TOPIC 2 [A] STEADY STATE HEAT CONDUCTION · HEAT TRANSFER (2151909) B.E. Semester – V Department...

HEAT TRANSFER (2151909)

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

TOPIC 2

[A] STEADY STATE HEAT CONDUCTION

CLASS TUTORIAL

1. The walls of a refrigerated truck consist of 1.2 mm thick steel sheet (k=18 W/m-K) at

the outer surface, 22 mm thick cork (k=0.04 W/m-K) on the inner surface. Consider

Heat transfer coefficient of 5 W/m2-K (between inside air and inside surface) and

Heat transfer coefficient of 30 W/m2-K (between outside air and outside surface).

The temperatures at the inside and outside air are 0℃ & 35℃respectively. Calculate

I. heat transfer rate

II. steel-cork interface temp.

2. A storage chamber of interior dimensions 10 𝑚𝑋 8 𝑚𝑋 2.5 𝑚 high has its inside

maintained at a temperature of −20℃ whilst the outside is at 25℃. The walls and

ceiling of the chamber have three layers made of

60 mm thick board (𝑘 = 0.2 𝑊 𝑚 − 𝑑𝑒𝑔⁄ ) on the inside

90 mm thick insulation (𝑘 = 0.04 𝑊 𝑚 − 𝑑𝑒𝑔⁄ ) at the mid

240 mm thick concrete (𝑘 = 1.8 𝑊 𝑚 − 𝑑𝑒𝑔⁄ ) on the outside

Neglecting flow of heat through the floor, determine the rate at which heat can flow

towards inside of the chamber. (D.S. Kumar, Example 3.13)

3. A steam pipe of 5 cm inside diameter and 6.5 cm outside diameter is insulated with

a 2.75 cm radial thickness of high temperature insulation (k = 1.1 W/mK). The surface

heat transfer coefficient for inside and outside surfaces are 4650 W/m2K and 11.5

W/m2K respectively. The thermal conductivity of the pipe material is 45 W/m K. If

the steam temperature is 200°C and ambient air temperature 25°C, determine

I. Heat loss per meter length of pipe

II. Temperature at the interface

III. Overall heat transfer coefficient

4. An 8 mm thick metal plate, having thermal conductivity 98.6 W m − K⁄ is exposed to

vapor at 100℃ on one side and cooling water at 30℃ on another side. The heat

transfer coefficients are 14200 W m2K⁄ on vapor side and 2325 W m2K⁄ on water

side. Determine the rate of heat transfer and drop in temperature on each side of the

plate. Assume area of the plate as unity.(Summer 2014)(Similar to D.S. Kumar,

Example 3.40)



5. A steel tube of 5 cm inner diameter and 8 cm outer diameter(𝑘 = 16 𝑊 𝑚𝐾⁄ ) , is

covered with an insulation of 3 cm thickness(𝑘 = 0.3 𝑊 𝑚𝐾⁄ ). A hot gas at350℃, ℎ =

400 𝑊 𝑚2𝐾⁄ flows. Calculate the heat loss from the tube for 20 meter length. Also

calculate the temperature at the interface of insulation and steel. Outside air

temperature is at30℃,ℎ = 60 𝑊 𝑚2𝐾⁄ . (May-2012) (Similar to Mahesh Rathod,

Example 3.29)

6. A refrigeration suction line having outer diameter 30 mm is required to be thermally

insulated. The outside air convective heat transfer coefficient is 12 𝑊 𝑚2𝐾⁄ . The

thermal conductivity of the insulating material is0.3 𝑊 𝑚𝐾⁄ . Determine:

I. Whether the insulation will be effective

II. Estimate the maximum value of thermal conductivity of insulating material to

reduce heat transfer

III. The thickness of cork insulation to reduce the heat transfer to 20% (k=0.04

W/m oC)(Summer 2013)

ASSIGNMENT

Theory

1. Derive an expression for three dimensional time dependent heat conduction with

internal heat generation and constant thermal conductivity in cartesian

coordinate system. Reduce it as

i. Poisson equation

ii. Fourier equation

iii. Laplace equation

(May-11, May-12, Winter-12, Winter-14, DEC-15, May-16)

2. Write the general heat conduction equation in cylindrical and reduce that

equation for steady state heat conduction in radial direction and solve it to obtain

temperature profile in radial direction through hollow cylinder.

(Summer-13, Winter-13, MAY-17, NOV-17, MAY-18)

3. Explain the following terms

I. Radiation

II. Thermal resistance

III. Thermal diffusivity

IV. Thermal conductivity

(Dec-11, MAY-17, NOV-17)



4. 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-12, Summer-13, Summer-14, Summer-15, MAY-16, MAY-17, MAY-18)

Examples

1. A furnace wall is made up of two layers of thickness 250 mm, 100 mm with

thermal conductivity of 1.65 and 9.2 W/m oC respectively. The inside is exposed

to gases at 1250oC with a convection coefficient of 25 W/m2 oC and the inside

surface is at 1100 oC, the outside surface is exposed to air at 25 oC with convection

coefficient of 12 W/m2 oC. The overall heat transfer coefficient. (MAY-18)

2. A steam pipe is covered with two layered of insulation, first layer being 3 cm thick

and second 5 cm. The pipe is made of steel (k = 58 W/mK) having ID of 160 mm

and OD of 170 mm. The inside and outside film coefficients are 30 and 5.8 W/m2K

respectively. Calculate the heat loss per meter of pipe if the steam temperature is

300°C and air temperature 50°C. The thermal conductivity of two insulating

materials are 0.17 and 0.093 W/mK respectively.

(DEC-16, MAY-17)



TOPIC 2

[B] FIN

CLASS TUTORIAL

1. A long rod 12 mm square section made of low carbon steel protrudes into air at 35°C

from a furnace wall at 200°C. The convective heat transfer coefficient is estimated at

22W/m2K. The conductivity of the material is 51.9 W/mK. Determine the location

from the wall at which the temperature will be 60°C. Also calculate the temperature

at 80 mm from base.

2. A temperature rise of 70 °C in a circular shaft of 60 mm diameter is caused by amount

of heat generated due to friction in the bearing mounted on the crankshaft. The

thermal conductivity of the shaft material is 50 W/mK and the heat transfer

coefficient is 10 W/m2K. Determine the amount of heat transfer through the shaft.

Assume that the shaft is a rod of infinite length.

3. Calculate the amount of heat transfer through an iron fin of length 60mm, width

100mm and thickness 10mm. assume that the thermal conductivity of material is 210

kJ/mh°C and heat transfer coefficient is 40 kJ/ m2h°C and temperature at the base is

90°C. also calculate the temperature at tip of the fin, if the atmosphere temperature is

25°C.

ASSIGNMENT

Theory

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

which is insulated at tip.

(Dec.-11, Winter-12, Winter-13, Winter-14, Dec.-15, MAY-16, MAY-18)

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, DEC-16)

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

insulated tip, show that

η of fin = tanh mL mL⁄ with usual notations

(Summer 2014, DEC-16, MAY-17, NOV-17)



Examples

1. A fin 30 cm long and 10 cm diameter throughout is made of material A (Select

Material from the table). The fin is attached to a plane heated wall at 200 ℃

temperature extends into surroundings at 25℃ and heat transfer coefficient of 120

W/m2-K. Find

I. The rate of heat transfer from the fin

II. The temperature distribution along the fin length at an interval of 5 cm from

the base

III. fin efficiency

IV. fin effectiveness.

For the following different condition

I. The length of the fin is infinite

II. The tip of the fin is insulated

Assume that thermal radiation effect is negligible.

SR.

NO.

MATERIAL Thermal Conductivity

(W/mK)

BATCH

1 Copper 393 AX1

2 Aluminium 240 AX2

3 Stainless Steel 17 AY1

4 Brass 137 AY2

5 Low carbon steel 56 ALL



TOPIC 2

[C] TRNASIENT HEAT CONDUCTION

CLASS TUTORIAL

1. A solid copper sphere of 12cm diameter, initially at a uniform temperature 260℃ is

suddenly dropped in a fluid which is maintained at a uniform temperature of 40℃.

The convective heat transfer coefficient is 200 𝑊 𝑚2𝐾⁄ . The properties of copper are

as follow:

𝑘 = 385 𝑊 𝑚𝐾⁄ , Density = 8954 𝑘𝑔 𝑚3⁄ , Sp. Heat = 383 𝐽 𝑘𝑔𝐾⁄

Calculate the temperature of the copper block at 5min after immersion.

2. A solid sphere of 1 cm made up of steel is at initially at 300℃ temperature.

Properties of steel: 𝑘 = 60 𝑊 𝑚𝐾⁄ , Density = 7800 𝑘𝑔 𝑚3⁄ , Sp. Heat = 434 𝐽 𝑘𝑔𝐾⁄

Calculate the time required for cooling it up to 50℃ in the following two cases

I. cooling medium is air at 25℃ with ℎ = 20 𝑊 𝑚2𝐾⁄

II. cooling medium is water at 25℃ with ℎ = 100 𝑊 𝑚2𝐾⁄ (Winter-2013)

(Similar to D.S. Kumar, Example 6.7)

ASSIGNMENT

Theory

1. Explain lumped heat capacity method and state its assumptions.

(MAY-16, MAY-17, MAY-18)

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

examples of heat conduction under unsteady state. (May-12, DEC-16)

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

numbers? (Winter-12, Winter-13, DEC-16)

Examples

1. Estimate the time required to cook a carrot in boiling water at atmospheric pressure.

The carrot is initially at room temp 32 °C and the cooking requirement stipulates that

a minimum temp. of 97 °C is reached at the center of carrot. Treat the carrot as a long

cylinder of 18 mm diameter and having the following properties: ρ=1025 kg/m3, Cp =

4000 J/kg K, k= 3.45 W/m-K, convective heat transfer coefficient h = 60 W/m2-K.

(DEC-15)



2. An aluminum sphere weighing 6 kg and initially at temperature of 350°C is suddenly

immersed in a fluid at 30°C with convective coefficient of 60 W/m2K. Estimate the

time required to cool the sphere to 100°C. Take thermo physical properties of sphere

as C = 900 J/kgK, ρ = 2700 kg/m3 k = 205 W/mK

(MAY-16)



TOPIC 4 – RADIATION

CLASS TUTORIAL

1. Consider a 20-cm-diameter spherical ball at 800 K suspended in air as shown in

Figure. Assuming the ball closely approximates a blackbody, determine (a) the total

blackbody emissive power, (b) the total amount of radiation emitted by the ball in 5

min

2. The effective temperature of body having an area of 0.12 m2 is 600 ℃. Calculate the

following:

I. The total rate of energy emission

II. The intensity of normal radiation

III. The wavelength of maximum monochromatic emissive power

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

T2=500 K and have emissivity ɛ1=0.2 and ɛ2=0.7, respectively, as shown in Figure.

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

surface area of the plates.

4. A refractory material which has ɛ=0.4 at 1500K and ɛ=0.43 at 1420K is exposed to

black surface wall at 1500K. What is the rate of gain of heat radiation per m2 area?

5. Calculate the rate of heat transfer rate per m2 area by radiation between the surfaces

of two long cylinders having radii 100mm and 50mm respectively. The smaller

cylinder being in the larger cylinder. The axis of the cylinders are parallel to each other

and separated by distance of 20mm. The surface of inner and outer cylinders is



maintained at 127℃ and 27℃ respectively. The emissivity of both the surfaces is 0.5.

Assume the medium between the two cylinders is non absorbing.

6. Liquid oxygen (boiling temperature= -182℃) is to be stored in the spherical container

of 30cm diameter. The system is insulated by an evacuated space between inner space

and surrounding 45cm inner diameter concentric sphere. For both sphere ɛ=0.03 and

temperature of the outer sphere is 30℃. Estimate the rate of heat flow by radiation to

the oxygen in the container.

7. 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 ɛ1=0.2 and ɛ2=0.7, respectively. 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.

ASSIGNMENT

Theory

1. Define:(May 2011, Summer 2013, Summer 2015, DEC-16, NOV-17)

I. Emissivity,

II. Radiosity,

III. Black body

IV. Irradiation,

V. Absorptivity,

VI. Grey body

VII. Solid angle.

2. Define total emissive power (Eb) and intensity of radiation (Ib). Show that Eb = π×Ib

(DEC-15, MAY-17, MAY-18)

3. (a) Explain Wien’s displacement law of radiation.

(b) Explain Kirchoff’s law of radiation.

(DEC-16, MAY-17, NOV-17)

4. What is Radiosity (J)? Show that the net radiant energy leaving the surface is given

by

(DEC-16)

5. What is radiation shield? Show that presence of n number of radiation shields reduces

the radiation heat transfer by a factor of (n+1).

(MAY-18)


B.E. Semester V Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 10

Examples

1. Consider two large parallel plates, one at temperature at 727 °C with emissivity 0.8

and other at 227 °C with emissivity 0.4. An aluminium radiation shield with an

emissivity of 0.05 on both sides is placed between two plates. Calculate reduction in

heat transfer rate between two plates as a result of shield.

(MAY-17)

2. An enclosure measures 1.5m* 1.5m with a height of 2m under steady state conditions,

the wall and ceiling are maintained at 525 K and floor is at 400K. Determine net

radiation to floor. Take emissivity of ceiling and wall = 0.85 and emissivity of floor =

0.75

(NOV-17)

ASSIGNMENT - CONVECTION HEAT TRANSFER (2151909)


CHAPTER – 3 CONVECTION Theory

1. Discuss and define:

a) Natural and Forced Convection.

b) Mean Film Temperature & Bulk Mean Temperature.

2. State the general equation for the rate of heat transfer by convection and hence define the coefficient of heat transfer. What are the various factors on which the value of this coefficient depends?

3. Define and discuss the following dimensionless numbers:

a) Reynolds Number

b) Prandtl Number

c) Grashoff Number

d) Nusselt Number.

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

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

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

7. 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. Calculate the rate of heat loss from a human body which may be considered as vertical cylinder 30 cm in diameter and 175 cm high in still air at 15°C. The skin temperature is 35°C and emissivity at the skin surface is 0.4. Neglect sweating and effect of clothing. Use Nu = 0.13 (Gr Pr)0.33. [Ans: 208.61 W] [D.S. Kumar 11.15]

2. 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]

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]

ASSIGNMENT - CONVECTION HEAT TRANSFER (2151909)


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 & heat transfer rate by natural convection. For a sphere, the general correlation is Nu = 2 + 0.43 (Ra)0.25.

[Ans: 772.086 W/m2-deg, 3880.9275 W] [D.S. Kumar; 11.4]

6. 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,𝑁𝑢𝑥 = 0.332 (𝑅𝑒𝑥)1

2⁄ (𝑃𝑟𝑥)1

3⁄ [Ans: 917.16 W]

7. 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]

8. 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]

9. Water at 50°C enters 1.5 cm diameter and 3 m long tube with a velocity of 1.5 m/s.

The tube wall is maintained at 100°C. Calculate the heat transfer coefficient and total

amount of heat transferred if the water exit temperature is 70°C. The relevant

properties of water are Pr = 3.15, ρ = 990 kg/m3, ν = 0.517 × 10-6 m2/s, Cp = 4184

J/kg-K, kf = 0.65 W/m-K. Use following correlation,

𝑁𝑢𝐷 = 0.023(𝑅𝑒𝐷)0.8(𝑃𝑟)0.4 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 Air 25 - - 15.53 0.0263 0.7 - 2 Bismuth 650 104 0.1507 - 13.02 - 3.12 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 - 6 Air 60 - - 18.97 0.02894 0.696 - 7 Air 50 1.093 1.005 17.95 0.02964 0.698 -

CLASS TUTORIAL HEAT TRANSFER (2151909)


CHAPTER – 3 CONVECTION

1. 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 𝑁𝑢 = 0.664(𝑅𝑒)0.5(𝑃𝑟)0.33 and the characteristic length

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

2. A hot square plate 40cm x 40cm at 100°C is exposed to atmospheric air at 20°C.

Make calculations for the heat loss from both surfaces of the plate, if (a) plate is kept

vertical (b) plate is kept horizontal.

The following empirical correlations have been suggested:

Nu = 0.125 (Gr Pr)0.33 for vertical position of plate, and

Nu = 0.72 (Gr Pr)0.25 for upper surface

Nu = 0.35 (Gr Pr)0.25 for lower surface

[Ans: 126.47 W] [D.S. Kumar 11.9, GTU - JAN 2013]

3. Estimate the heat transfer from a 40W incandescent bulb at 120°C to 20°C quiescent

air. Approximate the bulb as a 50 mm dia. Sphere. What percentage of power is lost

by free convection? The approximate co-relation is, 𝑁𝑢 = 0.60(𝐺𝑟𝑃𝑟)0.25.

[Ans: 7.8484 W; 19.62%]

4. A steam pipe 8 cm in diameter is covered with 3 cm thick layer of insulation which

has a surface emissivity of 0.9.The surface temperature of the insulation is 80 °C and

the pipe is placed in atmospheric air at 24 °C. Considering heat loss by both

radiation and natural convection calculate:

(1) The heat loss from the 7 m length of pipe.

(2) The overall heat transfer coefficient & heat transfer co-efficient due to radiation

alone.

Use empirical correlation for horizontal cylinders as, 𝑁𝑢 = 0.53(𝐺𝑟. 𝑃𝑟)0.25

[Ans: 2243.6579 W; 13.013 W/m2-°C; 7.0586 W/m2-°C][GTU – DEC 2011]

5. Water at 10 °C, flows over a flat plate (at 90 °C) measuring 1 m X 1 m, with a velocity

of 2 m/s. Determine,

(a) The length of plate over which the flow is laminar

(b) The rate of heat transfer up to the above length

(c) The rate of heat transfer from the entire plate.

Useful correlation:

𝑁𝑢 = 0.332(𝑅𝑒𝑥)1

2(𝑃𝑟)1

3 𝑙𝑜𝑐𝑎𝑙 𝑁𝑢𝑠𝑠𝑒𝑙𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 𝑓𝑜𝑟 𝑙𝑎𝑚𝑖𝑛𝑎𝑟 𝑓𝑙𝑜𝑤

𝑁𝑢 = [0.036(𝑅𝑒𝐿)0.8 − 836](𝑃𝑟)1/3𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑁𝑢𝑠𝑠𝑒𝑙𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 𝑓𝑜𝑟 𝑚𝑖𝑥𝑒𝑑 𝑓𝑙𝑜𝑤

[Ans: 0.139m; 36.951KW; 471KW][GTU – MAY 2013]

6. Air at 20°C is flowing over a flat plate which is 200mm wide and 500mm long. The

plate is maintained at 100°C. Find the heat loss from the plate if the air is flowing



parallel to 500mm side with 2m/s velocity. What will be the effect on heat transfer if

the flow is parallel to 200mm side? For laminar flow over flat plate, use following

correlation:

𝑁𝑢̅̅ ̅̅ = 0.664 (𝑅𝑒𝐿)1

2⁄ (𝑃𝑟)1

3⁄ [Ans: 54.14 W, 85.6 W] [R. K. Rajput; 7.15]

7. Air at 20°C and at a pressure of 1 bar is flowing over a flat plate at a velocity of

3m/sec. If the plate is 280 mm wide and at 56°C, calculate the following quantities at

x = 280 mm.

a. Hydrodynamic boundary layer thickness

b. Local and average friction coefficient

c. Shearing stress due to friction

d. Thickness of thermal boundary layer

e. Local and average convective heat transfer coefficient

f. Rate of heat transfer by convection

g. Total drag force on the plate and

h. Total mass flow rate through the boundary

[Ans: Using Blasius Solution:-6.26mm; 0.002969; 0.005938; 0.01519 N/m2;

7.05mm; 6.43W/m2K; 12.86W/m2K; 36.29W; 0.00238N; 0.01335kg/s] [4.6; P. K.

NAG]

8. A plate of length 750mm has been placed longitudinally in a stream of crude oil

which flows with a velocity of 5 m/sec. If the oil has a specific gravity of 0.8 and

kinematic viscosity of 1 x 10-4 m2/sec, calculate,

a. Boundary layer thickness at the middle of plate

b. Shear stress at the middle of plate and

c. Friction drag on one side of the plate.

[Ans: 0.0136m; 48.491N/m2; 51.433N]

9. Air at 20°C and at atmospheric pressure flows at a velocity 4.5 m/s past a flat plate

with a sharp leading edge. The entire plate surface is maintained at a temperature of

60°C. Assuming that the transition occurs at a critical Reynolds number of 5 × 105,

find the distance from the leading edge at which the boundary layer changes from

laminar to turbulent. At the location calculate: (1) thickness of hydrodynamic and

thermal boundary layer, (2) Local and average heat transfer coefficients, (3) Heat

transfer rate from both sides per unit width of plate.

Use 𝑁𝑢𝑥𝑐 = 0.332(𝑅𝑒𝑥𝑐)1/2(𝑃𝑟)1/3

Assume cubic velocity profile and approximate method.

[Ans: 12.34mm; 13.55mm; 3.05W/m2K; 6.1W/m2K; 917.4W] [GTU – MAY 2012]

[4.7; P. K. NAG]

10. The air at atmospheric pressure and temperature of 30°C flows over one side of

plate of a velocity of 90 m/min. This plate is heated and maintained at 100°C over its

entire length. Find out the following at 0.3 and 0.6 m from its leading edge. (1)

Thickness of velocity boundary layer and thermal boundary layer. (2) Mass flow rate



which enters the boundary layer between 0.3 m and 0.6 m per metre depth of plate.

Assume unit width of plate.

[Ans: 8.30mm; 9.119mm; 11.73mm; 12.88mm; 0.00374kg/s] [GTU – MAY 2012]

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 Air 20 - - 15.06 0.0259 0.703 -

2 Air 60 1.06 1.008 18.97 0.028 - -

3 Air 70 1.029 - 21.03 0.03045 0.692 -

4 Air 52 1.092 1.007 - 0.02781 - 0.07045

5 Water 50 988 4.18 0.556 0.648 - -

6 Air 60 - - 18.97 0.025 0.7 -

7 Air 38 1.1374 1.005 16.768 0.02732 - -

9 Air 40 1.128 - 16.96 0.02755 0.7 -

10 Air 30 1.165 1.005 16.00 0.02675 0.701 -

ASSIGNMENT – HEAT EXCHANGERS HEAT TRANSFER (2151909)


CHAPTER – 5 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. In a counter flow heat double pipe heat exchanger ,water is heated from 25°C to

65°C by oil with specific heat of 1.45 kJ/kg K and mass flow rate of 0.9 kg/s. The oil

is cooled from 230°C to 160°C. If overall Heat transfer coefficient is 420 W/m2 °C.

calculate following:

a. The rate of heat transfer

b. The mass flow rate of water , and

c. The surface area of heat exchanger

[Ans: 91.35KW, 0.545 kg/s, 1.45 m2] [GTU DEC-2013]

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:

ASSIGNMENT – HEAT EXCHANGERS HEAT TRANSFER (2151909)


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 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]

4. Hot water at 2.5 kg/s and 100°C enters a concentric tube counter flow heat

exchanger having a total area of 23m2. Cold water at 20°C enters at 5 kg/s and the

overall heat transfer coefficient is 1000 W/m2K. Determine the total heat transfer

rate and the outlet temperature of hot and cold fluids.

[GTU DEC-2015]

5. 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]

6. 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]



CHAPTER – 5 HEAT EXCHANGERS

1. Exhaust gases (Cp = 1.12 kJ/kg-deg) flowing through a tubular heat exchanger at the

rate of 1200 kg/hr are cooled from 400°C to 120°C. The cooling is affected by water

(Cp = 4.18 kJ/kg-deg) that enters the system at 10°C at the rate of 1500 kg/hr. If the

overall heat transfer co-efficient is 500 kJ/m2-hr-deg, what heat exchanger area is

required to handle the load for (a) Parallel flow and (b) Counter flow arrangement?

[Ans: 4.547 m2, 3.758 m2] [14.9, D. S. Kumar]

2. Calculate the surface area required for a heat exchanger which is required to cool

3600 kg/hr of benzene (Cp = 1.74 kJ/kg-K) from 75°C to 45°C. The cooling water (Cp

= 4.18 kJ/kg-deg) at 15°C has a flow rate of 2500 kg/hr. consider the following

arrangements:

a. Single pass counter flow

b. 1-4 exchanger (one shell pass and four tube passes)

c. Cross flow single pass with water mixed and benzene unmixed.

The overall heat transfer co-efficient for each configuration is approximated to be

0.3kW/m2-K. [Ans: 4.87 m2, 5.29 m2, 5.18 m2] [14.35, D. S. Kumar]

3. A heat exchanger is to be designed to condense 8 kg/s of an organic liquid (tsat =

80°C; hfg = 600 kJ/kg) with cooling water available at 15°C and at a flow rate of 60

kg/s. The overall heat transfer co-efficient is 480 W/m2-deg. Calculate:

a. The number of tubes required. The tubes are to be of 25 mm outer diameter,

2 mm thickness and 4.85 m length.

b. The number of tube passes. The velocity of the cooling water is not to exceed

2 m/s. [Ans: 478 tubes, 6 passes] [14.19, D. S. Kumar]

4. In a shell and tube heat exchanger, 6 kg/s of oil flows through the shell side. The oil

enters at 105°C and leaves at 40°C. Water flows in the tubes, entering at 32°C and

leaving at 50°C. In addition, Cpoil = 2282 J/kg-K and U = 416 W/m2-K. Determine

number of tubes, if outer diameter of tubes is 100 mm, length of each tube is 1.9 m

and take correction factor as 0.85. [GTU MAY-2016, MAY 2017]

5. A counter flow heat exchanger is used to cool 2000 kg/hr of oil (cp = 2.5 kJ/kg-K)

from 105°C to 30°C by the use of water entering at 15°C. If the overall heat transfer

co-efficient is expected to be 1.5 kW/m2K, make calculations for the water flow rate,

the surface area required and the effectiveness of heat exchanger. Presume that the

exit temperature of the water is not to be exceed 80°C. Use NTU-effectiveness

approach. [Ans: 1380.2 kg/hr, 3.55 m2, 0.833] [14.41, D. S. Kumar]

6. A tube type heat exchanger is used to cool hot water from 80°C to 60°C. The task is

accomplished by transferring heat to cold water that enters the heat exchanger at

20°C and leaves at 40°C. Should this heat exchanger operate under counter flow or

parallel flow conditions? Also determine the exit temperatures if the flow rates of

fluids are doubled. [Ans: 67.328°C, 32.672°C] [14.47, D. S. Kumar]

ASSIGNMENT – BOILING & CONDENSATION HEAT TRANSFER (2151909)


CHAPTER – 6 BOILING & CONDENSATION

Theory

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

Discuss in detail the various regimes in boiling and explain (i) the condition for the

growth of bubbles and (ii) effect of bubble size on boiling.

2. Distinguish

a. Sub-cooled 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?

4. Write note on influence of non-condensable gases on condensation.

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TOPIC 2 [A] STEADY STATE HEAT CONDUCTION · HEAT TRANSFER (2151909) B.E. Semester – V Department...

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