Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 7, Problem 7.24P
Steel (AISI 1010) plates of thickness
For an initial plate temperature of
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Steel (AISI 1010) plates of thickness δ = 8 mm and length L = 1.3 m on a side are conveyed from a heat treatment process and are concurrently cooled by atmospheric air of velocity u∞ = 11 m/s and T∞ = 23°C in parallel flow over the plates.
For an initial plate temperature of Ti = 329°C, what is the rate of heat transfer from the plate? What is the corresponding rate of change of the plate temperature? The velocity of the air is much larger than that of the plate.
Assuming that the velocity profile in a laminar boundary layer of thickness δ is given by where u is the velocity at distance y from the surface and Ue is the freestream velocity (as shown in Figure P9.23), demonstrate that where θ is the momentum thickness, τw is the viscous stress at the wall, Cf is the local skin friction coefficient at a distance x from the leading edge of the plate, ρ is the density and ν is the kinematic viscosity.
The exact expression for the local Nusselt number for laminar flow along a flat plate is given by: Nux=h(x)x/k=0.332Pr1/3Rex1/2. Atmospheric air at Tinf=400K with a velocity uinf=1.5m/s flows over a flat plate L=2m long maintained at a uniform temperature Tw=300K. Calculate the heat transfer rate from the airstream to the plate from x=0 to x=L=2m for w=0.5m.
A.
234 W
B.
334 W
C.
434 W
D.
134 W
Chapter 7 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 7 - Consider the following fluids at a film...Ch. 7 - Engine oil at 100C and a velocity of 0.1 m/s flows...Ch. 7 - Consider steady, parallel flow of atmospheric air...Ch. 7 - Consider a liquid metal (Pr1), with free stream...Ch. 7 - Consider the velocity boundary layer profile for...Ch. 7 - Consider a steady, turbulent boundary layer on and...Ch. 7 - Consider flow over a flat plate for which it is...Ch. 7 - A flat plate of width 1 m is maintained at a...Ch. 7 - An electric air heater consists of a horizontal...Ch. 7 - Consider atmospheric air at 25C and a velocity of...
Ch. 7 - Repeat Problem 7.11 for the case when the boundary...Ch. 7 - Consider water at 27°C in parallel flow over an...Ch. 7 - Explain under what conditions the total rate of...Ch. 7 - In fuel cell stacks, it is desirable to operate...Ch. 7 - The roof of a refrigerated truck compartment is of...Ch. 7 - The top surface of a heated compartment consists...Ch. 7 - Calculate the value of the average heat transfer...Ch. 7 - The proposed design for an anemometer to determine...Ch. 7 - Steel (AISI 1010) plates of thickness =6mm and...Ch. 7 - Consider a rectangular fin that is used to cool a...Ch. 7 - The Weather Channel reports that it is a hot,...Ch. 7 - In the production of sheet metals or plastics, it...Ch. 7 - An array of electronic chips is mounted within a...Ch. 7 - A steel strip emerges from the hot roll section of...Ch. 7 - In Problem 7.23. an anemometer design was...Ch. 7 - One hundred electrical components, each...Ch. 7 - The boundary layer associated with parallel flow...Ch. 7 - Forced air at 250C and 10 m/s is used to cool...Ch. 7 - Air at atmospheric pressure and a temperature of...Ch. 7 - Consider a thin, 50mm50mm fuel cell similar to...Ch. 7 - The cover plate of a flat-plate solar collector is...Ch. 7 - An array of 10 silicon chips, each of length...Ch. 7 - A square (10mm10mm) silicon chip is insulated on...Ch. 7 - A circular pipe of 25-mm outside diameter is...Ch. 7 - An L=1-m- long vertical copper tube of inner...Ch. 7 - A long, cylindrical, electrical heating element of...Ch. 7 - Consider the conditions of Problem 7.49, but now...Ch. 7 - Pin fins are to be specified for use in an...Ch. 7 - Prob. 7.52PCh. 7 - Prob. 7.53PCh. 7 - Hot water at 500C is routed from one building in...Ch. 7 - In a manufacturing process, long aluminum rods of...Ch. 7 - Prob. 7.58PCh. 7 - To determine air velocity changes, it is proposed...Ch. 7 - Determine the convection heat loss from both the...Ch. 7 - Prob. 7.63PCh. 7 - Prob. 7.64PCh. 7 - Prob. 7.67PCh. 7 - A thermocouple is inserted into a hot air duct to...Ch. 7 - Consider a sphere with a diameter of 20 mm and a...Ch. 7 - Prob. 7.76PCh. 7 - A spherical, underwater instrument pod used to...Ch. 7 - Worldwide. over a billion solder balls must be...Ch. 7 - Prob. 7.80PCh. 7 - Prob. 7.81PCh. 7 - Consider the plasma spray coating process of...Ch. 7 - Prob. 7.83PCh. 7 - Tissue engineering involves the development of...Ch. 7 - Consider temperature measurement in a gas stream...Ch. 7 - Prob. 7.89PCh. 7 - A preheater involves the use of condensing steam...Ch. 7 - Prob. 7.91PCh. 7 - A tube bank uses an aligned arrangement of...Ch. 7 - A tube bank uses an aligned arrangement of...Ch. 7 - Repeat Problem 7.94, but with NL=7,NT=10, and...Ch. 7 - Heating and cooling with miniature impinging jets...Ch. 7 - A circular transistor of 10-mm diameter is cooled...Ch. 7 - A long rectangular plate of AISI 304 stainless...Ch. 7 - A cryogenic probe is used to treat cancerous skin...Ch. 7 - Prob. 7.103PCh. 7 - Prob. 7.104PCh. 7 - Prob. 7.105PCh. 7 - Consider the packed bed of aluminum spheres...Ch. 7 - Prob. 7.108PCh. 7 - Prob. 7.109PCh. 7 - Prob. 7.111PCh. 7 - Packed beds of spherical panicles can be sintered...Ch. 7 - Prob. 7.114PCh. 7 - Prob. 7.116PCh. 7 - Prob. 7.117PCh. 7 - Prob. 7.118PCh. 7 - Prob. 7.119PCh. 7 - Prob. 7.120PCh. 7 - Dry air at 35°C and a velocity of 20 m/s flows...Ch. 7 - Prob. 7.123PCh. 7 - Benzene, a known carcinogen, has been spilled on...Ch. 7 - Prob. 7.125PCh. 7 - Prob. 7.126PCh. 7 - Condenser cooling water for a power plant is...Ch. 7 - Prob. 7.128PCh. 7 - In a paper-drying process, the paper moves on a...Ch. 7 - Prob. 7.131PCh. 7 - Prob. 7.132PCh. 7 - Prob. 7.133PCh. 7 - Prob. 7.134PCh. 7 - Prob. 7.136PCh. 7 - It has been suggested that heat transfer from a...Ch. 7 - Prob. 7.138PCh. 7 - Cylindrical dry-bulb and wet-bulb thermometers are...Ch. 7 - The thermal pollution problem is associated with...Ch. 7 - Cranberries are harvested by flooding the bogs in...Ch. 7 - A spherical drop of water, 0.5 mm in diameter, is...Ch. 7 - Prob. 7.143PCh. 7 - Prob. 7.144PCh. 7 - Prob. 7.145PCh. 7 - Prob. 7.146PCh. 7 - Prob. 7.147PCh. 7 - Consider an air-conditioning system composed of a...Ch. 7 - Prob. 7.149P
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- 1-The wind blows with velocity 0.4 m/s parallel to the both sides of a flat plate with rectangular area 10m×10 m. The plate temperature is T0=60◦C, and the temperature of the air free stream is 20◦C. Assume laminar flow and calculate: (a) maximum boundary layer thickness, (b) the total force experienced by the plate, (c) estimate the total heat transfer rate by laminar forced convection (d) Make a qualitative sketch of how the local heat flux qx and τx varies along the length L.arrow_forwardAir at atmospheric pressure and a temperature of 25°C is in parallel flow at a velocity of 5 m/s over a 1‐m‐long flat plate that is heated from below with a uniform heat flux of 1,250 W/m^2. Assume the flow is fully turbulent over the length of the plate. (a) Calculate the plate surface temperature, Ts(L), and the local convection coefficient, hx(L), at the trailing edge, x = L. (b) Calculate the average temperature of the plate surface, T¯s. (c) Plot the variation of the surface temperature, Ts(x), and the convection coefficient, hx(x), with distance on the same graph. Explain the key features of these distributionsarrow_forwardAir at atmospheric pressure and a temperature of 25 degrees C is in parallel flow at a velocity of 5 m/s over a 1-m-long flat plate that is heated from below with a uniform heat flux of 1250 W/m2 . Assume the flow is fully turbulent over the length of the plate. Take ν = 18.76 × 10−6 m2/s, k = 0.0284 W/m·K and Pr =0.703. (a) Calculate the plate surface temperature, Ts(L), and the local convection coefficient, hx(L), at the trailing edge, x = L. (b) Calculate the average temperature of the plate surface.arrow_forward
- Air at standard pressure flows across a flat plate at 3m/s. The temperature surface is 50oC and the surrounding temperature is 20o Consider a point 1m away from the leading edge of the plate. See Table A-15 in Appendix 1 for properties of air. Determine the Reynold’s number and Prandtl number for this flow at the location described above. Determine the local flow boundary layer thickness. Determine the local thermal boundary layer thickness for this flow.arrow_forwardAir at atmospheric pressure and temperature of 25 oC flows at a speed of 10 m/s along a flat plate that is 4 m long and has a uniform surface temperature of 140 oC. Ifcritical Reynolds number of 200,000:a) the local heat transfer kingdom at x = 2; 3; and 4 m from the front rim.b) the average heat transfer balance is 4 m long.c) the rate of heat transfer from the surface of the plate to the air if the width of the plate surface is 2 m.d) game problems b) and c) flow velocity 5 and 20 m/se) What is your analysis and conclusion on this case?arrow_forwardAir at -10° C flows over a smooth sharp-edged, almost flat aerodynamics surface that is held at 10°C, at a speed of 120 km/hr . What is the greatest length the plate can be if the flow is to remain laminar over the entire length of the plate? What would be the average film coefficient be of that plate and what is the heat flux? What are the heights of the fluid and thermal boundary layers at the end of that length? Use Re = 350,000 for the critical Reynolds number.arrow_forward
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