II

USN 06ME6s

Sixth Semester B.E. Degree Examination, December 2Ol2Heat and Mass Transfer

Time: 3 hrs Max. Marks:100Note: l. Answer FIW full questions, selecting

ut least TWO questionsfrom eaclt part.2. Use of IIMT duta book is permitted.

PART _ AI a. Starting from fundamental principles, derive the general, three-dimensional heat conduction

equation in Cartesian co-ordinates. (09 Marks)b. A liquid at 100'C flows through a pipe of 40 mm outer and 30 mm inner diameter. The

thermal conductivity of pipe material is 0.5 WmK. The pipe is exposed to air at 40'C. Theinner and outer convective heat transfer coefficients are 300 Wm2K and 5 Wm2Krespectively. Calculate the overall heat transfer coefficient and the heat loss per unit lengthof pipe. (08 Marks)

c. What is the technical need to under take a detailed study of heat transfer, having studiedthermodynam ics already? (03 Marks)

2 a. A tube with an outer diameter of 20 mm is covered with insulation. The thermalconductivity of insulating material is 0.18 WmK. The outer surface losses heat byconvection with a heat transfer coefficient of 12 Wim2K. Determine the critical thickness ofinsulation. Also calculate the ratio of heat loss liom the tube with critical thickness ofinsulation to that from the bare tube (without insulation). (10 Marks)

b' Derive the one-dimensional fin equation for a fin of uniforrn cross section. By integratingthe fin equation, obtain the expression for the temperature variation in a long fin. (t0 Marks)

3 a. Consider a solid, with an uniform initialtemperature, suddenly immersed in a liquid. Derivethe relevant governing differential equation, considering the system as lumped. By solvingthe differential equation, obtain the expression for the temperature variation with time.

(t0 Marks)b. A 50 mm thick iron plate (K:60 WmK, Cp:460 J/kg K, p:7800'kgim3,66: 1.6x10-sm'/s)

is initially at 225"C. Suddenly both surfaces are exposed to a fluid at 25"C, with a heattransfer coefficient of 500 Wm2K. Calculate the centre and the surface temperatures

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4 a. The velocity profile for boundary layer flow over a flat

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- I , - i{=l}', where boundary layer thickness E(x) =u. 26(x) Z[6txl]

(10 Marks)

plate is given by,

DBo*l . Develon an! l3u-

expression for local drag coefficient. Also develop an expression for average dragcoefficient for a length of L. (10 Marks)

b. Consider a square plate of size 0.6 m in a room with stagnant air at20'C. One side of plateis maintained at 100"C, while the other side is adiabatic. Deterrnine the heat loss if the plateis, i) vertical and ii) horizontalwith hot surface facing up.

I of2

(I0 Marks)

aL

06ME65

PART _ B5 a. Air at 0'C and 20 mls flows over a flat plate of length 1.5 m, that is maintained at 50"C.

Calculate the average heat transfer coefficient over the region where flow is laminar. Find

the average heat transfer coefficient and the heat loss for the entire plate per unit width.(12 Marks)

Air at -20"C and 30 m/s, flows over a sphere of diameter 25 mm, which is maintained at

80'C. Calculate the heat loss Ilom sphere. (08 Marks)

Derive an expression for the logarithmic mean temperature difference (LMTD) for a parallel

flow heat exchanger 02 Marks)

A cross flow heat exchanger, with both fluids unmixed, has an area of 8.4 m', is used to heat

air (Cp: 1005 J/kgK) with water (Cp:4180 J/kgK). Air enters at l5oC, at arate of 2 kg/s,

while water enters at 90"C at a rate of 0.25 kg/s. The overall heat transfbr coefficient is

250 Wm2K. Calculate exit temperatures of both fluids and the heat transfer, using

effectiveness - NTU method. (08 Marks)

b.

6a.

b.

7a.

b.

8a.b.

Saturated steam at 65oC condenses on a vertical tube with an outer diameter of 25 mm,

which is maintained at 35oC. Determin0 the length of tube needed, if the condensate flow

needed is 6x10-3 kg/s. (10 Marks)

Water at atmospheric pressure and saturation temperature is boiled in a 250 mm diameter,

polished stainless steel pan, which is maintained at 116'C. Calculate the heat flux and the

evaporation rate.

State and prove Kirchoff s law of radiation.

(10 Marks)

(06 Marks)

i

tII

Two large parallel plates with emissivities 0.5 and 0.8 are maintained at 800 K and 600 Krespectively. A radiation shield having an emissivity of 0.1 on one side and 0.05 on the other

side is placed in between. Calculate the heat transfer per unit area with and without the

radiation shield. (08 Marks)

c. Determine the view factors from the base of a cube to each of its five surfaces. (06 Marks)

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2 of2

USN

Time:3 hrs.

la.

b.

c.

2a.

b.

06ME6s

Sixth semester B.E. Degree Examination, Decemb er zoll,Heat and Mass Transfer

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Note:l. Answer any FrvE fult questions, selecting Max' Marks:100

at least TWO questionsfrom each part.2. Use of heat transfer data hand book is permitted.

PART _ AExplain briefly: i) Thermal conductivity ii) Thermal diffusivity

iii) overall heat transfer co-efficient. (06 Marks)Derive the general three dimensional conduction equation in Cartesian co-ordinates and statethe assumptions made (08 Marks)A square plate heater of size 20 cms x 20 cms is inserted between two slabs. Slab .A, is3 cms thick (K: 50 wmK) and slab 'B' is 1.5 cms (K: 0.2 wmK). The outside heattransfer co-efEcients on both sides of A and B are 200 and 50 W-/m2K respectively.Temperature of surrounding air is 25'c. If the rating of the heater is I kw, find! Maximum temperature in the system" ii) Outer surface temperature of two slabs.Draw the equivalent circuit for the system. (06 Marks)Derive an expression for the temperature distribution for a long pin of uniform cross sectionwithout insulated tip. (to Marks)A rod (K:200 wlmK) 10 mm in diameter and 5 cms long has its one end maintained at100oC' The surface of the rod^is exposed to ambient wr at 30"C with convective heattransfer co-efficient of 100 wmrK. Assuming other end insulated, determinei) The temperature of the rod at 25 mm distance from the end at 100.c.iD Heat dissipation rate from the surface of the rod andiii) Effectiveness. (10 Marks)Explain physical significance of Biot number and Fourier number. (04 Marks)Oblain an expression for instantaneous heat transfer and total heat transfer for lumped heatanal-vsis treatment of heat conduction problem. (08 Marks)A 15 mm diameter mild steel sphere K:42 WmoC is exposed to cooling air flow atZ1"Cresulting in the convective co-efficient h=120 Wm2oC.Deterrnine the following:i) Time required to cool the sphere from 550.C to 90.C.ii) Instantaneous heat transfer rute2minutes after the start of cooling. For mild steel

p : 7850 kg/ri I Cp : 475 J/kg.C; c, : 0.045 #m (08 Marks)

what do you rnean by hydrodynamic and thermar boundary layer? (04 Marks)Explain physical significance ofi) Grashoff number ii) prandtl number iii) Nusselt numberiv) Reynolds number (oE Marks)A nuclear reactor with its core constructed of parallel vertical plates 2.2 mhigh and 1.4 mrvide has been designed on free convection hcating of liquid bismuth. The maximumtemperafcre of the plate srirface is limited to 950"C w-hile the low-est allowable temperafur-eof bismuth is 340oC. Calculate the maximum possible heat dissipation from both sides ofeach plate. For the convective co-efficient the appiopriate correlation isN, = 0.13(Gr.Pr)o'333 . (08 Marxsy

4a.b.

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PART _ B

5 a. with the help of dimensional *urvri, derive expression which relates Reynolds number'

Nusselt number and Prandtl number' n L - (10 Marks)

b. Air at standard conditions of 760 mm of Hg at 20oC flows over a flat plate at 3 m/sec' The

plate is 50"; x 25 cms . Find the-heat losiper fto* if air flow is parallel to 50 cms side of

the plate. tiis "*, side is kd;;;i.l to ttr. air flow, what will be the effect on heat

transfer? T.;;;t;f tht plate is 100"C' (l0Marks)

6a.DeriveanexpressionforLMTDforcounterflowheatexchanger.Statetheassumptions(10 Marks)

06ME6s

Explain briefly the concept of a black body'(04 Marks)

State and exPlain,i) Kirchoff s law.

ii) Planck's law.

iiD Wein's displacement law. (08 Marks)

iv) Lambert's cosine law'

Calculate the net radiant heat exchange pil unit area ior two large parallel plates at

temperature of 427'C and 27"C r.rpJ.tiraty. €hotpl,t"=0'9',€"otapl",.=0'6- If a polished

aluminium shierd is placed between them. Find the percentage reduction in the heat transfer'(08 Marks)

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tltii, cooler consists of straight tube of 2 cms oD and 1'5 cm ID enclosed with in a pipe

and co-centric with it. The external pip. it welt insulated' The oil flows through the tube at

0.05 kg/sec (cp : z rlttg"c) *a "ootirrg

fluid flows in the annulus in opposite direction at

therateof0'1kg/sec(Cp:4KJ/kg"C)]fntoilentersthecooleratl80"Candleavesatg0"c while cooling tiquid enters the cooler at 30oC. Calculate the length of the pipe required

if heat transfer co-efficient from oil to tube surface is 1720 Wlm2oC and from metal surface

to coolant is 3450 W;;"C. Neglect the resistance of the tube wall' (10 Marks)

State and explain Fick's law of diffusion' ' (04 Marks)

Distinguish Uetween the nucleate boilin! and film boiling' ^ r^-n io pwn^sed

(06 Marls)

A vertical tube oi 60 mm outside ii*.t.t and f i m long is exposed to steam at

atmospheric pressure. The outer ,.rrfu". of the tube is maintained at a temperature of 50"c

iV,iiiJ"if"i cold *utrr through the tube' Calculate the following:

ii The raie of heat transfer to the coolant'

ii) The rate of condensation of steam' (10 Marks)

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Sixth Semester B.E. Degree Examination, June/July 2011

Heat and Mass Transfer

Time: 3 hrs. Max. Marks:100Note: l. Answer any FIVE full questions, selecting

at least TWO questions from each purt.2. (fse of IIMT data handbook permitted.

PART - Aa. Derive general 3-dimensional conduction equation in Cartesian co-ordinates. (0E Marks)

b. Write the mathematical fonnulation of one-dimensional, steady-state heat conduction for e

holiow sphere with constant thermal conductiyif in the region a I r { b, when hsat is

supplied to the sphere at a rate of 'qo' Wlmz from the boundary surface at r : a and

dissipated by convection from the boundary surface at r : b into a medium at zero

temperature with a heat transfer coefficient 'h'. (04 Marksi

c. A strearn pipe with internal and extemal diameters 18 cm and?l cm is covered with't'.volayers of-insulation each 30 mm thick with thermal conductivities 0.18 Wm"K a:rd

0.09 Wm.K. The differenee in temperature between inside and outside surfaces is 250"C.

Calculate the quantity of heat lost per meter length of the pipe if its thermal conductivity is60 Wm.K. What is the percentage error if the calculation is carried out considering the pipe

as a plane wall?

Clearly define i) F'in effieiency and ii) Fin effectiveness.llerive an expression for rate of heat transfer and temperature distribution for a ptraae wall

with variable thermal conduetivity. (S8 Mnrks)

c. Thin fins of brass whose K = 75 Wlm.K are welded longitudinally on a 5 sm diameter hrass

cylinder which stands vertically and is surrouuded by air at 20oC. The heat hanrfercoefficient from metal surface to the air is 17 Wlm2.K. If 16 uniforrnly spaced fins are used

each 0.8 mm thick and extending 1.25 ern from the cylinder, what is the rate of heat transfer

from the cylinder per meter length to the air when the cylinder surface is maintained at

1500c?

3 a. Define i) Biot number and ii) Fourier nurnber.

b. Show that the temperature distribution under lumped analysis is given by,

where To is the initial ternperature and T- is the surrormding temperature.c. A long cylinder 12 crn in diameter and initially at zA"C is placed into a furnace at 820"C

with locai heat transfer coefFrcient of 140 Wm2"K. Calculate the time required for the axis

temperature to reach 800'C. Also calculate the corresponding temperature at a radius of5.4 cm at that time. Take cr: 6.11x10-6 mzls, K:21 Wm.K. (08 Marks)

4 a. Using Buckingham n theorem, obtain a relationship between Nu, Pr and Gr for free

convection heat transfer. (08 Marks)

Explain the development of hydrodynamic boundary layer for flow over a flat swface.(06 Marks)

Considering the body of a man as a vertical cylinder of 300 mm diameter and 170 cm height,

calculate the heat generated by the body in one day. Take the body temperature as 36oC and(06 Marks)atmospheric temperature as 14oC.

1 of 2

VI f

5a.

b.

6a.b.

c.

7a.b.c.

8a.

b.

06ME65

3f.1',:[fll.,ffift"#ffiilHt:, iii) Nussert number iv) stanton number.(08 Marks)

50 kg of water per minute is heated from 30oC to 50oC by passing through a pipe of 2 cm

diameter. The pipe is heated by condensing the steam on its surface at 100oC. Find the

lenglh of the pipe required. Take for water at 90oC, p = 965 kglm3, K : 0.585 Wm.K,Co:4200 Jlkg.K and y: 0.33x10{ m2ls. (06 Marks)

c. Air at a temperature of 20oC flows through a rectangular duct with a velocity of 10 m/s. The

duct is 30cm x20cm in size and air leaves at 34C. Find the heat gain by air when it is

With proper assumptions derive an expression for LMTD for a parallel flow heat exchanger.(08 Marls)

A heat exchanger has an effectiveness of 0.5 when the flow is counter and the thennal

capacity of one fluid is twice that of the other fluid. Calculate the effectiveness of the heat

exchanger if the direction of flow of one of the fluids is reversed with the same mass flow

passed through 10m long duct.

Give the classification of heat exchangers with relevant sketches.

rate as before.

With a neat diagram explain the regimes of pool boiling.With proper notations and sketch define Fick's law of difftrsion"

(06 Marks)

(06 Marla)

(06 Marks)

(0E Marks)(05 Marlis)

A vertical cooling fin approximates a flat plate of 40 crn height and is exposed to saturated

steam at 100'C (hre = 2257 ktlkg). The fin is maintained at a temperature of 90oC. Calculate,

i) Thickness of film at bottom of fin.ii) Average heat transfer coefficient andiii) Heat transfer rate after incorporating Mc Adarn's correction.

Takethefollowingproperties: p:965.3kd*';K-=0.68Ww.Kandlr:3.153x104kg/m.s(07 &Iarks)

Cleariy detine:i) Black body ii) Planck's law iii) Wein's displacement law iv) Lambert's lawv) View f'actor vi) Radiation shield. (09 Marks)

It is desired to calculate the net radiant heat exchange between the floor of a furnace 4mx2.m

and a side n'all 3mx2m. The emissivity of the floor material is 0.63 and that of the side wall

material is 0.2. If the temperature of the floor and side wall are 600oC and 400"Crespectively. Calculate the net heat exchange between them. (05 Marks)

Two large parallel planes with emissivity 0.6 are at 900 K and 300 K. A radiation shieldwith one side polished and having emissivity of 0.05 and the other side unpolished withemissivity of 0.4 is proposed to be used between them. Which side of the shield should face

the hotter plane, if the temperature of the shield is to be kept minimum? Justify r"i#il:b

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Time: 3 hrs.

la.

b.

2a.b.

c.

Explain briefly: i) Thermal conductivity ii) Thermal diffrrsivity iii) Thermal contact

resistance. (06 Mar\<s)

The walls of a house in cold region consist of three layers, an outer brick'work 15 cm thiik,an inner wooden panel 1.2 cmthick, the intermediate layer is made of an insulating material

7 cm thick. The thermal conductivity of brick and wood are A.7 Wink and 0.18 Wlmk

respectively. The inside and outside temperatures of the composite wall are 21"C and -15"C

respectively. If the layer of insulation offers twice the thermal resistance of the brick wall,calculate,i) Heat loss per unit area of the wall.ii) Thermal conductivity of insulating material.

Sixth Semester B.E. Degree Examination, December 2010

Heat and Mass TransferMax- Marks:100

Note: l. Answer any FIVE full queslions, selecting at leasttwo questions from each Part.

2. Use of heat transfer data hand book is permitted.

PART _ A

(06 Marks)

An insulated stearn pipe having outside dihmeter of 30 mm is to be covered-.with two layers

of insulationo each having a thickness of 20 mm. The thermal conductivity of onematefial is

3 times that of the other. Assuming that the inner and outer surface temperatures ofcomposite insulation are fixed, how much heat transfer will be increasbd when the better

insulation material is next to the pipe than when it is at the outer layer? (08 Marks)

Define fin efficiency and fin effectiveness with respect to a fin with insulated tip. (04 Marks)

What is the physical significance of critical thickness of insulation? Derive an expression forcritical thickness of insulation for a sphere. (06 Marks)

The handle of a ladle used for pouring molten metal at 327"C is 30 cm long and is made of2.5 cm x 1.5 cm mild steel bar stock (K: 43 W/mK). In order to reduce the grip temperature

it is proposed to make a hollow handle of mild steel plate of 0.15 cm thick to the same

rectangular shape. If the surface heat transfer coeffrcient is 14.5 Wlm'zrc and the ambient

temperaflre is at 27'C, estimate the reduction in the temperature of grip. Neglect the heat

transfer from the inner surface of the hollow shape. (10 Marks)

3 a. Obtain an expression for instantaneous heat kansfer and total heat transfer for lumped heat

b.

c.

analysis treatment of heat conduction problems.Explain the physical significance of Biot number and Fourier number.

(08 Marks)(04 Marks)

An aluminium sphere weighing 5.5 kg and initially at a temperature of 290"C is suddenly

immersed in a fluid at 15"C. The convective heat transfer coefficient is 58 Wlm2K. Estimate

the time required to cool the aluminium to 95"C using the lumped capacity method ofanalysis (For aluminium, p:2700 kg/*', C : 900 JlkgK, K: 205 W/mK) (08 Marks)

4 a. What do you mean by hydrodynamic and thermal boundary layer? How does the ratio $or

vary with prandtl number? (06 Marks)b. Using Buckingham's ,r-theorem, obtain the relationship between various non-dimensional

numbers for free convection heat transfer. (08 Marks)c. Air at 20"C flows over a thin plate with a velocity of 3 m/sec. The plate is 2 m long and 1 m

wide. Estimate the boundary layer thickness at the trailing edge of the plate and the totaldrag force experienced by the plate.

I of2

(06 Marks)

5a.

6a.

b.

c.

06.i\/IE65

PART - B

Water at 25oC flows through a tube of 50 mm diameter. Determine the flow rate that will

result in a Reynolds number of 1600. The tube is provided with a nichrome heating element

on its surface and receives a constant heat flux of 800 Wm length of the tube. Determine the

average heat transfer coefficient between the water and the tube wall, assuming fully

develiped conditions. Also determine the length of the tube for the bulk temperature of

water to rise from 25oC to 50oC' (12 Marks)

Air stream atZT,C moving at 0.3 m/sec across 100 w incandescent bulb glowing at 127"C.

If the bulb is approximated by a 60 mm diameter sphere, estimate the heat transfer rate and

the percentage of power lost due to convection. Use correlation Nu : 0'37 Rli ' (08 Marks)

Define effectiveness and NTU of a heat exchanger. Explain why minimum heat capacity

value is used in the definition of effectiveness for the maximum possible rate of heat

transfer. (04 Marks)

Derive an expression for LMTD in case of parallel flow heat exchanger stating the

assumptions made. (08 Marks)

A counter flow heat exchanger is employed to cool 0.55 kg/sec (Cp : 2.45kJ/kgK) of oil

from il5oC to 40"C by the use of water. The inlet and outlettemperature of cooling water

are 15oC and 75oC respectively. The overall heat transfer coefficient is expected to be

1450 Wm2oC. Using NTU method, calculate the following:i) The mass flow rate of water.ii) The effectiveness ofheat exchanger.

iii) The surface area required'

Explain :

i) Filmwise condensation and dropwise condensation.

ii) Subcooled boiling and saturated boiling. (06 Marks)

A square array of 400 tubes 15 mm outer diameter is used to condense steam at atmospheric

pr.rr*". The tube walls are maintained at 88oC by a coolent flowing through the tubes.

Calculate the amount of steam condensed per hour per unit length of the tubes' (08 Marks)

ti

b.

la.

b.

c.

8a.

b.

State and explain Fick's law of diffusion.

For a black body enclosed in a hemispherical

body is rc time the intensity of radiation.State and explain:i) Kirchoffls law.ii) Planck's law.iii) Wein's displacement law.iv) Lambert's cosine law.Explain briefly the concept of a black body.

(08 Marks)

(06 Marks)

space show thit emissive power of the black(08 Marks)

(08 Marks)(04 Marks)c.

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