Heat and mass transfer


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Heat and mass transfer

  1. 1. II USN 06ME6s Sixth Semester B.E. Degree Examination, December 2Ol2 Heat and Mass Transfer Time: 3 hrs Max. Marks:100 Note: l. Answer FIW full questions, selecting o ut least TWO questionsfrom eaclt part. .9 o 2. Use of IIMT duta book is permitted. 6 a. tr PART _ A o I a. Starting from fundamental principles, derive the general, three-dimensional heat conduction a equation in Cartesian co-ordinates. (09 Marks) o b. A liquid at 100C 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 40C. The inner and outer convective heat transfer coefficients are 300 Wm2K and 5 Wm2K dU 4 respectively. Calculate the overall heat transfer coefficient and the heat loss per unit length co cco of pipe. (08 Marks) .E c.l c. What is the technical need to under take a detailed study of heat transfer, having studied thermodynam ics already? (03 Marks) OE rh_ 2 a. A tube with an outer diameter of 20 mm is covered with insulation. The thermal o2 conductivity of insulating material is 0.18 WmK. The outer surface losses heat by a: convection with a heat transfer coefficient of 12 Wim2K. Determine the critical thickness of oO insulation. Also calculate the ratio of heat loss liom the tube with critical thickness of insulation to that from the bare tube (without insulation). (10 Marks) .- 50= !q b Derive the one-dimensional fin equation for a fin of uniforrn cross section. By integrating the fin equation, obtain the expression for the temperature variation in a long fin. (t0 Marks) -o6 Z,U 3 a. Consider a solid, with an uniform initialtemperature, suddenly immersed in a liquid. Derive the relevant governing differential equation, considering the system as lumped. By solving -x the differential equation, obtain the expression for the temperature variation with time. -= c. o.. (t0 Marks) i.2 b. A 50 mm thick iron plate (K:60 WmK, Cp:460 J/kg K, p:7800kgim3,66: 1.6x10-sm/s) o1. is initially at 225"C. Suddenly both surfaces are exposed to a fluid at 25"C, with a heat -c JE transfer coefficient of 500 Wm2K. Calculate the centre and the surface temperatures >r: 2 minutes after the cooling begins using Heislers charts. (10 Marks) bo- o- :1 4 a. The velocity profile for boundary layer flow over a flat plate is given by, =o 5L u(x v) 1 - I , - i{=l}, DBo* L< = where boundary layer thickness E(x) = l . Develon an -6i u. 26(x) Z[6txl] ! l3u- o expression for local drag coefficient. Also develop an expression for average drag Z coefficient for a length of L. (10 Marks) f G b. Consider a square plate of size 0.6 m in a room with stagnant air at20C. One side of plate o o. is maintained at 100"C, while the other side is adiabatic. Deterrnine the heat loss if the plate E is, i) vertical and ii) horizontalwith hot surface facing up. (I0 Marks) I of2
  2. 2. a L 06ME65 PART _ B 5 a. Air at 0C 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) b. Air at -20"C and 30 m/s, flows over a sphere of diameter 25 mm, which is maintained at 80C. Calculate the heat loss Ilom sphere. (08 Marks) 6a. Derive an expression for the logarithmic mean temperature difference (LMTD) for a parallel flow heat exchanger 02 Marks) b. 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) 7a. 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) b. Water at atmospheric pressure and saturation temperature is boiled in a 250 mm diameter, polished stainless steel pan, which is maintained at 116C. Calculate the heat flux and the evaporation rate. (10 Marks) 8a. State and prove Kirchoff s law of radiation. (06 Marks) b. Two large parallel plates with emissivities 0.5 and 0.8 are maintained at 800 K and 600 K respectively. 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)itI c. Determine the view factors from the base of a cube to each of its five surfaces. (06 Marks)I ***rr* 2 of2
  3. 3. USN 06ME6s Sixth semester B.E. Degree Examination, Decemb er zoll, Heat and Mass Transfer Time:3 hrs. Max Marks:100 Note:l. Answer any FrvE fult questions, selecting at least TWO questionsfrom each part. 2. Use of heat transfer data hand book is permitted. PART _ A la. Explain briefly: i) Thermal conductivity ii) Thermal diffusivity o o iii) overall heat transfer co-efficient. (06 Marks) o b.Derive the general three dimensional conduction equation in Cartesian co-ordinates and 6 state a ft, the assumptions made (08 Marks) c. A square plate heater of size 20 cms x 20 cms is inserted between d two slabs. Slab .A, is E () 3 cms thick (K: 50 wmK) and slab B is 1.5 cms (K: 0.2 wmK). The outside heat 6 () transfer co-efEcients on both sides of A and B are 200 and 50 W-/m2K respectively. 3e Temperature of surrounding air is 25c. If the rating of the heater is I kw, find Maximum temperature in the system" ii) Outer surface temperature of two slabs. o= &. ! ao xr} Draw the equivalent circuit for the system. (06 Marks) bo" coQ 2a. Derive an expression for the temperature distribution for a long pin of uniform cross section .=N dt without insulated tip. (to Marks) d b. A rod (K:200 wlmK) 10 mm in diameter and 5 cms long has its 9.0 one end maintained at 6)C() 100oC The surface of the rod^is exposed to ambient wr at 30"C with convective su -d heat o> transfer co-efficient of 100 wmrK. Assuming other end insulated, determine Ee i) The temperature of the rod at 25 mm distance from the end at 100.c. qa 6= iD Heat dissipation rate from the surface of the rod and bU iii) Effectiveness. (10 Marks) (go o.o ootr 3a. Explain physical significance of Biot number and Fourier number. (04 Marks).gd b. Oblain an expression for instantaneous heat transfer and total heat transfer for lumped heat .d .i anal-vsis treatment of heat conduction problem. (08 Marks)"lJ cd c. A 15 mm diameter mild steel sphere K:42 WmoC,1 ts is exposed to cooling air flow atZ1"C 5E resulting in the convective co-efficient h=120 Wm2oC. d" g- Deterrnine the following: tro- 6cs o-t 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 dir!6 =qlE : p 7850 kg/ri CpI 475: J/kg.C; : c, 0.045 #m (08 Marks)d.:(BE59 4a.A.=boo what do you rnean by hydrodynamic and thermar boundary layer? (04 Marks)cbo b. Explain physical significance ofp. i) Grashoff number ii) prandtl number iii) Nusselt numbertrte;=in5L iv) Reynolds number (oE Marks) -x,J< A nuclear reactor with its core constructed of parallel vertical plates 2.2 mhigh and 1.4 m .;< c.l rvide has been designed on free convection hcating of liquid bismuth. The maximum{) temperafcre of the plate srirface is limited to 950"C w-hile the low-est allowable temperafur-eo of bismuth is 340oC. Calculate the maximum possible heat dissipation from both sides ofzd each plate. For the convective co-efficient the appiopriate correlation isLo" N, = 0.13(Gr.Pr)o333 . (08 Marxsy I of2
  4. 4. 06ME6s PART _ B which relates Reynolds number5 a. with the help of dimensional *urvri, derive expression (10 Marks) Nusselt number and Prandtl number n L - at 3 m/sec The flows over a flat plate b. Air at standard conditions of 760 mm of Hg at 20oC if air flow is parallel to 50 cms side of fto* plate is 50"; x 25 cms . Find the-heat losiper to ttr. air flow, what will be the effect on heat the plate. tiis side is kd;;;i.l "*, tht plate is 100"C transfer? T.;;;t;f (l0Marks) 6a.DeriveanexpressionforLMTDforcounterflowheatexchanger.Statetheassumptions (10 Marks) with in a pipe b. tltii, cooler consists of straight tube of 2 cms oD and 15 cm ID enclosed the tube at and co-centric with it. The external pip. it welt insulated The oil flows through direction at : fluid flows in the annulus in opposite 0.05 kg/sec (cp z rlttg"c) *a "ootirrg therateof01kg/sec(Cp:4KJ/kg"C)]fntoilentersthecooleratl80"Candleavesat the length of the pipe required g0"c while cooling tiquid enters the cooler at 30oC. Calculate is 1720 Wlm2oC and from metal surface if heat transfer co-efficient from oil to tube surface of the tube wall (10 Marks) to coolant is 3450 W;;"C. Neglect the resistance (04 Marks) 7a. State and explain Ficks law of diffusion (06 Marls) Distinguish Uetween the nucleate boilin! and film boiling b. outside ii*.t.t ^ long is pwn^sed and f i m r^-n io exposed to steam at c. A vertical tube oi 60 mm of 50"c atmospheric pressure. The outer ,.rrfu". of the tube is maintained at a temperature iV,iiiJ"if"i cold *utrr through the tube Calculate the following: ii The raie of heat transfer to the coolant (10 Marks) ii) The rate of condensation of steam (04 Marks) 8a. Explain briefly the concept of a black body b. State and exPlain, i) Kirchoff s law. ii) Plancks law. iiD Weins displacement law. (08 Marks) iv) Lamberts cosine law pil unit area ior two large parallel plates at Calculate the net radiant heat exchange €hotpl,t"=09,€"otapl",.=06- If a polished tr. temperature of 427C and 27"C r.rpJ.tiraty. the percentage reduction in the heat transfer aluminium shierd is placed between them. Find (08 Marks) e.*",0=004 ,r***!r 7 ofZ
  5. 5. USN 06ME6s Sixth Semester B.E. Degree Examination, June/July 2011 Heat and Mass Transfer Time: 3 hrs. Max. Marks:100 Note: l. Answer any FIVE full questions, selecting at least TWO questions from each purt. 2. (fse of IIMT data handbook permitted. d PART -A o P o a. Derive general 3-dimensional conduction equation in Cartesian co-ordinates. (0E Marks) L a 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 CI E a cd supplied to the sphere at a rate of qo Wlmz from the boundary surface at r : a and 6) dissipated by convection from the boundary surface at r : b into a medium at zero {) A^ .€ L temperature with a heat transfer coefficient h. (04 Marksi ox c. A strearn pipe with internal and extemal diameters 18 cm and?l cm is covered witht.vo O-!? layers of-insulation each 30 mm thick with thermal conductivities 0.18 Wm"K a:rd H(" 0.09 Wm.K. The differenee in temperature between inside and outside surfaces is 250"C.-h;ri doo Calculate the quantity of heat lost per meter length of the pipe if its thermal conductivity is.: ol (lt 60 Wm.K. What is the percentage error if the calculation is carried out considering the pipe l= bI) as a plane wall? (0S lvlarks) Y{) oC--E 6) a,r 6F 9?a 2a. Clearly define i) Fin effieiency and ii) Fin effectiveness. (0{ }far}s} b. llerive an expression for rate of heat transfer and temperature distribution for a ptraae wall with variable thermal conduetivity. (S8 Mnrks) BE bU (f0 c. Thin fins of brass whose K = 75 Wlm.K are welded longitudinally on a 5 sm diameter hrass-L cylinder which stands vertically and is surrouuded by air at 20oC. The heat hanrfer b0tr c!e coefficient from metal surface to the air is 17 Wlm2.K. If 16 uniforrnly spaced fins are usediL -o >9 each 0.8 mm thick and extending 1.25 ern from the cylinder, what is the rate of heat transfer eGt G{ from the cylinder per meter length to the air when the cylinder surface is maintained at xi 1500c? (08 Illarks) oe 6d 48.=d tro. 3 a. Define i) Biot number and ii) Fourier nurnber. (04 Marlis) oj T-L 69 L.4 9E b. Show that the temperature distribution under lumped analysis is given by, T, *L =e-Bilo. atE d.t l-O where To is the initial ternperature and T- is the surrormding temperature. (08 Marks) IE >i +r c. A long cylinder 12 crn in diameter and initially at zA"C is placed into a furnace at 820"C boo with locai heat transfer coefFrcient of 140 Wm2"K. Calculate the time required for the axis C ot) 6: *o = temperature to reach 800C. Also calculate the corresponding temperature at a radius of tr> Wm.K. xt) 5E 5.4 cm at that time. Take cr: 6.11x10-6 mzls, K:21 (08 Marks)(r<je.i 4 a. Using Buckingham n theorem, obtain a relationship between Nu, Pr and Gr for free o !U convection heat transfer. (08 Marks)Z b. Explain the development of hydrodynamic boundary layer for flow over a flat swface.o (06 Marks) d L a c. 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 atmospheric temperature as 14oC. (06 Marks) 1 of 2
  6. 6. VI 06ME65 f 5a. 3f.1,:[fll.,ffift"#ffiilHt:, iii) Nussert number iv) stanton number.(08 Marks) b. 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 passed through 10m long duct. (06 Marks) 6a. Give the classification of heat exchangers with relevant sketches. (06 Marla) b. With proper assumptions derive an expression for LMTD for a parallel flow heat exchanger. (08 Marls) c. 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 rate as before. (06 Marks) 7a. With a neat diagram explain the regimes of pool boiling. (0E Marks) b. With proper notations and sketch define Ficks law of difftrsion" (05 Marlis) c. A vertical cooling fin approximates a flat plate of 40 crn height and is exposed to saturated steam at 100C (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 and iii) Heat transfer rate after incorporating Mc Adarns correction. Takethefollowingproperties: p:965.3kd*;K-=0.68Ww.Kandlr:3.153x104kg/m.s (07 &Iarks) 8a. Cleariy detine: i) Black body ii) Plancks law iii) Weins displacement law iv) Lamberts law v) View factor vi) Radiation shield. (09 Marks) b. It is desired to calculate the net radiant heat exchange between the floor of a furnace 4mx2.m and a side nall 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"C respectively. 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 shield with one side polished and having emissivity of 0.05 and the other side unpolished with emissivity 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 *!t,1.*rt 2 ofZ
  7. 7. rf USN Sixth Semester B.E. Degree Examination, December 2010 06M865 Heat and Mass Transfer Time: 3 hrs. Max- Marks:100 Note: l. Answer any FIVE full queslions, selecting at least two questions from each Part. 2. Use of heat transfer data hand book is permitted. PART _ A la. Explain briefly: i) Thermal conductivity ii) Thermal diffrrsivity iii) Thermal contact o o o resistance. (06 Mar<s) b. The walls of a house in cold region consist of three layers, an outer brickwork 15 cm thiik, c, an inner wooden panel 1.2 cmthick, the intermediate layer is made of an insulating material d !o 7 cm thick. The thermal conductivity of brick and wood are A.7 Wink and 0.18 Wlmk (;) B 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, 3H calculate, ;3 i) Heat loss per unit area of the wall. dU ii) Thermal conductivity of insulating material. (06 Marks) bo trop ll An insulated stearn pipe having outside dihmeter of 30 mm is to be covered-.with two layers .= (-.l 6r+ of insulationo each having a thickness of 20 mm. The thermal conductivity of onematefial is b?p 3 times that of the other. Assuming that the inner and outer surface temperatures of IDE -.c() composite insulation are fixed, how much heat transfer will be increasbd when the better o> insulation material is next to the pipe than when it is at the outer layer? (08 Marks) 3z 2a. Define fin efficiency and fin effectiveness with respect to a fin with insulated tip. (04 Marks) da b. What is the physical significance of critical thickness of insulation? Derive an expression for bd critical thickness of insulation for a sphere. (06 Marks) (dO o"6 c. The handle of a ladle used for pouring molten metal at 327"C is 30 cm long and is made of 50d cO .d -oB 2.5 cm x 1.5 cm mild steel bar stock (K: 43 W/mK). In order to reduce the grip temperature >9 d< it is proposed to make a hollow handle of mild steel plate of 0.15 cm thick to the same -r, Cd rectangular shape. If the surface heat transfer coeffrcient is 14.5 Wlmzrc and the ambient -4(.) EO Crr temperaflre is at 27C, estimate the reduction in the temperature of grip. Neglect the heat ,o transfer from the inner surface of the hollow shape. (10 Marks) =d o. o. tro. o .-t 3 a. Obtain an expression for instantaneous heat kansfer and total heat transfer for lumped heat analysis treatment of heat conduction problems. (08 Marks) gE ,o lE ea b. Explain the physical significance of Biot number and Fourier number. (04 Marks) FE L (L} c. An aluminium sphere weighing 5.5 kg and initially at a temperature of 290"C is suddenly 5E xe bo- immersed in a fluid at 15"C. The convective heat transfer coefficient is 58 Wlm2K. Estimate <oo the time required to cool the aluminium to 95"C using the lumped capacity method of analysis (For aluminium, p:2700 kg/*, C : 900 JlkgK, K: 205 W/mK) 6J= o- ei (08 Marks) tr> =o UL ->r 4 a. What do you mean by hydrodynamic and thermal boundary layer? How does the ratio $ lJ< or .i c.i vary with prandtl number? (06 Marks) {) Z o b. Using Buckinghams ,r-theorem, obtain the relationship between various non-dimensional numbers for free convection heat transfer. (08 Marks) rO 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 o. wide. Estimate the boundary layer thickness at the trailing edge of the plate and the total drag force experienced by the plate. (06 Marks) I of2
  8. 8. 06.i/IE65 PART -B that will5a. Water at 25oC flows through a tube of 50 mm diameter. Determine the flow rate element result in a Reynolds number of 1600. The tube is provided with a nichrome heating 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 t develiped conditions. Also determine the length of the tube for the bulk temperature of i water to rise from 25oC to 50oC (12 Marks) b. 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 037 Rli (08 Marks) capacity6a. Define effectiveness and NTU of a heat exchanger. Explain why minimum heat value is used in the definition of effectiveness for the maximum possible rate of heat (04 Marks) transfer. b. Derive an expression for LMTD in case of parallel flow heat exchanger stating the assumptions made. : (08 Marks) c. 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. (08 Marks) iii) The surface area requiredla. Explain : i) Filmwise condensation and dropwise condensation. ii) Subcooled boiling and saturated boiling. (06 Marks) b. 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) (06 Marks) State and explain Ficks law of diffusion. c.8a. For a black body enclosed in a hemispherical space show thit emissive power of the black (08 Marks) body is rc time the intensity of radiation. b. State and explain: i) Kirchoffls law. ii) Plancks law. iii) Weins displacement law. (08 Marks) iv) Lamberts cosine law. c. Explain briefly the concept of a black body. (04 Marks) **{.*{< 2 ofZ