chapter 2 steady state heat conduction - … rivet per 0.1m2 of surface. the layer of material...

HEAT TRANSFER (2151909) CLASS TUTORIAL

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

CHAPTER – 2 STEADY STATE HEAT CONDUCTION

1. A storage chamber of interior dimensions high has its inside

maintained at a temperature of whilst the outside is at . The walls and

ceiling of the chamber have three layers made of

60 mm thick board ( ⁄ ) on the inside

90 mm thick insulation ( ⁄ ) at the mid

240 mm thick concrete ( ⁄ ) 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)

2. A 8 mm thick metal plate, having thermal conductivity ⁄ is exposed to

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

transfer coefficients are ⁄ on vapor side and ⁄ 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)

3. A composite wall has three layers of material held together by 3 cm diameter

aluminium rivet per 0.1m2 of surface. The layer of material consists of 10 cm thick

brick with hot surface at , 1cm thick wood with cold surface at . These two

layers are interposed by third layer of insulating material 25cm thick. The

conductivity of the material are:

⁄ ⁄

⁄ ⁄

Assuming one dimensional heat flow, calculate the percentage change in heat transfer

rate due to rivets. (Summer 2015)

4. A steel tube of 5 cm inner diameter and 8 cm outer diameter ( ⁄ ), is

covered with an insulation of 3 cm thickness ( ⁄ ). A hot gas at ,

⁄ 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 at , ⁄ . (May-2012) (Similar to Mahesh Rathod,

Example 3.29)

5. 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 and

the pipe is placed in atmospheric air at . Considering heat loss by both radiation

and natural convection calculate: (Dec-2011)

I. The heat loss from the 7 m length of pipe.

II. The overall heat transfer coefficient and the heat transfer coefficient due to

radiation alone.

The thermo physical properties of air at mean film temperature of 52 are as

following:

⁄ ⁄

⁄

⁄ (where the notations have their usual meaning.) use

empirical correlation for horizontal cylinders as ( ) .

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

insulated. The outside air convective heat transfer coefficient is ⁄ . The

thermal conductivity of the insulating material is ⁄ . 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)



CHAPTER – 3 FIN

1. Two long rods of the same diameter, one made of brass (k = 85 W/m-deg) and the

other of copper (k = 375 W/m-deg), having one of their ends inserted into a furnace.

At a section 10.5 cm away from the furnace, the temperature of the brass rod is

120 . At what distance from the furnace end, the same temperature would be

reached in the copper rod. Both rods are exposed to the same environment. (D.S.

Kumar, Example 5.1)

2. A rod of 10 mm square section and 160 mm length with thermal conductivity of 50

W/m-deg protrudes from a furnace wall at 200 , and is exposed to air at 30 with

convection coefficient 20 W/m2-deg. Make calculations for the heat convected upto

80 mm and 158 mm lengths and comment on the result. Adopt a long fin model for

the arrangement. (D.S. Kumar, Example 5.4)

3. A rod of 10 mm diameter and 80 mm length with thermal conductivity 16 W/m-deg

protrudes from a surface at 160 . The rod is exposed to air at 30 with a

convection coefficient of 25 W/m2-deg. How does the heat flow from this rod get

affected if the same material volume is used for two fins of the same length? Assume

short fin with end insulated. (D.S. Kumar, Example 5.11)

4. A 5 cm diameter rod, 90 cm long is having its lower face grinded smooth. The

remainder of the rod is exposed to the 32 room air and a surface coefficient heat

transfer equal to 6.5 W/m2-deg exists between the rod surface and the room air. The

grinder dissipates mechanical energy at the rate of 35 W. If thermal conductivity of

rod material is 41.5 W/m-deg, find the temperature of the rod at the point where the

grinding is taking place. (D.S. Kumar, Example 5.21)

5. A thermometric pocket is a hollow brass tube (k = 75 W/m-deg) having outer and

inner diameter of 15 mm of 10 mm respectively. The pocket extends to 5 cm depth

from the wall of a 15 cm diameter pipe which carries hot air. The heat transfer

coefficient between the pocket and air is prescribed by the relation:

Nusselt number Nu = 0.175 (Re)0.62.

Make calculation for the error in temperature measurement. Presume the following

data: (D.S. Kumar, Example 5.31)



Air temperature 160 and pipe wall temperature 40

Reynolds number 25000 and thermal conductivity of air 0.036 W/m-deg



CHAPTER – 4 TRNASIENT HEAT CONDUCTION

1. A potato with mean diameter of 4 cm is initially at . It is placed in boiling water

for 5 minute and 30 seconds and found to be boiled perfectly. For how long should

be a similar potato for the same consumer be boiled when taken from cold storage at

. (Summer-2015) (Similar to D.S. Kumar, Example 6.7)

Use lumped system analysis and take thermophysical properties of potato as

⁄ ⁄ ⁄ ⁄

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

Properties of steel: ⁄ , Density = ⁄ , Sp. Heat = ⁄

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

I. cooling medium is air at with ⁄

II. cooling medium is water at with ⁄ (Winter-2013)

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



CHAPTER – 5 & 6 RADIATION

1. Determine the view factor from any one side to any other side of the infinitely long

triangular duct whose cross section is given in figure 1. (Cengel; Example 13.4)

Figure 1 Infinitely long triangular duct

2. A furnace is shaped like a long equilateral triangular duct, as shown in Figure 2. The

width of each side is 1 m. The base surface has an emissivity of 0.7 and is maintained

at a uniform temperature of 600 K. The heated left-side surface closely approximates

a blackbody at 1000 K. The right-side surface is well insulated. Determine the rate at

which heat must be supplied to the heated side externally per unit length of the duct

in order to maintain these operating conditions. (Cengel; Example 13.9)

Figure 2 The triangular furnace

3. Determine the rate of heat loss by radiation from a steel tube of outside diameter 7

cm and length 3 m at a temperature of 227 if the tube is located within a square

brick conduit of 0.3 m side and at 27 . Take emissivity of steel and brick as 0.79 and

0.93 respectively. (Summer 2014) )(Similar to D.S. Kumar; Example 8.30)

4. Two large parallel plates with emissivity (ε) = 0.5 each, are maintained at different

temperatures and are exchanging heat only by radiation. Two equally large radiation



shields with surface emissivity 0.05 are introduced in parallel to the plates. Find

percentage reduction in net radiative heat transfer. (May 2011) (Similar to D.S.

Kumar; Example 8.38)

5. Calculate the net radiation heat transfer per m2 area of two large plates placed

parallel to each other at temperatures of and respectively.

( ) and ( ) .

If a polished aluminum shield is placed between them, find the % reduction in heat

transfer, ( ) . (Summer 2015) (Similar to D.S. Kumar; Example

8.38)



CHAPTER – 7 CONVECTION

1. 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]

2. 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]

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, ( ) .

[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, ( )

[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:

( )

( )

[ ( ) ]( )

[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:

( ) ⁄ ( )

⁄ [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;

6.88mm; 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 ( ) ( )

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 60 1.06 1.008 18.97 0.028 - -

2 Air 25 - - 15.53 0.0263 0.7 -

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 -



CHAPTER – 9 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. A counter flow concentric tube heat exchanger is used to cool the lubricating oil of a

large industrial gas turbine engine. The oil flows through the tube at 0.19 kg/s (Cp =

2.18 kJ/kg-K), and the coolant water flows in the annulus in the opposite direction at

a rate of 0.15 kg/sec (Cp = 4.18 kJ/kg-K). the oil enters the coolant at 425 K and

leaves at 345 K while the coolant enters at 285 K. how long must the tube be made

to perform this duty if the heat transfer co-efficient from oil to tube surface is 2250

W/m2K and from tube surface to water is 5650 W/m2K? The tube has a mean

diameter of 12.5 mm and its wall presents negligible resistance to heat transfer.

[Ans: 7.21 m] [14.17, D. S. Kumar]

3. A one-shell two-tube pass heat exchanger having 3000 thin wall brass tubes of 20

mm diameter has been installed in a steam power plant with a heat load of 2.3X108

W. the steam condenses at 50°C and the cooling water enters the tubes at 20°C at the

rate of 3000 kg/s. Calculate the overall heat transfer co-efficient, the tube length per

pass, and the rate of condensation of steam. Take the heat transfer co-efficient for

condensation on the outer surfaces of the tubes as 15500 W/m2K and the latent heat

of steam as 2380 kJ/kg. further presume the following fluid properties:

c = 4180 J/kg-K, μ = 855 X 10-6 Ns/m2, k = 0.613 W/m-k and Pr = 5.83

[Ans: 6524 W/m2K, 4.82 m, 96.64 kg/s] [14.18, D. S. Kumar]

4. 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]

5. A surface condenser used in a steam power plant deals with 27000 kg of steam per

hour at a pressure of 4.15 kN/m2 and 0.9 dryness fraction. The cooling medium will

be water that enters the condenser at 15°C and leaves at 25°C. From previous

experience, a water velocity of 1.5 m/s is maintained through the tubes and the

overall co-efficient of heat transfer is estimated at 3500 W/m2-K. Calculate :

a. Mass flow rate of water,

b. Surface area required for the given duty and

c. Passes and number of tubes.

The tubes used in condenser are 20 mm outside diameter, 1.5 mm thick and the

space limitation restricts the condenser length to 4 meters. At the condensing

pressure, steam has saturation temperature ts = 29.5°C and latent heat of

vaporization hfg = 2435 kJ/kg. Presume that the condensate coming out of the

condenser is saturated water at the condenser pressure, i.e., there is no under

cooling and the steam losses only latent part of its heat.

[Ans: 1.416 X 106 kg/hr, 0.2512 m2, 1158 tubes, 2 passes] [14.22, D. S. Kumar]

6. 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]



7. 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]

8. In a surface condenser, the water flowing through a series of tubes at the rate of 200

kg/hr is heated from 15°C to 75°C. The steam condenses on the outside surface of

tubes at atmospheric pressure and the overall co-efficient of heat transfer is

estimated at 860 kJ/m2-hr-deg. Use NTU method to work out the length of tube and

the steam condensation rate. Presume that the tube is 25 mm in diameter.

At the condensing pressure, steam has saturation temperature ts = 100°C and the

latent heat of vaporization hfg = 2160 kJ/kg. Further, the steam is initially just

saturated and the condensate leaves the exchanger without sub-cooling, i.e., only the

latent heat of condensing steam is transferred to water. Take specific heat of water

as 4 kJ/kg-K.

[Ans: 14.5 m, 22.22 kg/hr] [14.45, D. S. Kumar]

9. 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]

chapter 2 steady state heat conduction - … rivet per 0.1m2 of surface. the layer of material...

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