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MST Examples

S. Y. B. Tech. Prod Engg.ME0223 SEM-IV Applied Thermodynamics & Heat Engines

Mid – Semester Examination

Examples

Applied Thermodynamics & Heat Engines

S.Y. B. Tech.

ME0223 SEM - IV

Production Engineering

MST Examples


Example 1A 3-mm-diameter and 5 m long electric wire is tightly wrapped with a 2 mm thick plastic cover whose thermal conductivity is k = 0.15 W/m·°C. Electrical measurements indicate that a current of 10 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulated wire is exposed to a medium at T2 = 30 °C with a heat transfer coefficient of h = 12 W/m2·°C, determine the temperature at the interface of the wire and the plastic cover in steady operation. Also determine whether doubling the thickness of the plastic cover will increase or decrease this interface temperature.

Heat is generated in the wire and its temperature rises as a result of resistance heating.In steady operation, the rate of heat transfer becomes equal to the heat generated withinthe wire, which is determined to be :

WAVIVWQ e 80)10)(8(

The thermal resistance network for this problem involves a conduction resistance for the plastic cover and a convection resistance for the outer surface in series.

222 110.0)5(002.0

2

003.02)2( mmm

mLrA

MST Examples

S. Y. B. Tech. Prod Engg.

Example 1….contd

WCmCmWAh

RConv /76.0)110.0)(./12(

1122

2

WCmCmW

mmmm

Lk

rrRPlastic /18.0

)5)(./15.0(2

)5.1/5.3(ln

2

)/(ln 12

Thus; RTotal = RPlastic +RConvection = 0.76 + 0.18 = 0.94 ºC/W

Interface temperature can be detected as;

C

WCWC

RQTTR

TTQ Total

Total

105

)/94.0)(80()30(

11

….Ans

ME0223 SEM-IV Applied Thermodynamics & Heat Engines

MST Examples


To answer the second part of the question, we need to know the Critical Radius of

Insulation of the plastic cover.

mmCmW

CmW

h

krC 5.12

./12

./15.02

Example 1….contd

which is larger than the radius of the plastic cover. Therefore, increasing the

thickness of the plastic cover will enhance heat transfer until the outer radius

of the cover reaches 12.5 mm. ….Ans


MST Examples


Example 2A reversible heat engine operating between a source temperature of 1000 K and a sink temperature of 300 K The engine drives a reversible heat pump which operates between 250 K to 300 K .The engine is supplied with 600 kW heat from source. All the work produced by engine is used for running the heat pump. Calculate the heat removed by the heat pump from cold body at 250 K.

T1 = 1000 K

Q1 = 600 kW

Heat Engine

Heat Pump

T2 = 300 K

Q4

T3 = 250 K

Q3= Q4 + W

ηmax = 1 - T2 = 1 - T1

300

1000= 0.7

W

Q1

= 0.7 W = 0.7 X 600 = 420 kW

COPmax = T2

T2 – T3

300

300 - 250= = 6

COPmax = Q3

W= 6

Q3 = COP X W = 6 X 420 = 2520 kW

Q4 = Q3 - W = 2520 - 420 = 2100 kW ….Ans


MST Examples


Example 3A counter-flow double-pipe heat exchanger is to heat water from 20 °C to 80 °C at a rate of 1.2 kg/s. The heating is to be accomplished by geothermal water available at 160 °C at a mass flow rate of 2 kg/s. The inner tube is thin-walled and has a diameter of 1.5 cm. If the overall heat transfer coefficient of the heat exchanger is 640 W/m2·°C, determine the length of the heat exchanger required to achieve the desired heating.

The rate of heat transfer in the heat exchanger can be determined from,

kWCCCkgkJkgTTCmQwater

outinP 301)2080()./18.4(sec)/2.1(

The outlet temperature of the geothermal water is determined to be,

C

CkgkJkg

kWC

Cm

QTTTTCmQ

P

inoutgeothermal

outinP

124

)./18.4(sec)/2(

301160


MST Examples


Knowing the inlet and outlet temperatures of both fluids, the logarithmic mean temperature difference (LMTD) for this counter-flow heat exchanger becomes,

Example 3….contd

CCCTTT

CCCTTT

inout

outin

ch

ch

104)20124(

80)80160(

,,2

,,1

C

TT

TTTm

5.91104/80ln

10480

/ln 21

21

22

14.5)5.91()./640(

301m

CCmW

kW

TU

QATAUQ

msms

The surface area of the heat exchanger is determined to be,

To provide this much heat transfer surface area, the length of the tube must be,

mm

m

D

ALLDA s

s 109)015.0(

14.5 2

….Ans


MST Examples


Example 4Consider a 20 cm diameter spherical ball at 800 K suspended in air 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.

222 1257.0)2.0( mmDAs

(b) The total amount of radiation energy emitted from the entire ball in 5 min is determined by multiplying the blackbody emissive power obtained above by the total surface area of the ball and the given time interval:

sec300min5 t

kJmmkWtAEQ sbrad 876)300()1257.0()/2.23( 22 ….Ans

(a) The total blackbody emissive power is determined from the Stefan – Boltzmann law to be,

244284 /2.23)800()./1067.5( mWKKmWXTEb ….Ans

MST Examples


Example 5Nitrogen gas at 300 K, 101 kPa and 0.1 m3 is compressed slowly in an isothermal process to 500 kPa. Calculate the work done during the process.

KkgJmolkgkg

KmolkgJ

MR ./93.296

./28

../8314

R

.…AnsJ

X

XK

Kkg

Jkg

P

PTRmW

45.16156

10500

10101ln.)300(.

.93.296.)1134.0(

ln

3

3

2

1

And,

kgKKkgJ

mPaX

TR

VPm 1134.0

)300()./93.296(

)1.0()10101( 33

Now,

MST Examples


Example 61.2 kg of liquid water initially at 15 °C is to be heated to 95 °C in a teapot equipped with a 1200 W electric heating element inside. The teapot is 0.5 kg and has an average specific heat of 0.7 kJ/kg·°C. Taking the specific heat of water to be 4.18 kJ/kg·°C and disregarding any heat loss from the teapot, determine how long it will take for the water to be heated.

Taking the teapot and the water in it as the system, which is a closed system (fixed mass). The energy balance in this case can be expressed as;

kJ

CCCkgkJkg

CCCkgkJkg

TCmTCm

UUUE

EEE

teapotpwaterp

teapotwatersystemin

systemoutin

3.429

)1595()./7.0()5.0(

)1595()./18.4()2.1(

MST Examples


Example 6….contd

The 1200-W electric heating unit will supply energy at a rate of 1.2 kW or 1.2 kJ per second. Therefore, the time needed for this heater to supply 429.3 kJ of heat is determined as,

min6sec358sec/2.1

3.429 kJ

kJ

E

E

TransferEnergyofRate

TransferEnergyTotalt

transfer

in

….Ans


MST Examples


Example 7Engine oil at 60 °C flows over the upper surface of a 5 m long flat plate whose temperature is 20 °C with a velocity of 2 m/s. Determine the rate of heat transfer per unit width of the entire plate.The properties of engine oil at the film temperature of Tf = (Ts + T∞)/2 = (20 + 60)/2 = 40 °C: ρ = 876 kg/m3 , Pr = 2870k = 0.144 W/m.°C, ν = 242 X 10-6 m2/sec.

Noting that L = 5 m, the Reynolds number at the end of the plate is,

426

1013.4sec)/10242(

)5(sec)/2(Re X

mX

mmLL

V

which is less than the critical Reynolds number. Thus we have Laminar Flow overthe entire plate.

The Nusselt number is determined using the laminar flow relations for a flat plate,

191828701013.4664.0PrRe664.0 33.05.0433.05.0 Xk

LhNu L

MST Examples


Example 7….contd

CmWm

CmWNu

L

kh

./2.55)1918(

)5(

)./144.0( 2

This leads to,

And,

WCCmXmTTAhQ Ss 11040)2060()15()1918(

….Ans


MST Examples


Show that the Reynolds number for flow in a circular tube of diameter D can be expressed

as Re =

Example

DAm /4

Dm /4

D

m

D

Dm

A

Dm

A

DQ

A

DVA

A

ADV

DV

4

4

)(

)()()(

Re

2

….Ans

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