Heat & Mass Transfer July, 2011 (2006 Scheme)

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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.

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

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Heat & Mass Transfer July, 2011 (2006 Scheme)

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