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 6.40P
Consider the electronic elements that are cooled by forced convection in Problem 6.39. The cooling system is designed and tested at sea level
- Estimate the surface temperature of the chip located 120 mm from the leading edge of the board when the board is operated in Mexico City. The dependence of various thermophysical properties on pressure is noted in Problem 6.22.
- It is desirable for the chip operating temperature to be independent of the location of the customer. What air velocity is required for operation in Mexico City if the chip temperature is to be the same as at sea level?
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(I) [40 Points] Using centered finite difference approximations as done in class, solve the equation for O:
d20
dx²
+ 0.010+ Q=0
subject to the boundary conditions shown in the stencil below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q= √(0.5 + 2x)e-sinx (cos(5x)+x-0.5√1.006-x| + e −43*|1+.001+x* | * sin (1.5 − x) +
(cosx+0.001 + ex-1250+ sin (1-0.9x)|) * x - 4.68x4. For Case (a) (that is, Q = 0.3), use the stencil in Fig.
1. For Case (b), calculate with both the stencils in Fig. 1 and Fig 2. For all the three cases, show a table as
well as a plot of O versus x. Discuss your results. Use MATLAB and hand in the MATLAB codes.
1
0=0
x=0
2
3
4
0=1
x=1
Fig 1
1 2 3 4 5 6 7 8 9 10
11
0=0
x=0
0=1
x=1
Fig 2
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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- Fig 2 (II) [60 Points] Using centered finite difference approximation as done in class, solve the equation: 020 020 + მx2 მy2 +0.0150+Q=0 subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3, and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b), use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus (x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].) 0=0 0=0 4 8 12 16 10 Ꮎ0 15 25 9 14 19 24 3 11 15 0=0 8-0 0=0 3 8 13 18 23 2 6 сл 5 0=0 10 14 6 12 17 22 1 6 11 16 21 13 e=0 Fig 3 Fig 4 Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth Edition (2021).arrow_forwardShip construction question. Sketch and describe the forward arrangements of a ship. Include componets of the structure and a explanation of each part/ term. Ive attached a general fore end arrangement. Simplfy construction and give a brief describion of the terms.arrow_forwardProblem 1 Consider R has a functional relationship with variables in the form R = K xq xx using show that n ✓ - (OR 1.) = i=1 2 Их Ux2 Ихэ 2 (177)² = ² (1)² + b² (12)² + c² (1)² 2 UR R x2 x3arrow_forward
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