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Chapter 1 Comments 1 The Conversion Efficiency For Most
PROBLEM 1.47 KNOWN: Total rate of heat transfer leaving nacelle (from Example 1.3). Dimensions and emissivity of the nacelle, ambient and surrounding temperatures, convection heat transfer coefficient exterior to nacelle. Temperature of exiting forced air flow. FIND: Required mass flow […]
Chapter 1 Inner surface temperature and thermal conductivity
PROBLEM 1.1 KNOWN: Temperature distribution in wall of Example 1.1. FIND: Heat fluxes and heat rates at x = 0 and x = L. SCHEMATIC: PROPERTIES: Thermal conductivity of wall (given): k = 1.7 W/m·K. ANALYSIS: The heat flux in […]
Chapter 1 Plate is of uniform surface temperature
PROBLEM 1.58 KNOWN: Temperatures at 15 mm and 30 mm from the surface and in the adjoining airflow for a thick stainless steel casting. FIND: Surface convection coefficient, h. SCHEMATIC: ANALYSIS: From a surface energy balance, it follows that ′′ […]
Chapter 1 Potential Energy Storage Assumptions 1 Constant Properties
PROBLEM 1.19 KNOWN: Chip width and maximum allowable temperature. Coolant conditions. FIND: Maximum allowable chip power for air and liquid coolants. SCHEMATIC: ANALYSIS: All of the electrical power dissipated in the chip is transferred by convection to the coolant. Hence, […]
Chapter 1 The diminished performance and higher cost of
PROBLEM 1.33 KNOWN: Power plant and operating conditions of Example 1.7. Change in cold-side heat transfer surface area and convection heat transfer coefficient. FIND: Modified efficiency and power output. ASSUMPTIONS: (1) Steady–state conditions, (2) power plant operates as an internally […]
Chapter 10 Film condensation occurs in condensation section
ROBLEM 10.54 KNOWN: Thin-walled thermosyphon. Absorbs heat by boiling saturated water at atmospheric pressure on boiling section Lb. Rejects heat by condensing vapor into a thick film which falls length of condensation section Lc back into boiling section. FIND: (a) […]
Chapter 10 The Jakob number can be based on the liquid or vapor specific
PROBLEM 10.1 KNOWN: Water at 1 atm with Ts – Tsat = 8°C. FIND: Show that the Jakob number is much less than unity; what is the physical significance of the result; does result apply to ethylene glycol? PROPERTIES: Table […]
Chapter 10 The power requirement for boiling and the evaporation rate are
PROBLEM 10.13 KNOWN: Saturated ethylene glycol at 1 atm heated by a chromium-plated heater of 200 mm diameter and maintained at 480K. FIND: Heater power, rate of evaporation, and ratio of required power to maximum power for critical heat flux. […]
Chapter 10 The two operating conditions are shown on the boiling curve
PROBLEM 10.24 (Cont.) () ( ) 44 s sat rad s sat TT hTT εσ − =− () ( ) 4 44 2 rad 0.25 623 373 K h 7.4 W / m K 350 100 K − = = […]
Chapter 10 Whether flow regime would stay the same
PROBLEM 10.35 KNOWN: Vertical tube experiencing condensation of steam on its outer surface. FIND: Heat transfer and condensation rates. SCHEMATIC: ASSUMPTIONS: (1) Film condensation, (2) Negligible non-condensibles, (3) D/2 >> δ, vertical plate behavior. PROPERTIES: Table A-6, Water, vapor (1.0133 […]
Chapter 10 Substituting numerical values with the limits
PROBLEM 10.47 (Cont.) Substitute Eq. (3) into Eq. (1) for D h and recognize 32 ss 1 V / A D / D D / 6, 6 ππ = = o where the limits of integration have been identified, with […]
Chapter 11 A model was developed using the effectiveness
PROBLEM 11S.6 KNOWN: Single pass, cross–flow heat exchanger with hot exhaust gases (mixed) to heat water (unmixed) FIND: Required surface area. SCHEMATIC: ASSUMPTIONS: (1) Negligible heat loss to surroundings, (2) Negligible kinetic and potential energy changes, (3) Exhaust gas properties […]
Chapter 11 Geometry and operating conditions of tube bank
PROBLEM 11.13 KNOWN: The shell and tube Hxer (two shells, four tube passes) of Problem 11.12, known to have an area 4.75m2, provides 95°C water at the cold outlet (rather than 120°C) after several years of operation. Flow rates and […]
Chapter 11 Negligible Sensible Energy Change Phase Change Material
PROBLEM 11.33 (Cont.) Hence, 1 11 2 o i U h h 2003 W / m K − −− =+= ⋅ (b) If the tube-side convection coefficient is doubled, 2 i h 5008 W / m K= […]
Chapter 11 Oil cooling process approximates constant wall
PROBLEM 11.46 KNOWN: Engine oil cooled by air in a cross-flow heat exchanger with both fluids unmixed. FIND: (a) Heat transfer coefficient on oil side of exchanger assuming fully-developed conditions and constant wall heat flux, (b) Effectiveness, and (c) Outlet […]
Chapter 11 Our design process will involve the following steps
PROBLEM 11.58 KNOWN: Rankine cycle with saturated steam leaving the boiler at 2 MPa and a condenser pressure of 10 kPa. Net reversible work of 0.5 MW. FIND: (a) Thermal efficiency of ideal Rankine cycle, (b) Required cooling water flow […]
Chapter 11 Overall coefficient based upon the outer surface
PROBLEM 11.1 KNOWN: Overall heat transfer coefficient of clean boiler. Rate at which fouling factors on inner and outer tube surfaces increase with time. Percent reduction in overall heat transfer coefficient that corresponds to need for cleaning. FIND: Time after […]
Chapter 11 The UA product required for the chilling process
PROBLEM 11.23 KNOWN: Cooling milk from a dairy operation to a safe-to–store temperature, Th,o ≤ 13°C, using ground water in a counterflow concentric tube heat exchanger with a 50-mm diameter inner pipe and overall heat transfer coefficient of 1000 W/m2⋅K. […]
Chapter 11 Without accounting for the increase in the air
PROBLEM 11.68 (Cont.) [ ] 2 2 ,/( ) 0.003 m /(180 W/m K 0.02 m ) 0.042 K/W t b b hs R L kW= = ⋅× = min 3 ( )( 1) 8.89 m/s 0.015 m 0.0018 m […]
Chapter 12 Because the titanium has an emissivity that increases
PROBLEM 12.17 KNOWN: Isothermal enclosure of surface area, As, and small opening, Ao, through which 52W emerges. FIND: (a) Temperature of the interior enclosure wall if the surface is black, (b) Temperature of the wall surface having ε = 0.15. […]
Chapter 12 Opaque surface at steady-state temperature of
PROBLEM 12.1 KNOWN: Opaque, horizontal plate, well insulated on backside, is subjected to a prescribed irradiation. Also known are the reflected irradiation, emissive power, plate temperature and convection coefficient for known air temperature. FIND: (a) Emissivity, absorptivity and radiosity and […]
Chapter 12 Schematic Assumptions 1 Plate Opaque Diffuse And
PROBLEM 12.95 KNOWN: Plate temperature and spectral and directional dependence of its absorptivity. Direction and magnitude of solar flux. FIND: (a) Expression for total absorptivity, (b) Expression for total emissivity, (c) Net radiant flux, (d) Effect of cut-off wavelength associated […]
Chapter 12 Solar irradiation and associated blackbody temperature.
PROBLEM 12.73 (Cont.) ( ) 2 i 3 dT 4 W 15.4 1500 300 K kg J dt mK 8933 385 0.01m kg K m = − ⋅ ⋅ (c) Using the IHT […]
Chapter 12 Spectral distributions of earth and solar emission
PROBLEM 12.83 KNOWN: Spectral distribution of coating on satellite surface. Irradiation from earth and sun. FIND: (a) Steady–state temperature of satellite on dark side of earth, (b) Steady–state temperature on bright side. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Opaque, diffuse-gray […]
Chapter 12 The cylinder temperature exceeds the air temperature
PROBLEM 12.61 KNOWN: Cross flow of air over a cylinder placed within a large furnace. FIND: (a) Steady–state temperature of the cylinder when it is diffuse and gray with e = 0.5, (b) Steady- state temperature when surface has spectral […]
Chapter 12 The rim would appear brighter than the central region
PROBLEM 12.31 KNOWN: Incandescent sphere suspended in air within a darkened room exhibiting these characteristics: initially: brighter around the rim after some time: brighter in the center FIND: Plausible explanation for these observations. ASSUMPTIONS: (1) The sphere is at a […]
Chapter 12 When performing an analysis with both convection
PROBLEM 12.46 KNOWN: Plate exposed to solar flux with prescribed solar absorptivity and emissivity; convection and surrounding conditions also prescribed. FIND: Steady–state temperature of the plate, convection and radiation fluxes at plate surface. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Plate […]
Chapter 13 Furnace power requirement and temperature of a heated
PROBLEM 13.56 KNOWN: Dimensions, surface radiative properties, and operating conditions of an electrical furnace. FIND: (a) Equivalent radiation circuit, (b) Furnace power requirement and temperature of a heated plate. SCHEMATIC: ANALYSIS: (a) Since there is symmetry about the plate, only […]
Chapter 13 Irradiation Considering Radiation From The Cover And
PROBLEM 13.13 KNOWN: Heat flux gage positioned normal to a blackbody furnace. Cover of furnace is at 350 K while surroundings are at 300 K. FIND: (a) Irradiation on gage, Gg, considering only emission from the furnace aperture and (b) […]
Chapter 13 Negligible convection in region between shield and wall
PROBLEM 13.85 KNOWN: Dimensions and inclination angle of a flat–plate solar collector. Absorber and cover plate temperatures and emissivities. FIND: (a) Rate of heat transfer by free convection and radiation, (b) Effect of the absorber plate temperature on the heat […]
Chapter 13 Plates are sufficiently large to form a two
PROBLEM 13.30 (Cont.) (a) For α = 0, 11 13a 1 a (b a) F tan tan 2x x −− −− = − π For F13c we note that […]
Chapter 13 Radiation transfer rate for black surfaces
PROBLEM 13.42 KNOWN: Emissivities, diameters and temperatures of concentric spheres. FIND: (a) Radiation transfer rate for black surfaces. (b) Radiation transfer rate for diffuse–gray surfaces, (c) Effects of increasing the diameter and assuming blackbody behavior for the outer sphere. (d) […]
Chapter 13 Switching the gas from air to argon reduces the heat
PROBLEM 13.75 KNOWN: Emissivity of glass sheets. Inside and outside temperatures and convection heat transfer coefficients. Type of gas within gap. FIND: Heat flux through the window for case 1: ε 1 = ε 2 = 0.95, case 2: ε […]
Chapter 13 The two disk-shaped ends of the tube become small
PROBLEM 13.1 KNOWN: Various geometric shapes involving two areas A1 and A2. FIND: Shape factors, F12 and F21, for each configuration. SCHEMATIC: ASSUMPTIONS: (1) Surfaces are diffuse, (2) Length normal to the page is large compared to other dimensions. ANALYSIS: […]
Chapter 13 Which Indicates The Plate Temperature Increasing
PROBLEM 13.66 KNOWN: Four surface enclosure with all sides of equal area; temperatures of three surfaces are specified while the fourth is re-radiating. FIND: Temperature of the re–radiating surface A4. SCHEMATIC: ANALYSIS: To determine the temperature of the re–radiating surface […]
Chapter 13 Entering the energy balance into the IHT workspace
PROBLEM 13.91 (Cont.) where, assuming 47 L io 10 Ra 10 , h and h≤≤ are given by Eqs. 9.52 and 9.26, respectively, g T 825 K= < The corresponding value of qh is h q 108 kW= < where […]
Chapter 14 Canceling terms and dividing numerator
PROBLEM 14.1 KNOWN: Mixture of O2 and N2 with partial pressures in the ratio 0.21 to 0.79. FIND: Mass fraction of each species in the mixture. SCHEMATIC: ASSUMPTIONS: (1) Ideal gas behavior. 2 O N2 p0.21 p 0.79 = ANALYSIS: […]
Chapter 14 Mole fraction of NO at the catalytic surface
PROBLEM 14.31 KNOWN: Conditions of the exhaust gas passing over a catalytic surface for the removal of NO. FIND: (a) Mole fraction of NO at the catalytic surface, (b) NO removal rate. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional species […]
Chapter 14 Temperature and relative humidity of environment
PROBLEM 14.51 (Cont.) With Bim = 9.5, find ζ1 = 1.4219 rad and C1 = 1.2609 from Table 5.1, so that Eq. 5.44 becomes COMMENTS: (1) Since Bim = 9.5, the uniform concentration assumption is not valid, and we expect […]
Chapter 14 Uniform temperature and pressure throughout the column
PROBLEM 14.15 KNOWN: Column containing liquid phase of water (A) evaporates into the air (B) flowing over the mouth of the column. FIND: Evaporation rate of water (kg/h⋅m2) using the known value of the binary diffusion coefficient for the water […]
Chapter 14 Water Stagnant 4 Stationary Medium Analysis A
PROBLEM 14.46 KNOWN: Thick plate of pure iron at 1000°C subjected to a carburizing process with sudden exposure to a carbon concentration CC,s at the surface. FIND: (a) Consider the heat transfer analog to the carburization process; sketch the mass […]
Chapter 2 All laser irradiation is absorbed and can be characterized
PROBLEM 2.26 KNOWN: Wall thickness. Thermal energy generation rate. Temperature distribution. Ambient fluid temperature. FIND: Thermal conductivity. Convection heat transfer coefficient. SCHEMATIC: ASSUMPTIONS: (1) Steady state, (2) One–dimensional conduction, (3) Constant properties, (4) Negligible radiation. ANALYSIS: Under the specified conditions, […]
Chapter 2 Applying an energy balance to a control surface
PROBLEM 2.41 (Cont.) Substitute T(r) into the HDE to see if it is satisfied: (1) Ts,1 > Ts,2 (2) Decreasing gradient with increasing radius, r, since the heat rate is constant through the insulation. (b) Using Fourier’s law for the […]
Chapter 2 Axisymmetric object with varying cross-sectional area
PROBLEM 2.1 KNOWN: Axisymmetric object with varying cross–sectional area and different temperatures at its two ends, insulated on its sides. FIND: Shapes of heat flux distribution and temperature distribution. SCHEMATIC: ANALYSIS: For the prescribed conditions, it follows from conservation of […]
Chapter 2 Homework Size and thermal conductivities of a spherical particle
PROBLEM 2.47 (Cont.) If the volumetric energy generation rate, q , is unchanged, Equation (1) requires that the temperature gradient everywhere in Material B will be reduced by half if the thermal conductivity of Material B is doubled. Hence, […]
Chapter 2 One dimensional heat transfer in samples
PROBLEM 2.15 KNOWN: Identical samples of prescribed diameter, length and density initially at a uniform temperature Ti, sandwich an electric heater which provides a uniform heat flux ′′ qo for a period of time ∆to. Conditions shortly after energizing and […]
Chapter 3 An overall energy balance on the cylindrical shell
PROBLEM 3.71 (Cont.) COMMENT: An overall energy balance on the cylindrical shell can be expressed as ( ) qr 21 q(r ) =− () 22 Lq qV 21 rr π −= where V is the volume of the shell. […]
Chapter 3 Analysis A The Fin Heat Transfer Rate
PROBLEM 3.96 (Cont.) For irradiation of the right side of the nanotube (bottom circuit), ,2 ,2lr qq q= + (5) max,2 ,2 2,, /2 /2 l tcl cn cn cn cn TT qss R kA kA ξ ∞ − =− […]
Chapter 3 Comments 1 Liquid Water Opaque Thermal Radiation
PROBLEM 3.1 KNOWN: One-dimensional, plane wall separating hot and cold fluids at T and T ,1 ,2∞ ∞ , respectively. FIND: Temperature distribution, T(x), and heat flux, ′′ q x , in terms of T T h ,1 ,2 1∞ […]
Chapter 3 Homework Then With Mlc 4hkd12
PROBLEM 3.110 (Cont.) The new UP replaces the old hP in the fin heat transfer analysis, therefore the new heat transfer rate is given by f cb c UP q = UPkA θ tanh L kA […]
Chapter 3 Negligible temperature drop across container wall
PROBLEM 3.84 KNOWN: Radius, thermal conductivity, heat generation and convection conditions associated with a solid sphere. FIND: Temperature distribution. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional radial conduction, (3) Constant properties, (4) Uniform heat generation. ANALYSIS: Integrating the appropriate form […]
Chapter 3 Specifically Heat Transfer Rates For Cases And
PROBLEM 3.136 (Cont.) (ii) For He, the ideal gas constant, specific heat at constant volume, and ratio of specific heats are: The mean free path is ( ) ( ) 23 7 mfp 2 2-9 5 2 1.381 10 J/K […]
Chapter 3 The fin heat transfer rate is maximized
PROBLEM 3.121 KNOWN: Dimensions and number of rectangular aluminum fins. Convection coefficient with and without fins. FIND: Percentage increase in heat transfer resulting from use of fins. SCHEMATIC: PROPERTIES: Table A-1, Aluminum, pure: k ≈ 240 W/m⋅K. ANALYSIS: Evaluate the […]
Chapter 3 The Maximum Insulation Temperature Could Reduced Reducing
PROBLEM 3.42 (Cont.) 0.2 0.26 0.32 0.38 0.44 0.5 Outer radius of insulation, m 0 500 1000 1500 Heat rates , W/m Total heat rate Convection heat rate Radiation heat rate Beyond r3 ≈ 0.40 m, there are rapidly diminishing […]
Chapter 3 The reduction in the effective thermal conductivity
PROBLEM 3.29 KNOWN: Thermal conductivity of ice cream containing no air at T = -20°C. Shape and volume fraction of air bubbles. FIND: The thermal conductivity of commercial ice cream characterized by e = 0.20 at T = –20°C. SCHEMATIC: […]
Chapter 3 Thermal circuits with and without contact lens
PROBLEM 3.57 KNOWN: Representation of the eye with a contact lens as a composite spherical system subjected to convection processes at the boundaries. FIND: (a) Thermal circuits with and without contact lens in place, (b) Heat loss from anterior chamber […]
Chapter 3 Thicknesses of three materials which form a composite
PROBLEM 3.15 KNOWN: Dimensions and materials associated with a composite wall (2.5 m × 6.5 m, 10 studs each 2.5 m high). FIND: Wall thermal resistance. SCHEMATIC: ASSUMPTIONS: (1) Steady–state, one–dimensional conditions, (2) Planes parallel to x are adiabatic, (3) […]
Chapter 3 By adding the two heat sinks to the thermoelectric
PROBLEM 3.131 (Cont.) The total thermal resistance is given by ,, tot base , 2 22 1 tc tc b to ot RR L R RR W W kW hA η ′′ ′′ =+ +=+ + where Equation 3.108 has […]
Chapter 4 Known Cylinder Extending Between Two
PROBLEM 4.14 KNOWN: Dimensions and temperature of water droplet. FIND: Time for droplet to freeze completely. ASSUMPTIONS: (1) Constant properties, (2) Negligible convection and radiation, (3) Isothermal water particle, (4) Semi-infinite medium. PROPERTIES: Table A.4, Air (265 K): ka = […]
Chapter 4 Metal sheathing is very thin relative to cylinder
PROBLEM 4.63 KNOWN: Diameter of long cylinder, thickness of metal sheathing, volumetric generation rate within the sheathing, thermal conductivity of sheathing and convection heat transfer coefficient dependence upon angle q . Emissivity of the sheathing. FIND: (a) Temperature distribution within […]
Chapter 4 Node 9 treat as interior node; for others
PROBLEM 4.71 (Cont.) COMMENTS: (1) The IHT Workspace for the 5×5 coarse node analysis with results follows. // Finite–difference equations – energy balances // First row – treating as interior nodes considering symmetry T1 = 0.25 * ( Tc + […]
Chapter 4 The thermal circuit for the conduction heat flow between
PROBLEM 4.31 KNOWN: Disc-shaped electronic devices dissipating 100 W mounted to aluminum alloy block with prescribed contact resistance. FIND: (a) Temperature device will reach when block is at 27°C assuming all the power generated by the device is transferred by […]
Chapter 4 Two-dimensional rectangular plate subjected to prescribed
PROBLEM 4.1 KNOWN: Method of separation of variables for two–dimensional, steady-state conduction. FIND: Show that negative or zero values of λ2, the separation constant, result in solutions which cannot satisfy the boundary conditions. SCHEMATIC: ASSUMPTIONS: (1) Two-dimensional, steady-state conduction, (2) […]
Chapter 4 Heat transfer rate per unit plate length from
PROBLEM 4.47 KNOWN: Square channels of known dimension, evenly spaced along centerline of plate of known thickness and thermal conductivity. Hot and cold fluids with known temperatures and heat transfer coefficients flowing through alternate channels. N = 50 channels. Use […]
Chapter 4 Nodal temperatures from a steady-state finite-difference
PROBLEM 4.55 (Cont.) k = 15 h = 240 Tinf = 20 //Node 7 k*(T6 – T7)*dy/dx + k*(T12 – T7)*dx/dy + k*(T8 – T7)*dy/dx + k*(T2 – T7)*dx/dy = 0 //Node 8 k*(T7 – T8)*dy/dx + k*(T13 – T8)*dx/dy […]
Chapter 5 A much faster approach would be to solve these
PROBLEM 5.41 (Cont.) (1) can be used to find the required value of * o θ . Then Equation (2) can be used to determine Fo and a new value of L can be determined from Equation (6). Finally, Bi […]
Chapter 5 Corresponding Value Film Surface Temperature Schematic
PROBLEM 5.14 (Cont.) The heat transfer coefficient at T = 110°C is h = 1010 W/m2⋅K3×(10 K)2 = 101,000 W/m2∙K. Hence, for the case where the heat transfer coefficient is constant Equation 5.6 becomes Equations (1) and (2) may be […]
Chapter 5 Hot dog with prescribed thermophysical properties
PROBLEM 5.100 KNOWN: Conditions associated with heat generation in a rectangular fuel element with surface cooling. See Example 5.11. FIND: (a) The temperature distribution 1.5 s after the change in operating power; compare your results with those tabulated in the […]
Chapter 5 Initially All Nodes Are 25c When Suddenly
PROBLEM 5.107 (Cont.) Using finite–difference equations (14-16) with Eq. (13), the calculations may be performed to obtain p t(s) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10(°C) 0 0 200 200 200 200 200 200 200 200 200 […]
Chapter 5 Minimum temperature of rod should not be less than
PROBLEM 5.53 KNOWN: Long plastic rod of diameter D heated uniformly in an oven to Ti and then allowed to convectively cool in ambient air (T∞, h) for a 3 minute period. Minimum temperature of rod should not be less […]
Chapter 5 Soil Assumptions 1 Uniform Properties 2 One dimensional
PROBLEM 5.79 KNOWN: Mass and initial temperatures of frozen ground beef. Rate of microwave power absorbed in packaging material. FIND: Time for beef adjacent to packaging to reach 0°C. SCHEMATIC: ASSUMPTIONS: (1) Beef has properties of ice, (2) Radiation and […]
Chapter 5 The IHT model represents the series solution
PROBLEM 5.64 KNOWN: Temperature requirements for cooling the spherical material of Example 5.6 in air and in a water bath. FIND: (a) For step 1, the time required for the center temperature to reach T(0,t) = 335°C while cooling in […]
Chapter 5 The Situation Reversed Shortly After Cooling Begins
PROBLEM 5.1 KNOWN: Electrical heater attached to backside of plate while front surface is exposed to convection process (T∞,h); initially plate is at a uniform temperature of the ambient air and suddenly heater power is switched on providing a constant […]
Chapter 5 The time needed to traverse the rod through the oven
PROBLEM 5S.3 KNOWN: Inlet and outlet temperatures of steel rods heat treated by passage through an oven. FIND: Rod speed, V. SCHEMATIC: ASSUMPTIONS: (1) One-dimensional radial conduction (axial conduction is negligible), (2) Constant properties, (3) Negligible radiation. PROPERTIES: Table A-1, […]
Chapter 5 These results could also have been obtained using the energy
PROBLEM 5.91 (Cont.) Solving for the nodal temperature at time step p+1 results in p pp pp p p+1 m,n,q m+1,n,q m-1,n,q m,n+1,q m,n-1,q m,n,q+1 m,n,q-1 p m,n,q T = Fo(T + T + T + T + T + […]
Chapter 5 adiation exchange with surroundings is negligible
PROBLEM 5.30 KNOWN: Diameters, initial temperature and thermophysical properties of WC and Co in composite particle. Convection coefficient and freestream temperature of plasma gas. Melting point and latent heat of fusion of Co. FIND: Times required to reach melting and […]
Chapter 6 Area-averaged mass transfer coefficient for evaporation
PROBLEM 6.47 KNOWN: Species concentration profile, CA(y), in a boundary layer at a particular location for flow over a surface. FIND: Expression for the mass transfer coefficient, hm, in terms of the profile constants, CA,∞ and DAB. Expression for the […]
Chapter 6 Comments Due Bottom Heat Losses Which Have
PROBLEM 6.30 (Cont.) The two fluids are subjected to the same temperature difference between the surface and the free stream. Since the thermal boundary layer thickness is the distance over which the temperature varies from the surface temperature to the […]
Chapter 6 Incompressible fluid with constant properties
PROBLEM 6S.6 KNOWN: Couette flow with moving plate isothermal and stationary plate insulated. FIND: Temperature of stationary plate and heat flux at the moving plate. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Incompressible fluid with constant properties, (3) Couette flow. ANALYSIS: […]
Chapter 6 Initial temperature and droplet diameter of water mist
PROBLEM 6.62 KNOWN: Water freezing under conditions for which the air temperature exceeds 0°C. FIND: (a) Lowest air temperature, T∞, before freezing occurs, neglecting evaporation, (b) The mass transfer coefficient, hm, for the evaporation process, (c) Lowest air temperature, T∞, […]
Chapter 6 Temperature at which extreme values of average convection
PROBLEM 6.17 KNOWN: Velocity and temperature of water flowing over a flat plate. Length of plate. Variation of local convection coefficient with x for laminar and turbulent flow. FIND: Minimum and maximum average convection coefficient for roughness applied over the […]
Chapter 6 This is consistent with the fact that the surface
PROBLEM 6.1 KNOWN: Temperature distribution at x2 in laminar thermal boundary layer. FIND: (a) Whether plate is being heated or cooled, (b) Temperature distributions at two other x locations. Locations of largest and smallest heat fluxes, (c) Temperature distribution at […]
Chapter 7 A trial-and-error solution reveals that a larger
PROBLEM 7.46 (Cont.) Therefore, the heat transfer rate from the cylinder is, 33 2 ( ) 5.64 10 m 50 10 m 76.52W / m K(80 25) 3.73W cs q DL h T T C ππ −− ∞ = −=××××× […]
Chapter 7 For each fluid plot the boundary layer thicknesses
PROBLEM 7.1 KNOWN: Temperature and velocity of fluids in parallel flow over a flat plate. FIND: (a) Velocity and thermal boundary layer thicknesses at a prescribed distance from the leading edge, and (b) For each fluid plot the boundary layer […]
Chapter 7 For parallel flow over plate, flow is turbulent
PROBLEM 7.81 KNOWN: Air at 10 m/s and 15°C is available for cooling hot plastic plate. An array of slotted nozzles with prescribed width, pitch and nozzle-to–plate separation. FIND: (a) Improvement in cooling rate achieved using the slotted nozzle arrangement […]
Chapter 7 invoke the heat-mass transfer analogy using
PROBLEM 7.102 KNOWN: Paper mill process using radiant heat for drying. FIND: (a) Evaporative flux at a distance 1 m from roll edge; corresponding irradiation, G (W/m2), required to maintain surface at Ts = 300 K, and (b) Compute and […]
Chapter 7 Steady-state incompressible flow conditions
PROBLEM 7.57 KNOWN: Temperature, diameter, and velocity of oil droplets in air. Air temperature. FIND: Heat transfer rate from oil to air for two droplets before and after coalescence. SCHEMATIC: Air D2 + D1= 100 μm Before oil droplet collision […]
Chapter 7 The electric power output and silicon temperature
PROBLEM 7.14 (Cont.) The thermal resistances are -3 -3 t,g g g R = L /k A = 3 × 10 m (1.4 W/m K × 1 m × 0.1 m) = 21.43 × 10 K/W⋅ -3 -6 t,a a […]
Chapter 7 the maximum velocity occurs on the transverse plane
PROBLEM 7.68 KNOWN: Conditions associated with Example 7.7, but with reduced longitudinal and transverse pitches. FIND: (a) Air side convection coefficient, (b) Tube bundle pressure drop, (c) Heat rate. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Uniform tube surface temperature, (3) […]
Chapter 7 The relative humidity may now be obtained from
PROBLEM 7.109 (Cont.) Convection Calculations: For the prescribed conditions, the Reynolds number associated with the dry-bulb thermometer is Approximating the Prandtl number ratio as unity, from Eq. 7.53 and Table 7.4, ( ) ( ) ( ) ( ) 0.5 […]
Chapter 7 The temperature distribution in the copper tubing above
PROBLEM 7.35 (Cont.) (b) When the tube is half full, the upper half of the tube will act as a fin. The total rate of heat loss per unit mass will be qM = qM1 + qM2 where qM1 is […]
Chapter 7 Velocity and temperature of air in cross flow
PROBLEM 7.23 (Cont.) COMMENTS: (1) In Problem 7.15, we see that, for air cooling and Llens = 400 mm, Tsi = 126 C, P = 14.3 W. Use of liquid cooling increases the electrical power output to 23.4 W, or […]
Chapter 7 We would expect the actual convection heat transfer
PROBLEM 7.90 (Cont.) From Equation 7.82, or equivalently from an energy balance on the air, , () () po i cbpo i q mcT T VAcT T ρ = −= − 32 1.0782 kg/m 10 m/s (0.04 m) 1008 […]
Chapter 8 Air is an ideal gas with negligible viscous
PROBLEM 8.37 KNOWN: Surface temperature and diameter of a tube. Velocity and temperature of air in cross flow. Velocity and temperature of air in fully developed internal flow. FIND: Convection heat flux associated with the external and internal flows. SCHEMATIC: […]
Chapter 8 Footnote The Mean Outlet Temperature
PROBLEM 8.25 KNOWN: Oil flow rate. Pipe diameter. Inlet, outlet, and pipe surface temperatures. FIND: Length of tube required to achieve desired outlet temperature. SCHEMATIC: ASSUMPTIONS: (1) Steady–state, (2) Incompressible flow, (3) Negligible viscous dissipation. PROPERTIES: Table A-5, Engine oil […]
Chapter 8 Homework Constant properties and steady-state conditions
PROBLEM 8.91 KNOWN: Diameters and length of three microchannels machined in a copper block. Inlet temperature of water flowing through the channels, copper block temperature, pressure difference from inlet to outlet of the channels. FIND: (a) Mass flow rate and […]
Chapter 8 Homework However All Such Fluids Such Air Are
PROBLEM 8.81 KNOWN: Inlet temperatures and flow rates of a pharmaceutical product and pressurized water, tube diameter, coil diameter and number of coils. FIND: (a) The outlet temperature of the pharmaceutical product, (b) The variation of the pharmaceutical outlet temperature […]
Chapter 8 Homework A concentric tube arrangement for removing heat generated from a biochemical
PROBLEM 8.72 KNOWN: Inner and outer tube surface conditions for an annulus. FIND: (a) Velocity profile, (b) Temperature profile and expression for inner surface Nusselt number. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Laminar, fully developed flow, (3) Uniform heat flux […]
Chapter 8 Smooth Surface Using With The Expressions
PROBLEM 8.1 KNOWN: Flowrate and temperature of water in fully developed flow through a tube of prescribed diameter. FIND: Maximum velocity and pressure gradient. SCHEMATIC: ASSUMPTIONS: (1) Steady–state conditions, (2) Isothermal flow, (3) Horizontal tube. PROPERTIES: Table A-6, Water (300 […]
Chapter 8 The Average Wall Surface Temperature Follows From
PROBLEM 8.49 KNOWN: Hot fluid passing through a thin-walled tube with coolant in cross flow over the tube. Fluid flow rate and inlet and outlet temperatures. FIND: Outlet temperature, Tm,o , if the flow rate is increased by a factor […]
Chapter 8 The Calculations May Checked Determining
PROBLEM 8.60 KNOWN: Features of tubing used in a ground source heat pump. Temperature of surrounding soil. Fluid inlet temperature and flowrate. FIND: (a) Effect of tube length on outlet temperature, (b) Recommended tube length and the effect of variations […]
Chapter 8 the pumping power is significantly affected
PROBLEM 8.12 (Cont.) The mean outlet temperature can be found from Equation 8.41b: The heat transfer rate can be calculated from Equation 8.34 (with a change in sign to calculate heat transfer from the air to the tube wall): ,, […]
Chapter 9 Depending on the desired accuracy of the solution
PROBLEM 9.82 KNOWN: Diameter and temperature of cylinder. Velocity and temperature of fluid in cross flow. Four different fluids. FIND: Whether heat transfer by free convection is significant. SCHEMATIC: ASSUMPTIONS: (1) Steady state, (2) Constant properties, (3) Air can be […]
Chapter 9 Heat Loss Also Associated With Radiation Exchange
PROBLEM 9.57 (Cont.) (d) From hydrostatic considerations and the assumption of a constant density ρm, the balance between the gravitational and net pressure forces may be expressed as dp/dz = –ρm(g/gc). The momentum equation is then of the form or, […]
Chapter 9 Horizontal pipe with aluminum foil having emissivity
PROBLEM 9.48 KNOWN: Insulated, horizontal pipe with aluminum foil having emissivity which varies from 0.12 to 0.36 during service. Pipe diameter is 300 mm and its surface temperature is 90°C. FIND: Effect of emissivity degradation on heat loss with ambient […]
Chapter 9 Inner tube surface temperature at outlet
PROBLEM 9.1 KNOWN: Thickness and thermal conductivity of plane wall. Fluid temperatures. FIND: Expected minimum and maximum steady-state heat fluxes through the wall for (a) free convection in gases, (b) free convection in liquids, (c) forced convection in gases, (d) […]
Chapter 9 The Churchill and Chu correlation yields
PROBLEM 9.88 KNOWN: Plate dimensions and initial temperature. Velocity and temperature of air in parallel flow over plates. FIND: Initial rate of heat transfer from plate. Initial rate of change of plate temperature. Graph of the free, forced and mixed […]
Chapter 9 The Minimum Heat Transfer Rate Corresponds The
PROBLEM 9.71 (Cont.) (b) The unit conduction resistance of a glass pane is 2 cond p p R L / k 0.00429 m K / W, ′′ = = ⋅ and the smallest convection resistance is ( ) conv,o o […]
Chapter 9 The Outside Convection Coefficient May Obtained First
PROBLEM 9.17 KNOWN: Room and ambient air conditions for window glass. Thickness and thermal conductivity of glass. FIND: Inner and outer surface temperatures and rate of heat loss. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction in the glass, (3) […]
Chapter 9 The rate of heat loss per unit length for a calm day
PROBLEM 9.40 KNOWN: Diameter and emissivity of horizontal glass cylinder. Temperature of air and surroundings. FIND: Temperature at which lumped capacitance approximation may be applied. SCHEMATIC: ASSUMPTIONS: (1) The quasi-steady approximation holds: the heat transfer coefficient can be evaluated based […]
Chapter 9 where h is estimated from the appropriate correlation
PROBLEM 9.28 KNOWN: Electric heater at bottom of tank of 500 mm diameter maintains surface at 65°C with engine oil at 10°C. FIND: Power required to maintain 65°C surface temperature. SCHEMATIC: T ∞ = 10° C ASSUMPTIONS: (1) Oil is […]