ ) is provided. Given that surrounding temperature remains

constant and the heat transfer coefficient for both the configurations is

⁄ . (D.S. Kumar, Example 3.51)

11. A wire of radius 3 mm and 1.25 m length is to be maintained at by insulating it

by a material of thermal conductivity ⁄ . The temperature of surrounding

air is 2 with heat transfer coefficient ⁄ . For maximum heat dissipation,

determine:

i. minimum thickness of insulation and the heat loss

ii. Percentage increase in heat loss due to insulation.

(D.S. Kumar, Example 3.99)



ASSIGNMENT – 2 FIN

Theory

1. Derive an expression for heat dissipation in rectangular Fin of uniform cross section

which is insulated at tip. (Dec.-2011, Winter-2012, Winter-2013, Winter-2014)

2. Derive the governing differential equation for temperature distribution of constant

cross-sectional area fin. Hence derive expression for temperature distribution for

long fin stating the assumption made. (Summer 2013, Summer 2015)

3. Explain the terms fin efficiency and fin effectiveness. (Winter-2012)

4. Why fins are used? Define effectiveness and efficiency of fin. For long fin with

insulated tip, show that (Summer 2014)

⁄

5. Define effectiveness of fin? How to increase the effectiveness of fin? What happens if

, and . (May-2011,May-2012)

Examples

1. Estimate the energy input required to solder tighter two very long pieces of bare

copper wire 0.1625 cm in diameter with a solder that melts at 195 . The wires are

positioned vertically in air at 24 and the heat transfer coefficient on the wire

surface is 17 W/m2-deg. For the wire alloy, take the thermal conductivity 335 W/m-

deg. (D.S. Kumar, Example 5.3)

2. An array of 10 fins of anodized aluminium (k = 180 W/m-deg) is used to cool a

transistor operating at a location where the ambient conditions correspond to

temperature 35 and convective coefficient 12 W/m2-deg. Each fin measures 3 mm

wide, 0.4 mm thick and 5 cm length and has its base at 60 . Determine the power

dissipated by the fin array. (D.S. Kumar, Example 5.7)

3. A steel strap is serving as support for the steam pipe. The strap is welded to the pipe

and bolted to the ceiling. The junction between the support strut and the ceiling is

adiabatic, and the outside temperature of the steam pipe is 105 . The strut is 60 cm

high, 12.5 cm wide and 0.3 cm thick. Work out the rate at which heat is lost to the

surrounding air by the support strut. It may be assumed that thermal conductivity

for steel is 45 W/m-deg, the total outside surface coefficient is 17 W/m2-deg, and the

surrounding air is at 32 . (D.S. Kumar, Example 5.10)



4. A very long copper rod 20 mm in diameter extends horizontally from a plane heated

wall maintained at 100 . The surface of the rod is exposed to an air environment at

20 with convective heat transfer coefficient of 8.5 W/m2-deg. Workout the heat

loss if the thermal conductivity of copper is 400 W/m-deg. Further estimate how

long the rod be in order to be considered infinite. (D.S. Kumar, Example 5.18)

5. A horizontal steel shaft, 30 mm diameter and 600 mm long, has its first bearing

located 100 mm from the end connected to the impeller of a centrifugal pump. If the

impeller is immersed in a hot liquid metal at , work out the temperature at the

bearings under the conditions: (a) the shaft is very long (b) the heat flow through

the end of the shaft is negligible and (c) the heat is transferred to the surroundings

from the end.

The temperature and convection coefficient associated with the fluid adjoining the

shaft are and ⁄ . For steel shaft, thermal conductivity is

⁄ . (D.S. Kumar, Example 5.20)

6. A cylinder 5 cm in diameter and 1 m long is provided with 10 longitudinal straight

fins of material having thermal conductivity 120 W/m-deg. The fins are 0.75 mm

thick and protrude 12.5 mm from the cylinder surface. The system is place in an

atmosphere at 40 and the heat transfer coefficient from the cylinder and fins to

the ambient air is 20 W/m2-deg. If the surface temperature of the cylinder is 150 ,

calculate the rate of heat transfer and the temperature at the end of fins. Consider

the fin to be of finite length. (D.S. Kumar, Example 5.23)

7. An aluminium alloy fin (k = 200 W/m K), 3.5 mm thick and 2.5 cm long protrudes

from a wall. The base is at 420 and ambient air temperature is 30 . The heat

transfer coefficient may be taken as 11 W/m2K. Find the heat loss and fin efficiency,

if the heat loss from fin tip is negligible. (Mahesh M. Rathod, Example 5.18)



ASSIGNMENT – 3 TRANSIENT HEAT CONDUCTION

Theory

1. Differentiate between steady state and transient heat conduction. Explain two

examples of heat conduction under unsteady state. (May-2012)

2. What are Fourier and Biot Number? What is the physical significance of these

numbers? (Winter-2012, Winter-2013)

3. Derive the relation for temperature variation with respect to time, instantaneous

heat transfer rate and total heat transfer using lumped parameter analysis.

(Summer-2013)

4. What is lumped system analysis? When is it applicable?

5. Consider a hot baked potato on a plate. The temperature of the potato is observed to

drop by 4 during the first minute. Will the temperature drop during the second

minute be less than, equal to, or more than 4 ? Why?

6. Consider a potato being baked in an oven that is maintained at a constant

temperature. The temperature of the potato is observed to rise by 5 during the

first minute. Will the temperature rise during the second minute be less than, equal

to, or more than 5 ? Why?

Examples

1. A long copper rod of diameter 2.0cm is initially at a uniform temperature of 100 . It

is now exposed to an air stream at 20 with a heat transfer coefficient of 200 W/m2

K. How long would it take for the copper road to cool to an average temperature of

25 ? (Cengel Unsolved Example 4.16)

2. The temperature of a gas stream is to be measured by a thermocouple whose

junction can be approximated as a 1.2mm diameter sphere. The properties of the

junction are k = 35 , ρ = 8500 kg/m3, and cp = 320 , and the heat

transfer coefficient between the junction and the gas is h = 90 . Determine

how long it will take for the thermocouple to read 99 percent of the initial

temperature difference. (Cengel Similar to Example 4.1)

3. A cylindrical stainless steel ( ⁄ ) ingot, 10 cm in diameter and 25 cm

long, passes through a heat treatment furnace which is 5 m in length. The initial

ingot temperature is , the furnace gas is at and the combined radiant and



convective surface coefficient is ⁄ . Determine the maximum speed with

which the ingot moves through the furnace if it must attain temperature.

Take thermal diffusivity ⁄ . (D.S. Kumar, Example 6.4)

4. Glass spheres of 2 mm radius and at are to be cooled by exposing them to an

air stream at . Make calculations for the maximum value of convection

coefficient that is permissible, and the minimum time required for cooling to a

temperature of . Assume the following property values:

⁄ , ⁄ , ⁄ (D.S. Kumar, Example 6.5)

5. A long thin glass walled, 0.3 cm diameter, mercury thermometer is placed in a

stream of air with convection coefficient of 60 ⁄ for measuring transient

temperature of air. Consider cylindrical thermometer bulb consists of mercury only.

For which (Mahesh Rathod, Example 6.5)

⁄ ⁄



ASSIGNMENT – 4 RADIATION

Theory

1. Define: (May 2011, Summer 2013, Summer 2015)

I. Emissivity,

II. Radiosity,

III. Monochromatic emissive

power,

IV. Irradiation,

V. Absorptivity,

VI. Total emissive power,

VII. Solid angle.

2. Enumerate the factors on which the rate of emission of radiation by body depends.

(Dec 2011)

3. What is black body? How does it differ from gray body? Give examples of each. (Dec

2011)

4. Define: absorptivity, reflectivity and transmissivity with respect to radiation heat

transfer. (Dec 2011)

5. State and explain Stefan boltzman law. (Winter 2014)

6. Derive the expression for radiant heat exchange between two finite black surfaces

by radiation. (May 2012)

7. Derive the expression for radiant heat exchange between two non black parallel

surfaces. (Summer 2014)

8. (i) Derive a general relation for the radiation shape factor in case of radiation

between two surfaces. (ii) Explain Wein’s displacement law of radiation. (Winter

2012)

9. (i) Explain emissivity and absorptivity of a surface. Also differentiate between black

body and grey body. (ii) Explain Kirchoff’s law of radiation. (Winter 2012)

10. Define intensity of radiation and prove that the intensity of normal radiation is 1/π

times the total emissive power. Also explain Planck’s law radiation heat transfer.

(Winter 2012, Summer 2014, Winter 2014)

11. Define shape factor. Discuss salient features of shape factor. (Summer 2014,

Winter 2014)

12. Derive expression for Radiation Heat exchange between two concentric infinite long

grey cylinders. (Winter 2013)



Examples

1. Consider 5 m X5 m X 5 m cubical furnace, whose surface closely approximated black

surfaces. The base, top and side surfaces of the furnace are maintained at uniform

temperatures of 800 K, 1500 K and 500 K, respectively. Determine

I. the net rate of radiation heat transfer between the base and the surfaces,

II. the net rate of radiation heat transfer between the base and the top surface, and

III. the net radiation heat transfer from the base surface. (Cengel, Example 13.6)

2. Two very large parallel plates are maintained at uniform temperatures T1 = 800 K and T2

= 500 K and have emissivities and , respectively. Determine the net rate

of radiation heat transfer between two surfaces per unit surface area of the plates.

(Cengel, Example 13.7)

Figure 1 Figure 2

3. A sphere of 50 mm outside diameter and with a surface temperature of 800 K is located at

the geometric centre of another sphere of 300 mm inside diameter and an inner surface

temperature of 300 K. How much of emission from the inner surface of the large sphere is

incident upon the outer surface of the small sphere? Also calculate the net interchange of

heat between the two spheres. Assume black body behavior for both sides of the two

spheres. (D.S. Kumar Example 8.29)

4. For a hemispherical furnace, the flat floor is at 700 K and has an emissivity of 0.5. the

hemispherical roof is at 1000 K and has emissivity of 0.25. Find the net radiative heat

transfer from roof to floor. (R.K. Rajput Example 12.31)

5. A thin aluminum sheet with an emissivity of 0.1 on both sides is placed between two very

large parallel plates that are maintained at uniform temperatures T1 = 800 K and T2 = 500

K and have emissivities 1 = 0.2 and 2 = 0.7, respectively, as shown in Figure 2.

Determine the net rate of radiation heat transfer between the two plates per unit surface

area of the plates and compare the result to that without the shield.

(Cengel, Example 13.11)



ASSIGNMENT – 5 CONVECTION Theory

1. Discuss and define:

a) Natural and Forced Convection.

b) Mean Film Temperature & Bulk Mean Temperature.

2. Define and discuss the following dimensionless numbers:

a) Reynolds Number

b) Prandtl Number

c) Grashoff Number

d) Nusselt Number.

3. Derive the generalized co-relation for natural convection by using Buckingham’s π

theorem method.

4. Derive the generalized co-relation for forced convection by using Buckingham’s π

theorem method.

5. Derive the momentum equation for hydrodynamic boundary layer over a flat plate.

6. Define and discuss the hydrodynamic and thermal boundary layers over a flat plate.

Show the thickness of these layers for different Prandtl numbers.

Examples

1. A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and

1.5 wide has been designed on free convection heating of liquid bismuth.

Metallurgical considerations limit the maximum surface temperature of the plate to

975°C and the lowest allowable temperature of bismuth is 325°C. Estimate the

maximum possible heat dissipation from both sides of each plate.

The appropriate correlation for the convection coefficient is Nu = 0.13 (Gr Pr)1/3.

Where, the different parameters are evaluated as the mean film temperature.

[Ans: 153 MW] [D.S. Kumar;11.6]

2. Calculate the rate of heat loss from a human body which may be considered as a

vertical cylinder 300mm dia. and 1750 mm high. while standing in a 30 Km/hr wind

at 10˚C. The surface temperature of the human body is 30°C. The approximate co-

relation for laminar flow is ( ) ( ) and the characteristic length

is the diameter of human body. [Ans: 686.39 W]

3. A sheet metal air duct carries air-conditioned air at an average temperature of 10°C.

The duct size is 320mm x 200mm and length of the duct exposed to the surrounding

air at 30°C is 15m long. Find the heat gain by the air in the duct. Assume 200mm side

is vertical and top surface of the duct is insulated. Use the following correlation:



Nu = 0.6 (Gr Pr)0.25 for vertical surface, and Nu = 0.27 (Gr Pr)0.25 for horizontal

surface. [Ans: 7772.9W] [R. K. Rajput; 8.5]

4. A gas pipe is kept in an atmosphere of 20°C. The radius of pipe is 3.75cm and is

lagged with insulation thickness of 2.5cm. The emissivity of the surface is 0.9.The

length of pipe is 6 m. Surface temperature ts=80°C.Calculate (i) The total heat loss

from pipe (ii) The overall heat transfer coefficient (iii) The heat transfer co efficient

due to only radiation.

For convection use co-relation, Nu =0.53(Gr.Pr)1/4.

[Ans: 1863.24W; 13.1797 W/m2-K; 6.9378 W/m2-K] [GTU – DEC 2013]

5. A spherical heater of 20cm diameter and at 60°C is immersed in a tank of water at

20°C. Determine the value of convective heat transfer coefficient. For a sphere, the

general correlation is Nu = 2 + 0.43 (Gr Pr)0.25.

[Ans: 772.086 W/m2-deg] [D.S. Kumar; 11.4]

6. Air at a temperature of 25°C is blown across a flat plate at a mean velocity of 7.5

m/s. If the plate surface temperature is 575°C, make calculations for the heat

transferred per meter width from both sides of the plate over distance of 20 cm from

the leading edge.

For heat transfer from a plate with large temperature between the plate and the

fluid, the local Nusselt number is

( ) ( )

( )

Where all the properties are at the mean film temperature, Ts and Ta are plate

surface and stream temperature in K respectively. The characteristic linear

dimension is the distance from the leading edge.

The thermo-physical properties of air at mean film temperature are:

ρ = 0.615 kg/m3, K = 0.1659 KJ/m-hr-K, Cp = 1.0465 KJ/kg K, µ = 29.724 x 10-6 kg/m-

sec.

[Ans: 5878.18 W]

7. Air at 30°C and at atmospheric pressure flows over a flat plate at a speed of 1.9

m/sec. If the plate is maintained at 90°C, calculate the heat transfer per unit width of

the plate; assuming the length of the plate along the flow of air is 2 meters. Where

local Nusselt number is given by, ( ) ⁄ ( )

⁄

[Ans: 917.16 W]

8. Air at 30°C and at atmospheric pressure is flowing over a flat plate with velocity 4

m/sec. If the plate is 2m long and the wall temperature is 70°C. Calculate the

following at a location 2m from leading edge.

a. Hydrodynamic boundary layer thickness.



b. Local heat transfer co-efficient.

[Ans: 13.90mm; 2.9169W/m2K]

9. Air at 27°C and 1 atm flows over a flat plate at a velocity of 3 m/s. Calculate the

boundary layer thickness at distances of 25 and 45 cm from the leading edge of the

plate. Calculate the mass flow which enters the boundary layer between x = 25cm

and x = 45cm. The viscosity of air at 27°C is 1.85E-05 kg/m-s. Assume parabolic

velocity distribution and unit depth in z-direction.

[Ans: 5.31mm; 7.125; 0.004 kg/s] [4.17; P. K. NAG]

Use following properties of fluid at required temperature,

Example

No. Fluid

Temp

°C

ρ

kg/m3

Cp

KJ/kg-deg

ν x 106

m2/sec

K

W/m-deg Pr

µ

kg/m-hr

1 Bismuth 650 104 0.1507 - 13.02 - 3.12

2 Air 20 - - 15.06 0.0259 0.703 -

3 Air 20 1.204 0.10 15.1 0.256 0.71 -

4 Air 50 1.092 1.007 - 0.02781 - 0.07045

5 Water 40 992.2 - 0.659 0.633 4.34 -

7 Air 60 - - 18.97 0.02894 0.696 -

8 Air 50 1.093 1.005 17.95 0.02964 0.698 -



ASSIGNMENT – 6 BOILING & CONDENSATION

1. Discuss various regimes of pool boiling with neat sketch.

2. Distinguish

a. Subcooled and Saturated boiling

b. Pool boiling and Forced convection boiling

c. Nucleate and Film boiling.

3. What is condensation? When does it occur? Differentiate between film wise and

drop wise condensation. Which type has better heat transfer coefficient? In

condenser design which of condensation is usually selected and why?



ASSIGNMENT – 7 HEAT EXCHANGERS

Theory

1. Discuss various types of heat exchangers. Also discuss the importance of heat

exchangers for industrial use.

2. What is mean by fouling factor? How does it affect the performance of a heat

exchanger?

3. Explain difference between regenerator and recuperator.

4. Define: Overall heat transfer co-efficient, Heat capacity ratio, Number of transfer

units.

5. Is it better to arrange for the flow in a heat exchanger to be parallel or counter flow?

Explain with appropriate reasons. Also draw rough sketch of temperature

distribution curve for condenser and evaporator type heat exchangers.

6. Derive equation of logarithmic mean temperature difference for Parallel flow heat

exchanger.

7. Derive equation of logarithmic mean temperature difference for Counter flow heat

exchanger.

8. Define effectiveness of heat exchanger. Derive equation for effectiveness of a Parallel

flow heat exchanger.

9. Define effectiveness of heat exchanger. Derive the relationship between the

effectiveness and number of transfer units for a counter flow heat exchangers.

Examples

1. An existing heat exchanger of 20 m2 surface area is to be used to condense low

pressure steam. The cooling medium will be feed water available at 40°C; its flow

rate being 0.9 kg/s. From previous experience, the overall heat transfer co-efficient

is estimated at 120 w/m2K. Calculate the quantity of steam condensed and the exit

temperature of feed water. At the condensing pressure steam has saturation

temperature ts = 100°C and latent heat of vaporization hfg = 2257 kJ/kg. Presume

that the steam is initially just saturated and that the condensate leaves the

exchanger without sub-cooling, i.e., only the latent heat of condensing steam is

transferred to water.



How would the performance of the exchanger be affected if the overall heat

transfer co-efficient can be doubled by a modification of feed water flow through the

exchanger?

[Ans: 68.29°C, 0.0471 kg/s, 53.07%] [14.16, D. S. Kumar]

2. Dry saturated steam at 10 bar enters a counter-flow heat exchanger at the rate of 15

kg/s and leaves at 300°C. The entry of gas at 600°C is with mass flow rate of 25 kg/s.

If the condenser tubes are 30 mm diameter and 3 m long, make calculations for the

heating surface area and the number of tubes required. Neglect the resistance

offered by the metallic tubes.

Take the following properties for steam and gas:

For steam: tsat = 180°C (at 10 bar); cps = 2.7 kJ/kg-K; hs = 600 W/m2-deg

For gas: cpg = 1 kJ/kg-K; hg = 250 W/m2-deg.

[Ans: 105.5 m2, 374] [14.20, D. S. Kumar]

3. A two pass surface condenser is required to handle the exhaust from a turbine

developing 15 MW with specific steam consumption of 5 kg/kWh. The quality of

exhaust steam is 0.9, the condenser vacuum is 66 cm of mercury while the bar meter

reads 76 cm of mercury. The condenser tubes are 28 mm inside diameter, 4 mm

thick and water flows through tubes with a speed of 3 m/s and inlet temperature

20°C. All the steam is condensed, the condensate is saturated water and temperature

of cooling water at exit is 5°C less than the condensate temperature.

Assuming that overall co-efficient of heat transmission is 4 kW/m2-deg,

determine:

a. Mass of cooling water circulated.

b. Surface area required

c. Length and number of tubes in each pass.

[Ans: 446.13 kg/s, 851.84 m2, 242 tubes per pass, 17.51 m] [14.23, D. S. Kumar]

4. A single pass shell and tube heat exchanger, consisting of a bundle of 100 tubes

(inner diameter 25 mm and thickness 2 mm) is used for heating 8 kg/s of water

from 25°C to 75°C with the help of steam condensing at atmospheric pressure on the

shell side with condensing heat transfer co-efficient 5000 W/m2-deg. Make

calculations for the overall heat transfer co-efficient based on the inner area and

length of the tube bundle.



Take fouling factor on the water side to be 0.0002 m2-deg/W per tube and

neglect effect of fouling on the shell side and thermal resistance of the tube wall.

The thermo-physical properties of water at the mean bulk temperature of 50°C are:

ρ = 998 kg/m3; cp = 4175 J/kg-deg; k = 0.65 W/m-deg; µ = 55 X 10-5 kg/m-s

[Ans: 847.46 W/m2-deg, 5.52 m] [14.27, D. S. Kumar]

5. A steam power plant of large capacity incorporates a shell and tube type heat

exchanger having 30000 thin wall tubes of 25 mm diameter. The steam condenses

on the outside surface of these tubes with convection co-efficient 10 kW/m2-deg.

Water serves as the coolant entering the tubes at 20°C at mass flow rate of 30 X 103

kg/s. If the condenser (heat exchanger) arrangement involves one shell pass and

two passes and the heat transfer rate is 2000 MW, determine:

a. Temperature of cooling water at exit from the condenser;

b. Overall heat transfer co-efficient for heat exchanger;

c. Heat transfer area and length of tube per pass.

Assume the following data:

cp = 4186 J/kg-K; k = 0.65 W/m-deg; µ = 860 X 10-6 Ns/m2, Pr = 5.82

[Ans: 35.93°C, 4295.5 W/m2-deg, 22129 m2, 4.698 m] [14.38, D. S. Kumar]

6. Hot water having specific heat 4200 J/kg-K flows through a heat exchanger at the

rate of 4 kg/min with an inlet temperature of 100°C. A cold fluid having a specific

heat 2400 J/kg-K flows in at a rate of 8 kg/min and with inlet temperature 20°C.

Make calculations for the maximum possible effectiveness if the fluid flow conforms

to (a) parallel flow arrangement (b) counter flow arrangement.

[Ans: 0.533, 1] [14.40, D. S. Kumar]

7. Oil (cp = 3.6 kJ/kg-°C) at 100°C flows at the rate of 30000 kg/h and enters into a

concurrent heat exchanger. Cooling water (cp = 4.2 kJ/kg-°C) enters the heat

exchanger at 10°C at the rate of 50000 kg/h. The heat transfer area is 10 m2 and U =

1000 W/m2-°C. Calculate the following:

a. The outlet temperatures of oil and water;

b. The maximum possible outlet temperature of water.

[Ans: 71.2°C, 24.8°C, 40.5°C] [10.37, R. K. Rajput]

ASSIGNMENT 1 STEADY STATE HEAT · PDF fileASSIGNMENT – 1 STEADY STATE HEAT CONDUCTION...

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