3-1 ht [nov 2009 regular]

Code No: V3114/R07 Set No. 1

III B.Tech I Semester Regular Examinations, November 2009HEAT TRANSFER

(Mechanical Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

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1. (a) How do the temperature distributions in a solid vary it its thermal conductivityvarious linearly with temperature?

(b) A thin metallic plate is insulated at the back surface and is exposed to the sunat the front surface. The front surface absorbs solar radiation at 900 W/m 2

and dissipates in mainly by convection to the ambient air at 30 0C. If the heattrasfer coefficient between the plate and the air is 15 W/m2 K, what is thetemperature of the plate? [6+10]

2. (a) Derive an expression for 1- Dimensional, steady state heat conduction state,with internal heat generation for plane wall.

(b) Nichrome, having a resistivity of 100µΩ-cm is to be used as a heating elementin a 10kW heater. The Nichrome surface temperature should not exceed12200C. Other design features include surrounding air temperature is 200C,Outside surface coefficient is 1.15 kW/m3k, Thermal conductivity of Nichrome=- 17 W/mk. Find out which diameter Nichrome wire is necessary for a 1meter long heater. Also find the rate of current flow. [8+8]

3. (a) What are Biot and Fourier numbers? Explain their physical significance.

(b) A slab of Aluminum 10cm thick is originally at a temperature of 5000C. It issuddenly immersed in a liquid at 1000C resulting it a heat transfer coefficientof 1200 W/m2k. Determine the temperature at the centerline and the surface1 min after the immersion. Also the total thermal energy removal per unit areaslab during this period. The properties of aluminum for the given conditionare: α = 8.4 × 10−5m2 /s, K=215 W/mk, ρ = 2700 kg/m3, Cp= 0.9 kJ/kg.

[6+10]

4. (a) Derive momentum equation for hydrodynamic boundary layer over a flat plate.

(b) Show by dimensional analysis for free convection Nu= f(Pr, Gr). [8+8]

5. (a) What is the criterion for deciding laminar or turbulent flow in case of freeconvection?

(b) Air flow through a long rectangular duct (30 cm × 20 cm) used in air condi-tioning maintains the outer duct surface temperature at 5oC. If the duct isinstalled vertically in a room at 25oC, find the heat gain by the duct. [4+12]

6. Air free saturated steam at 65oC condenses on the outer surface of a 25 mm outerdiameter 3m long vertical tube maintained at a uniform temperature of 35oC byflow of cooling water through the tube. Assuming film condensation and 20% in

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excess of Nusselt’s value calculate the average heat transfer coefficient over theentire length of the tube and the rate of condensate flow at the bottom of the tube.Confirm that the flow is laminar. [16]

7. Water flowing at the rate of 12.6 kg/s is to be cooled from 90oC to 65oC by meansof an equal flow rate of cold water entering at 40oC. The water velocity will besuch that the overall coefficient of heat transfer U is 2300 W/m2K. Calculate theheat exchanger surface area needed for each of the following arrangements.

(a) Parallel flow

(b) Counter flow

(c) A multipass heat exchanger with the hot water making one pass through awell baffled shell and the cold water making two tube passes through the tubesand

(d) A cross flow heat exchanger with both sides unmixed. [16]

8. (a) What is the shape factor with respect to itself if the surface is concave, convexor flat?

(b) Show that for two infinite parallel gray planes exchanging radiant energy, the

mean emissivity is given by[

1/

(

1

ε1+ 1

ε2− 1

)

]

. [6+10]

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1. (a) State Fourier‘s law of heat conduction. Why is the negative sign used.

(b) A fluid at an average temperature of 200 0C flows through a plastic pipe(k=0.5 W/m K) of 4 cm outer diameter and 3 cm inner diamenter. If the heattransfer coefficient at the inside is 300 W/m2 K and that the outer surface is10 W/m2 K, and if the pipe is located in a room at 300C, find the heat lossper unit length of pipe. [16]



3. (a) What are Biot and Fourier numbers? Explain their physical significance.

(b) A slab of Aluminum 10cm thick is originally at a temperature of 5000C. It issuddenly immersed in a liquid at 1000C resulting it a heat transfer coefficientof 1200 W/m2k. Determine the temperature at the centerline and the surface1 min after the immersion. Also the total thermal energy removal per unit areaslab during this period. The properties of aluminum for the given conditionare: α = 8.4 × 10−5m2 /s, K=215 W/mk, ρ = 2700 kg/m3, Cp= 0.9 kJ/kg.

[6+10]

4. (a) Define

i. Boundary layer thickness

ii. Nusselt number and

iii. Prandtal number .

(b) Air is flowing over a flat plate 5m long and 2.5 m wide with a velocity of4m/sec and 150C. If ρ=1.21 kg/m3 and ν=1.47 × 10−5 m2/sec. Calculate:

i. Length of the plate over which the boundary layer is laminar and thicknessof boundary layer (laminar).

ii. Shear stress at the location where boundary layer ceases to be laminar,and

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iii. Total drag force on the both sides on that portion of the plate whereboundary layer is laminar. [6+10]

5. Find the location and magnitude of maximum velocity in the boundary layer formedon heated or cooled vertical plate. [16]

6. (a) What is Leidenfrost point? What is its significance?

(b) Water at saturation temperature and atmospheric pressure is boiled in thestable film boiling regime with an electrically heated, horizontal platinum wireof diameter 1.27 mm. Calculate the surface temperature necessary to producea heat flux of 150 kW/m2 [6+10].

7. A shell and tube heat exchanger is to heat 10,000 kg/h of water from 16oC to84oC by hot engine oil flowing through the shell. The oil makes a single shell pass,entering at 160oC and leaving at 94oC, with an average heat transfer coefficient of400 W/m2K. The water flows through 11 brass tubes of 22.9 mm inner diameterand 25.4 mm of outer diameter, with each tube making four passes through theshell. Assuming fully developed flow for the water, find the required tube lengthper pass. [16]

8. (a) What is shape factor? Show that A1F12 = 1/θ∫

A1

∫A2

[(Cos θ1 Cos θ2) / r2]dA1 dA2.

(b) State and explain the reciprocity theorem. [10+6]

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1. (a) Write Fourier‘s heat conduction equation and explain each term along withtheir units.

(b) A pipe with a diameter of 2 cm is kept at a surface temperature of 40 0C. Findthe heat transfer rate per m length of this pipe if it is

i. Placed in an air flow in which the temperature is 50 0C and

ii. placed in a tank of water kept a temperature of 30 0C. The heat transfercoefficient in these two situations, which involve

A. forced convectiion in air and

B. free convection in water, are estimated to be 20 W/m2 K and 70 W/m2

K respectively. [6+10]



3. (a) A large slab of aluminum at a uniform temperature of 2000C is suddenlyexposed to a convective surface environment of 700C with a heat transfercoefficient of 525 W/m2k.Estimate time required for a point 4cm from thesurface to come up to a temperature level of 1200C.(Take k = 215 W/mk, α = 8.4 ×10−5 m2/s).

(b) A 40×40 cm copper slab 5mm thick at a uniform temperature of 2500C. Sud-denly has its surface temperature lowered to 300C. Find the time at which theslab temperature becomes 900C, ρ = 9000 kg/m3, Cp = 0.38 kJ/kg.k, K =370 W/mk and h = 90 W/m2k. [8+8]

4. (a) Derive momentum equation for hydrodynamic boundary layer over a flat plate.

(b) Show by dimensional analysis for free convection Nu= f(Pr, Gr). [8+8]

5. Show that for laminar flow of air (Pr = 0.714), the local and average values ofNusselt number for natural convection heat transfer from or to a vertical plate aregiven byNux = 0.378 Gr

1/4

x ; NuL = 0.504Gr1/4

L . [16]

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6. Saturated steam at 1.46 bar and 110oC condenses on a 25 mm outer diametervertical tube which is 50 cm long. The tube wall is maintained at 100oC. Calculatethe average heat transfer coefficient and the rate of condensation. Check that thecondensate flow is laminar. The properties of the condensate at 105oC are K= 0.68W/m K, ρ = 954.7 kg/m3, µ = 0.271× 10−3 kg/ms and hfg = 2243.7 kJ/kg. [16]

7. Oil with a specific heat of 2 kJ/kg K is cooled from 110oC to 70oC by a flow ofwater in a counter flow exchanger. Water flows at the rate of 2 kg/s and is heatedfrom 35oC to 65oC. The overall heat transfer coefficient is estimated to be 0.37kW/m2K. Determine the exit temperatures of oil and water, if the water flow ratedrops to 1.5 kg/s at the same oil flow rate. Take cp of water as 4.18 kJ/kg K. [16]

8. Three thin hollow cylinders of 100, 200 and 300 mm diameters are arranged con-centrically. If the inner (100 mm dia.) and the outer ( 300 mm dia.) cylinders aremaintained at 727oC and 27oC respectively, and assuming vacuum in the annularspaces, estimate the steady state temperature of the middle cylinder(200 mm dia.).Take ε1 = ε2 = ε3 = 0.05. Determine the rate of heat loss per meter length of thecomposite cylinder and the convective heat transfer coefficient on the outer surface,if the surrounding air temperature is 10oC. [16]

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1. (a) State Fourier‘s law of heat conduction. Why is the negative sign used.

(b) A fluid at an average temperature of 200 0C flows through a plastic pipe(k=0.5 W/m K) of 4 cm outer diameter and 3 cm inner diamenter. If the heattransfer coefficient at the inside is 300 W/m2 K and that the outer surface is10 W/m2 K, and if the pipe is located in a room at 300C, find the heat lossper unit length of pipe. [16]

2. (a) Sketch various types of fin configurations?

(b) Aluminum fins of rectangular profile are attached on a plane wall with 5 mmspacing. The fins have thickness 1 mm, length = 10 mm and the normalconductivity K = 200 W/mk. The wall is maintained at a temperature of2000C and the fins dissipate heat by convection into ambient air at 400C, withheat transfer coefficient = 50 W/m2k. Find the heat loss. [6+10]

3. (a) Explain the lumped heat capacity analysis?

(b) An aluminum sphere weighing 5.5kg and initially at a temperature of 2900C issuddenly immersed in a fluid at 150C. The convective heat transfer coefficientin 59 W/m2k. Estimate the time required to cool the aluminum to 950C.

[6+10]

4. (a) Using a linear velocity profile u/uα=y/δ, for flow over a flat plate, obtain anexpression for the boundary layer thickness as a functions of x.

(b) Air at 270C flows over a flat plate at a velocity of 2 m/s. The plate is heatedover its entire length to a temperature of 600C. Calculate the heat transfer forthe first 20 cm of the plate. [8+8]

5. Show that for laminar flow of air (Pr = 0.714), the local and average values ofNusselt number for natural convection heat transfer from or to a vertical plate aregiven byNux = 0.378 Gr

1/4

x ; NuL = 0.504Gr1/4

L . [16]

6. (a) When does a bubble grow or collapse as it moves up through the liquid?

(b) An electrically heated copper kettle with a flat bottom of diameter 25 cmis to boil water at atmospheric pressure at a rate of 2.5 kg/h. What is thetemperature of the bottom surface of the kettle? [6+10]

7. (a) In a gas to liquid heat exchanger, why are fins provided on gas side?

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(b) Determine the overall heat transfer coefficient based on the outer area of a3.81 cm O.D. and 3.175 cm I.D. brass tube ( k = 103.8 W/mK) if the heattransfer coefficients for flow inside and outside the tube are 2270 and 2840W/m2K respectively and the unit fouling resistances at inside and outside areRfi = Rfo = 0.0088m2K/W. [4+12]

8. A 10 cm OD steel pipe carrying steam at 4.905 ×105 Pa is lagged with 5 cmthick insulation. The surrounding air temperature is 27oC. The conductivity andemissivity of the insulating material are 0.14 W/mK and 0.92 respectively. If theheat transfer coefficient on the outer surface of lagged pipe is 11.63 W/m2K andneglecting the pipe resistance and internal boundary resistance, calculate

(a) Heat loss per meter of the pipe by convection

(b) Heat loss per meter of the pipe by radiation

(c) Radiation and overall heat transfer coefficients

(d) Rate of condensation for 50 m pipe length. [16]

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3-1 ht [nov 2009 regular]

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