Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 6, Problem 6.23P
To determine
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A plate is cooled by a fluid with Prandtl number Pr >> 1. Surface temperature varies with
distance form the leading edge according to
where C is constant. For such a
fluid it is reasonable to assume
that axial velocity within the
thermal boundary layer is linear
given by
u=V%
y
Determine the local Nusselt
number and show that surface
heat flux is uniform. Use a third
degree polynomial temperature
profile and assume laminar
boundary layer flow
y
YA
To
Vo
T₁(x,0)=T +C√√x
U
-8
&₁
X
T₁(x) = T₁ +C√x
1. Consider a new wind tunnel to test and utilise the effects of boundary layer conditions
in order to maintain the velocity of a fluid. Laminar airflow enters a square duct design
through a 0.25m² opening, as is shown in Figure 1. Because the boundary layer
displacement thickness increases in the direction of flow, it is necessary to increase the
cross-sectional size of the duct if a constant U=1 m/s velocity to be maintained outside
the boundary layer. Assume standard air temperature in the calculation.
U =
1 m/s
0.25 m2
d(x)
1 m/s
Figure 1
a) Determine the expression of the duct size, d, in consideration to maintain the
velocity outside the boundary layer.
b) Plot a graph of the duct size, d, as a function of x for 0
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Chapter 6 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 6 - The temperature distribution within a laminar...Ch. 6 - In flow over a surface, velocity and temperature...Ch. 6 - In a particular application involving airflow over...Ch. 6 - Water at a temperature of T=25C flows over one of...Ch. 6 - For laminar flow over a flat plate, the local heat...Ch. 6 - A flat plate is of planar dimension 1m0.75m. For...Ch. 6 - Parallel flow of atmospheric air over a flat plate...Ch. 6 - For laminar free convection from a heated vertical...Ch. 6 - A circular. hot gas jet at T is directed normal to...Ch. 6 - Experiments have been conducted to determine local...
Ch. 6 - A concentrating solar collector consists of a...Ch. 6 - Air at a free stream temperature of T=20C is in...Ch. 6 - The heat transfer rate per unit width (normal to...Ch. 6 - Experiments to determine the local convection heat...Ch. 6 - An experimental procedure for validating results...Ch. 6 - If laminar flow is induced at the surface of a...Ch. 6 - Consider the rotating disk of Problem 6.16. A...Ch. 6 - Consider airflow over a flat plate of length L=1m...Ch. 6 - A fan that can provide air speeds up to 50 m/s is...Ch. 6 - Consider the flow conditions of Example 6.4 for...Ch. 6 - Assuming a transition Reynolds number of 5105,...Ch. 6 - To a good approximation, the dynamic viscosity the...Ch. 6 - Prob. 6.23PCh. 6 - Consider a laminar boundary layer developing over...Ch. 6 - Consider a laminar boundary layer developing over...Ch. 6 - Experiments have shown that the transition from...Ch. 6 - An object of irregular shape has a characteristic...Ch. 6 - Experiments have shown that, for airflow at T=35C...Ch. 6 - Experimental measurements of the convection heat...Ch. 6 - To assess the efficacy of different liquids for...Ch. 6 - Gases are often used instead of liquids to cool...Ch. 6 - Experimental results for heat transfer over a flat...Ch. 6 - Consider conditions for which a fluid with a free...Ch. 6 - Consider the nanofluid of Example 2.2. Calculate...Ch. 6 - For flow over a flat plate of length L, the local...Ch. 6 - For laminar boundary layer flow over a flat plate...Ch. 6 - Sketch the variation of the velocity and thermal...Ch. 6 - Consider parallel flow over a flat plate for air...Ch. 6 - Forced air at T=25C and V=10m/s is used to cool...Ch. 6 - Consider the electronic elements that are cooled...Ch. 6 - Consider the chip on the circuit board of Problem...Ch. 6 - A major contributor to product defects in...Ch. 6 - A microscale detector monitors a steady flow...Ch. 6 - A thin, flat plate that is 0.2m0.2m on a side is...Ch. 6 - Atmospheric air is in parallel flow...Ch. 6 - Determine the drag force imparted to the top...Ch. 6 - For flow over a flat plate with an extremely rough...Ch. 6 - A thin, flat plate that is 0.2m0.2m on a side with...Ch. 6 - As a means of preventing ice formation on the...Ch. 6 - A circuit board with a dense distribution of...Ch. 6 - On a summer day the air temperature is 27C and the...Ch. 6 - It is observed that a 230-mm-diameter pan of water...Ch. 6 - The rate at which water is lost because of...Ch. 6 - Photosynthesis, as it occurs in the leaves of a...Ch. 6 - Species A is evaporating from a flat surface into...Ch. 6 - Prob. 6.57PCh. 6 - Prob. 6.58PCh. 6 - An object of irregular shape has a characteristic...Ch. 6 - Prob. 6.60PCh. 6 - An object of irregular shape 1 m long maintained...Ch. 6 - Prob. 6.62PCh. 6 - Prob. 6.63PCh. 6 - Prob. 6.64PCh. 6 - Prob. 6.65PCh. 6 - A streamlined strut supporting a bearing housing...Ch. 6 - Prob. 6.67PCh. 6 - Consider the conditions of Problem 6.7, for which...Ch. 6 - Using the naphthalene sublimation technique. the...Ch. 6 - Prob. 6.70PCh. 6 - Prob. 6.71PCh. 6 - Prob. 6.72PCh. 6 - Dry air at 32C flows over a wetted (water) plate...Ch. 6 - Dry air at 32C flows over a wetted plate of length...Ch. 6 - Prob. 6.75PCh. 6 - Prob. 6.76PCh. 6 - Prob. 6.77PCh. 6 - An expression for the actual water vapor partial...Ch. 6 - A mist cooler is used to provide relief for a...Ch. 6 - A wet-bulb thermometer consists of a...Ch. 6 - Prob. 6.81PCh. 6 - Prob. 6.83PCh. 6 - An experiment is conducted to determine the...Ch. 6 - Prob. 6.85PCh. 6 - Consider the control volume shown for the special...Ch. 6 - Prob. 6S.2PCh. 6 - Prob. 6S.3PCh. 6 - Consider two large (infinite) parallel plates, 5...Ch. 6 - Prob. 6S.5PCh. 6 - Consider Couette flow for which the moving plate...Ch. 6 - A shaft with a diameter of 100 mm rotates at 9000...Ch. 6 - Consider the problem of steady, incompressible...Ch. 6 - Prob. 6S.11PCh. 6 - A simple scheme for desalination involves...Ch. 6 - Consider the conservation equations (6S.24) and...
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- Consider two cases involving parallel flow of dry air at V=V= 2.5 m/s, T∞=45°C, and atmospheric pressure over an isothermal plate at Ts=20°C. In the first case, Rex,c=Rex,c=5 × 105, while in the second case the flow is tripped to a turbulent state at x=0 m. a. At what x‐location, in m, are the thermal boundary layer thicknesses of the two cases equal? in m b. what is the q'' lam at W / m^2 c. what is the q'' turb at W / m^2arrow_forwardsolve fastarrow_forwardQuestion 9 Consider the flow of water over a flat plate. In a different experiment consider the flow of air over a flat plate. In both cases the flow is steady, the boundary layers that are formed are laminar and the gravitational acceleration can be neglected. In both cases the velocity far from the plates is the same (v.) and the temperature is also the same (80 °F). For the same distance x from the leading edge, in which boundary layer will the friction coefficient be higher? (a) The friction coefficient is the same for both cases. (b) In water. (c) In air. (d) It depends on the velocity profile that is assumed inside the boundary layer.arrow_forward
- Q4-Q6: A device is used to cool hot copper spheres of diameter 5 mm from an average temperature of 200C to 50C by letting them fall in air at 25°C and latm. Use drag coefficient C, = 0.4 and Whitaker correlation in your calculations. Assume the spheres fall at their terminal velocities during the process. Q4 improve the accuracy? Iteration is not required. ) Determine the terminal velocity of a sphere. Is the use of C, = 0.4 appropriate? If not, how toarrow_forwardConsider two cases involving parallel flow of dry air at V = 3.5 m/s, T = 45°C, and atmospheric pressure over an isothermal plate at T = 20°C. In the first case, Rex.c = 5 × 105, while in the second case the flow is tripped to a turbulent state at x = 0m. At what x -location, in m, are the thermal boundary layer thicknesses of the two cases equal? What are the local heat fluxes, in W/m², at this location for the two cases? x = 9'1'am 9 turb = = i i i m W/m² W/m²arrow_forwardCalculate the drag coefficient and viscous forces on the surface of the red blood cell (diameter = 8 µm, viscosity = 10 mm/s), assuming that the only force which acts on the blood cell is shear stress due to the flowing blood. The blood viscosity is 4 cp and the density is 1100 kg/m³. Also simplify the geometry of the red blood cell so that the area of interest can be considered a perfect sphere.arrow_forward
- Q1: Find the boundary layer thickness (6) equation, the shear stress (to) and the coefficient of drag (Cò ) if the velocity distribution in the laminar boundary layer over the face of a spillway was observed to be: *--(C)- ()*+C). U Then calculate the boundary layer thickness and drag force if the air flows over a sharp edged flat plate 0.25m long and 0.5m wide at a velocity 1 m/s, take the air density 1.23 kg/m³ and the kinematic viscosity is 1.46*10-5 m/s².arrow_forwardProblem 1. The extent of the laminar boundary-layer region before transition to turbulent flow on the surface of an aircraft wing varies with altitude. (a) Calculate the critical length for laminar boundary-layer transition, LSL, at sea level moving at a velocity of 100 mph. (b) Plot the ratio of the critical length, Ler, at altitude to LSL as a function of altitude up to an altitude of z = 30 km. When evaluating properties, use the conditions defined by the U.S. Standard Atmosphere and the Sutherland correlation for viscosity from Appendix A of your textbook (or an online database). (c) Briefly discuss how the laminar boundary-layer length changes with altitude for a given speed and why.arrow_forwardA flow of air at 37m/s and at 1.6m from the leading edge. The transition Reynolds number is 3 x 10^5. If the boundary layer is laminar at this point If the boundary layer is turbulent at this point What is the boundary layer thickness in metres? Assuming that the air density is 1.226 kg/m3 and dynamic viscosity is 1.79 x 10-5 kg/msarrow_forward
- % change in laminar boundary layer thickness in the end of the platearrow_forward(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = 6. Based on Table 2 and setting given to you; () Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2 : Equation of Velocity Profile Setting Equation wU = 3(y/8)/2 – (y/8j?/2arrow_forwardQ1: Find the boundary layer thickness (8) equation, the shear stress (to) and the coefficient of drag (C₁) if the velocity distribution in the laminar boundary layer over the face of a spillway was observed to be: (40%) 2 5 --0-0-0) = 2 + Then calculate the boundary layer thickness and drag force if the air flows over a sharp edged flat plate 0.25m long and 0.5m wide at a velocity 1 m/s, take the air density 1.23 kg/m³ and the kinematic viscosity is 1.46*10-5 m/s².arrow_forward
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