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Heat Transfer 10th edition Jack Holman - Solutions

A cylinder having a diameter of 15 cm and a length of 30 cm is initially uniform in temperature at 300ºC. It is suddenly exposed to a convection environment at 20ºC with h = 35W/m2 · ºC. Properties of the solid are k = 2.3W/m ∙ ºC, ρ = 300 kg/m3, and c = 840 J/kg · ºC. Calculate the time
The corner shown in Figure P4-74 is initially uniform at 200ºC and then suddenly exposed to convection around the edge with h = 50W/m2 · ºC and T = 30ºC. Assume the solid has the properties of fireclay brick. Examine nodes 1, 2, 3, and 4 and determine the maximum time
An aluminum rod 2.5 cm in diameter and 20 cm long protrudes from a wall maintained at 200ºC and is exposed to a convection environment with h = 50W/m2 · ºC and a temperature of 20ºC. Using ∆x = 4 cm write a transient nodal equation for the node at the tip of the fin and determine the maximum
Write the nodal equation for node 3 in Figure P4-76 for use in a transient analysis. Determine the stability criterion for this node.
Write a nodal equation for analysis of node (m, n) in Figure P4-77 to be used in a transient analysis of the solid.
Write the nodal equation and establish the stability criteria for node 1 in Figure P4-78 (transient analysis). Materials A and B have the properties given in Problem 4-73.In Problem 4-73
Write the transient equation for node 1 in Figure P4-79 and determine the maximum allowable time increment that may be employed in the calculation. The properties of materials A, B, and C are the same as those given in Problem 4-73.In Problem 4-73
Calculate the maximum time increment that can be used for node 5 in Figure P4-80 for a transient numerical analysis. Also write the nodal equation for this node.
The corner shown in Figure P4-81 is initially uniform at 300ºC and then suddenly exposed to a convection environment at 50ºC with h = 60 W/m2 · ºC. Assume the solid has the properties of fireclay brick. Examine nodes 1, 2, 3, 4, and 5 and determine the maximum time increment
Write a steady-state nodal equation for node 3 in Figure P4-82 assuming unit depth perpendicular to the page and using the node spacing shown. The thermal conductivity of the solid is 15W/m· ºC and the convection heat-transfer coefficient on the side surface is 25 W/m2 ·
Write the transient nodal equation for node 7 in Figure P4-84 and determine the maximum allowable time increment for the node. Properties of materials A and B are given in the figure.
For the section shown in Figure P4-85, calculate the maximum time increment allowed for node 2 in a transient numerical analysis. Also write the entire nodal equation for this node.
A transient numerical analysis is to be performed on the composite material section shown in Figure P4-86. Calculate the maximum time increment that can be used for node 5 to ensure convergence.
For the section shown in Figure P4-87, calculate the maximum time increment allowed for node 4 in a transient numerical environment. Also write the complete nodal equation for node 4.
Write the transient nodal temperature equation for node 1 in Figure P4-88. Also determine the maximum allowable time increment for the node. The right face is exposed to the convection condition shown. Properties for materials A and B are given in the figure.
Write the nodal equation for a transient analysis of node 2 in Figure P4-89 and determine the stability criterion for this node. The properties for materials A and B are given in the figure.
An infinite plate of thickness 2L is suddenly exposed to a constant-temperature radiation heat source or sink of temperature Ts. The plate has a uniform initial temperature of Ti. The radiation heat loss from each side of the plate is given by q = σεA(T4 − T4s), where σ and ε are constants
The solid in Problem 3-51 is initially uniform in temperature at 10ºC. At time zero the right face is suddenly changed to 38ºC and the left face exposed to the convection environment. Nodes 3 and 6 remain at 10ºC. Select an appropriate value for ∆τ and calculate the temperatures of nodes 1,
The solid in Problem 3-53 has k = 11W/m· ºC and is initially uniform in temperature at 1000ºC. At time zero the four surfaces are changed to the values shown. Select an appropriate ∆τ and calculate the temperatures of nodes 1, 2, 3, and 4 after 10 time increments. Also obtain the limiting
The solid in Problem 3-58 is initially uniform in temperature at 100ºC and then suddenly exposed to the convection condition while the right and bottom faces are held constant at 100ºC. Select a value for ∆τ and calculate the nodal temperatures after 10 time increments. Take ρ = 3000 kg/m3
The solid in Problem 3-59 is initially uniform in temperature at 50ºC and suddenly is exposed to the convection condition. Select a value for ∆τ and calculate the nodal temperatures after 10 time increments. Take ρ = 2500 kg/m3 and c = 900 J/kg · ºC.
The fin in Problem 3-61 is initially uniform in temperature at 200ºC, and then suddenly exposed to the convection boundary and heat generation. Select a value for ∆τ and calculate the nodal temperatures for 10 time increments. Take ρ = 7600 kg/m3 and c = 450 J/kg · ºC. The base stays
The solid in Problem 3-62 is initially uniform in temperature at 500ºC and suddenly exposed to the convection boundary while the inner surface is kept constant at 500ºC. Select a value for ∆τ and calculate the nodal temperatures after 10 time increments. Take ρ = 500 kg/m3 and c = 810 J/kg ·
Compare the heat-transfer results of Equations (6-17) and (6-18) for water at Reynolds numbers of 103, 104, and 105 and a film temperature of 90oC.Equations (6-17)Equations (6-17)
A pipeline in the Arctic carries hot oil at 50oC.Astrong arctic wind blows across the 50-cm-diameter pipe at a velocity of 13 m/s and a temperature of − 35oC. Estimate the heat loss per meter of pipe length.
Two tubes are available, a 4.0-cm-diameter tube and a 4.0-cm-square tube. Air at 1 atm and 27oC is blown across the tubes with a velocity of 20 m/s. Calculate the heat transfer in each case if the tube wall temperature is maintained at 50oC.
A 3.0-cm-diameter cylinder is subjected to a cross flow of carbon dioxide at 200oC and a pressure of 1 atm. The cylinder is maintained at a constant temperature of 50oC and the carbon dioxide velocity is 40 m/s. Calculate the heat transfer to the cylinder per meter of length.
Water having an average bulk temperature of 100oF flows in a smooth tube with a diameter of 1.25 cm. The flow rate is such that a Reynolds number of 100,000 is experienced, and the tube wall is maintained at an average temperature of 160oF. If the tube length is 1.5 m calculate the exit bulk
Water at the rate of 3 kg/s is heated from 5 to 15oC by passing it through a 5-cm-ID copper tube. The tube wall temperature is maintained at 90oC. What is the length of the tube?
Helium at 150 kPa and 20oC is forced at 50 m/s across a horizontal cylinder having a diameter of 30 cm and a length of 6 m. Calculate the heat lost by the cylinder if its surface temperature is maintained constant at 100oC.
A 0.25-inch-diameter cylinder is maintained at a constant temperature of 300oC and placed in a cross flow of CO2 at p = 100 kPa and T = 30oC. Calculate the heat loss for a 4.5-m length of the cylinder if the CO2 velocity is 35 m/s.
A20-cm-diameter cylinder is placed in a cross-flow CO2 stream at 1 atm and 300 K. The cylinder is maintained at a constant temperature of 400 K and the CO2 velocity is 50 m/s. Calculate the heat lost by the cylinder per meter of length.
Air flows across a 4-cm-square cylinder at a velocity of 12 m/s. The surface temperature is maintained at 85oC. Free-stream air conditions are 20oC and 0.6 atm. Calculate the heat loss from the cylinder per meter of length.
Water flows over a 3-mm-diameter sphere at 5 m/s. The free-stream temperature is 38oC, and the sphere is maintained at 93oC. Calculate the heat-transfer rate.
A spherical water droplet having a diameter of 1.3 mm is allowed to fall from rest in atmospheric air at 1 atm and 20oC. Estimate the velocities the droplet will attain after a drop of 30, 60, and 300 m.
A heated sphere having a diameter of 3 cm is maintained at a constant temperature of 90oC and placed in a water flow stream at 20oC. The water flow velocity is 3.5 m/s. Calculate the heat lost by the sphere.
A small sphere having a diameter of 6 mm has an electric heating coil inside, which maintains the outer surface temperature at 220oC. The sphere is exposed to an airstream at 1 atm and 20oC with a velocity of 20 m/s. Calculate the heating rate which must be supplied to the sphere.
Water at the rate of 0.8 kg/s is heated from 35 to 40oC in a 2.5-cm-diameter tube whose surface is at 90oC. How long must the tube be to accomplish this heating?
Air at a pressure of 3 atm blows over a flat plate at a velocity of 75 m/s. The plate is maintained at 200oC and the free-stream temperature is 30oC. Calculate the heat loss for a plate which is 1 m square.
Air at 3.5 MPa and 38oC flows across a tube bank consisting of 400 tubes of 1.25-cm OD arranged in a staggered manner 20 rows high; Sp = 3.75 cm and Sn = 2.5 cm. The incoming-flow velocity is 9 m/s, and the tube-wall temperatures are maintained constant at 20oC by a condensing vapor on the inside
A tube bank uses an in-line arrangement with Sn = Sp =1.9 cm and 6.33-mmdiameter tubes. Six rows of tubes are employed with a stack 50 tubes high. The surface temperature of the tubes is constant at 90oC, and atmospheric air at 20oC is forced across them at an inlet velocity of 4.5 m/s before the
Air at 1 atm and 300 K flows across an in-line tube bank having 10 vertical and 10 horizontal rows. The tube diameter is 2 cm and the center-to-center spacing is 4 cm in both the normal and parallel directions. Calculate the convection heat-transfer coefficient for this situation if the entering
Condensing steam at 150oC is used on the inside of a bank of tubes to heat a cross-flow stream of CO2 that enters at 3 atm, 35oC, and 5 m/s. The tube bank consists of 100 tubes of 1.25-cm OD in a square in-line array with Sn = Sp =1.875 cm. The tubes are 60 cm long. Assuming the outside-tube-wall
An in-line tube bank is constructed of 2.5-cm-diameter tubes with 15 rows high and 7 rows deep. The tubes are maintained at 90oC, and atmospheric air is blown across them at 20oC and u∞ =12 m/s. The arrangement has Sp = 3.75 and Sn = 5.0 cm. Calculate the heat transfer from the tube bank per
Air at 300 K and 1 atm enters an in-line tube bank consisting of five rows of 10 tubes each. The tube diameter is 2.5 cm and Sn = Sp = 5.0 cm. The incoming velocity is 10 m/s and the tube wall temperatures are constant at 350 K. Calculate the exit air temperature.
Atmospheric air at 20oC flows across a 5-cm-square rod at a velocity of 15 m/s. The velocity is normal to one of the faces of the rod. Calculate the heat transfer per unit length for a surface temperature of 90oC.
A certain home electric heater uses thin metal strips to dissipate heat. The strips are 6 mm wide and are oriented normal to the airstream, which is produced by a small fan. The air velocity is 2 m/s, and seven 35-cm strips are employed. If the strips are heated to 870oC, estimate the total
Water flows through a 2.5-cm-ID pipe 1.5 m long at a rate of 1.0 kg/s. The pressure drop is 7 kPa through the 1.5-m length. The pipe wall temperature is maintained at a constant temperature of 50oC by a condensing vapor, and the inlet water temperature is 20oC. Estimate the exit water temperature.
A square duct, 30 cm by 30 cm, is maintained at a constant temperature of 30oC and an airstream of 50oC and 1 atm is forced across it with a velocity of 6 m/s. Calculate the heat gained by the duct. How much would the heat flow be reduced if the flow velocity were reduced in half?
Using the slug-flow model, show that the boundary-layer energy equation reduces to the same form as the transient-conduction equation for the semi-infinite solid of Section 4-3. Solve this equation and compare the solution with the integral analysis of Section 6-5.
Liquid bismuth enters a 2.5-cm-diameter stainless-steel pipe at 400oC at a rate of 1 kg/s. The tube wall temperature is maintained constant at 450oC. Calculate the bismuth exit temperature if the tube is 60 cm long.
Liquid sodium is to be heated from 120 to 149oC at a rate of 2.3 kg/s. A 2.5-cm diameter electrically heated tube is available (constant heat flux). If the tube wall temperature is not to exceed 200oC, calculate the minimum length required.
Determine an expression for the average Nusselt number for liquid metals flowing over a flat plate. Use Equation (6-42) as a starting point.Equation (6-42)
Water at the rate of 0.8 kg/s at 93oC is forced through a 5-cm-ID copper tube at a suitable velocity. The wall thickness is 0.8 mm.Air at 15oC and atmospheric pressure is forced over the outside of the tube at a velocity of 15 m/s in a direction normal to the axis of the tube. What is the heat loss
Air at 1 atm and 350 K enters a 1.25-cm-diameter tube with a flow rate of 35 g/s. The surface temperature of the tube is 300 K, and its length is 12 m. calculate the heat lost by the air and the exit air temperature.
Air flows across a 5.0-cm-diameter smooth tube with free-stream conditions of 20oC, 1 atm, and u∞ = 25 m/s. If the tube surface temperature is 120oC, calculate the heat loss per unit length.
Engine oil enters an 8-m-long tube at 20oC. The tube diameter is 20 mm, and the flow rate is 0.4 kg/s. Calculate the outlet temperature of the oil if the tube surface temperature is maintained at 80oC.
Air at 1 atm and 300 K with a flow rate of 0.2 kg/s enters a rectangular 10-by-20-cm duct that is 250 cm long. If the duct surface temperature is maintained constant at 400 K, calculate the heat transfer to the air and the exit air temperature.
Water at the rate of 1.3 kg/s is to be heated from 60oF to 100oF in a 2.5-cm-diameter tube. The tube wall is maintained at a constant temperature of 40oC. Calculate the length of tube required for the heating process.
Air at 1 atm and 300 K flows inside a 1.5-mm-diameter smooth tube such that the Reynolds number is 1200. Calculate the heat-transfer coefficients for tube lengths of 1, 10, 20, and 100 cm.
Water at an average bulk temperature of 10oC flows inside a channel shaped like an equilateral triangle 2.5 cm on a side. The flow rate is such that a Reynolds number of 50,000 is obtained. If the tube-wall temperature is maintained 15oC higher than the water bulk temperature, calculate the length
Air at 1 atm and 300 K flows normal to a square noncircular cylinder such that the Reynolds number is 104. Compare the heat transfer for this system with that for a circular cylinder having diameter equal to a side of the square. Repeat the calculation for the first, third, and fourth entries of
Air at 1 atm and 300 K flows across a sphere such that the Reynolds number is 50,000. Compare Equations (6-25) and (6-26) for these conditions. Also compare with Equation (6-30).Equations (6-25)Equations (6-26) Equations (6-30)
Water at 10oC flows across a 2.5-cm-diameter sphere at a free-stream velocity of 4 m/s. If the surface temperature of the sphere is 60oC, calculate the heat loss.
A tube bank consists of a square array of 144 tubes arranged in an in-line position. The tubes have a diameter of 1.5 cm and length of 1.0 m; the center-to-center tube spacing is 2.0 cm. If the surface temperature of the tubes is maintained at 350 K and air enters the tube bank at 1 atm, 300 K, and
Though it may be classified as a rather simple mistake, a frequent cause for substantial error in convection calculations is failure to select the correct geometry for the problem. Consider the following three geometries for flow of air at 1 atm, 300 K, and a Reynolds number of 50,000: (a) Flow
Water flows at an average flow velocity of 10 ft/s in a smooth tube at an average temperature of 60oF. The tube diameter is 2.5 cm. Calculate the length of tube required to cause the bulk temperature of the water to rise 10oC if the tube wall temperature is maintained at 150oF.
It has been noted that convection heat transfer is dependent on fluid properties, which in turn are dependent on temperature. Consider flow of atmospheric air at 0.012 kg/s in a smooth 2.5-cm-diameter tube. Assuming that the Dittus-Boelter relation [Equation (6-4a)] applies, calculate the average
Repeat Problem 6-98 for the same mass flow of atmospheric helium with properties evaluated at 255, 477, and 700 K and comment on the results. Problem 6-98 It has been noted that convection heat transfer is dependent on fluid properties, which in turn are dependent on temperature. Consider flow of
Engine oil enters a 5.0-mm-diameter tube at 120oC. The tube wall is maintained at 50oC, and the inlet Reynolds number is 1000. Calculate the heat transfer, average heat-transfer coefficient, and exit oil temperature for tube lengths of 10, 20, and 50 cm.
Water at the rate of 1 kg/s is forced through a tube with a 2.5-cm ID. The inlet water temperature is 15oC, and the outlet water temperature is 50oC. The tube wall temperature is 14oC higher than the water temperature all along the length of the tube. What is the length of the tube?
Air at 300 K flows in a 5-mm-diameter tube at a flow rate such that the Reynolds number is 50,000. The tube length is 50 mm. Estimate the average heat-transfer coefficient for a constant heat flux at the wall.
Water at 15.6oC flows in a 5-mm-diameter tube having a length of 50 mm. The flow rate is such that the Peclet number is 1000. If the tube wall temperature is constant at 49oC, what temperature increase will be experienced by the water?
Air at 1 atm flows in a rectangular duct having dimensions of 30 cm by 60 cm. The mean flow velocity is 7.5 m/s at a mean bulk temperature of 300 K. If the duct wall temperature is constant at 325 K, estimate the air temperature increase over a duct length of 30 m.
Glycerin at 10oC flows in a rectangular duct 1 cm by 8 cm and 1 m long. The flow rate is such that the Reynolds number is 250. Estimate the average heat transfer coefficient for an isothermal wall condition.
Air at 300 K blows normal to a 6-mm heated strip maintained at 600 K. The air velocity is such that the Reynolds number is 15,000. Calculate the heat loss for a 50-cm-long strip.
Repeat Problem 6-104 for flow normal to a square rod 6 mm on a side. Problem 6-104 Air at 300 K blows normal to a 6-mm heated strip maintained at 600 K. The air velocity is such that the Reynolds number is 15,000. Calculate the heat loss for a 50-cm-long strip.
Repeat Problem 6-104 for flow parallel to a 6-mm strip. (Calculate heat transfer for both sides of the strip.)Problem 6-104Air at 300 K blows normal to a 6-mm heated strip maintained at 600 K. The air velocity is such that the Reynolds number is 15,000. Calculate the heat loss for a 50-cm-long
Air at 1 atm flows normal to a square in-line bank of 400 tubes having diameters of 6 mm and lengths of 50 cm. Sn =Sd =9 mm. The air enters the tube bank at 300 K and at a velocity such that the Reynolds number based on inlet properties and the maximum velocity at inlet is 50,000. If the outside
Repeat Problem 6-107 for a tube bank with a staggered arrangement, the same dimensions, and the same free-stream inlet velocity to the tube bank. Problem 6-107 Air at 1 atm flows normal to a square in-line bank of 400 tubes having diameters of 6 mm and lengths of 50 cm. Sn = Sd = 9 mm. The air
Compare the Nusselt number results for heating air in a smooth tube at 300 K and Reynolds numbers of 50,000 and 100,000, as calculated from Equation (6-4a), (6-4b), and (6-4c). What do you conclude from these results?Equation (6-4a)Equation (6-4b) for 0.5
Engine oil enters a 1.25-cm-diameter tube 3 m long at a temperature of 38oC. The tube wall temperature is maintained at 65oC, and the flow velocity is 30 cm/s. Estimate the total heat transfer to the oil and the exit temperature of the oil.
Repeat Problem 6-109 for heating water at 21oC.Problem 6-109Compare the Nusselt number results for heating air in a smooth tube at 300 K and Reynolds numbers of 50,000 and 100,000, as calculated from Equation (6-4a), (6-4b), and (6-4c). What do you conclude from these results?Equation
Compare the results obtained from Equations (6-17), (6-21), (6-22), and (6-23) for air at 1 atm and 300 K flowing across a cylinder maintained at 400 K, with Reynolds numbers of 50,000 and 100,000. What do you conclude from these results?Equations (6-17)Equations (6-21) Equations (6-22) Equations
Repeat Problem 6-111 for flow or water at 21oC across a cylinder maintained at 32.2oC. What do you conclude from the results?Problem 6-111Compare the results obtained from Equations (6-17), (6-21), (6-22), and (6-23) for air at 1 atm and 300 K flowing across a cylinder maintained at 400 K, with
Using the values of the local Nusselt number given in Figure 6-11, obtain values for the average Nusselt number as a function of the Reynolds number. Plot the results as log Nu versus log Re, and obtain an equation that represents all the data. Compare this correlation with that given by Equation
A heat exchanger is constructed so that hot flue gases at 700 K flow inside a 2.5-cm-ID copper tube with 1.6-mm wall thickness.A5.0-cm tube is placed around the 2.5-cm-diameter tube, and high-pressure water at 150oC flows in the annular space between the tubes. If the flow rate of water is 1.5 kg/s
Consider the application of the Dittus-Boelter relation [Equation (6-4a)] to turbulent flow of air in a smooth tube under developed turbulent flow conditions. For a fixed mass flow rate and tube diameter (selected at your discretion) investigate the effect of bulk temperature on the heat-transfer
A convection electric oven is one that employs a fan to force air across the food in addition to radiant heat from electric heating elements. Consider two oven temperature settings at 175oC and 230oC. Make assumptions regarding airflow velocities in order to estimate oven heating performance with
Air at 1 atm and 15oC flows through a long rectangular duct 7.5 cm by 15 cm. A 1.8-m section of the duct is maintained at 120oC, and the average air temperature at exit from this section is 65oC. Calculate the airflow rate and the total heat transfer.
Water at the rate of 0.5 kg/s is forced through a smooth 2.5-cm-ID tube 15 m long. The inlet water temperature is 10oC, and the tube wall temperature is 15oC higher than the water temperature all along the length of the tube. What is the exit water temperature?
Water at an average temperature of 300 K flows at 0.7 kg/s in a 2.5-cm-diameter tube 6 m long. The pressure drop is measured as 2 kPa. A constant heat flux is imposed, and the average wall temperature is 55oC. Estimate the exit temperature of the water.
An oil with Pr = 1960, ρ = 860 kg/m3, ν = 1.6 × 10−4 m2/s, and k = 0.14W/m· oC enters a 2.5-mm-diameter tube 60 cm long. The oil entrance temperature is 20oC, the mean flow velocity is 30 cm/s, and the tube wall temperature is 120oC. Calculate the heat-transfer rate.
Liquid ammonia flows through a 2.5-cm-diameter smooth tube 2.5 m long at a rate of 0.4 kg/s. The ammonia enters at 10oC and leaves at 38oC, and a constant heat flux is imposed on the tube wall. Calculate the average wall temperature necessary to effect the indicated heat transfer.
Liquid Freon 12 (CC12F2) flows inside a 1.25-cm-diameter tube at a velocity of 3 m/s. Calculate the heat-transfer coefficient for a bulk temperature of 10oC. How does this compare with water at the same conditions?
Water at an average temperature of 10oC flows in a 2.5-cm-diameter tube 6 m long at a rate of 0.4 kg/s. The pressure drop is measured as 3 kPa. A constant heat flux is imposed, and the average wall temperature is 50oC. Estimate the exit temperature of the water.
Water at the rate of 0.4 kg/s is to be cooled from 71 to 32oC. Which would result in less pressure drop-to run the water through a 12.5-mm-diameter pipe at a constant temperature of 4oC or through a constant-temperature 25-mm-diameter pipe at 20oC?
Water at an average bulk temperature of 80oF flows inside a horizontal smooth tube with wall temperature maintained at 180oF. The tube length is 2 m, and diameter is 3 mm. The flow velocity is 0.04 m/s. Calculate the heat-transfer rate.
Air at 1400 kPa enters a duct 7.5 cm in diameter and 6 m long at a rate of 0.5 kg/s. The duct wall is maintained at an average temperature of 500 K. The average air temperature in the duct is 550 K. Estimate the decrease in temperature of the air as it passes through the duct.
Air flows at 100oC and 300 kPa in a 1.2-cm-(inside)-diameter tube at a velocity such that a Reynolds number of 15,000 is obtained. The outside of the tube is subjected to a cross-flow of air at 100 kPa, 30oC, and a free-stream velocity of 20 m/s. The tube wall thickness is 1.0 mm. Calculate the

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