(I) [40 Points] Using centered finite difference approximations as done in class, solve the equation for O:d20dx²+ 0.010+ Q=0subject 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 aswell as a plot of O versus x. Discuss your results. Use MATLAB and hand in the MATLAB codes.10=0x=02340=1x=1Fig 11 2 3 4 5 6 7 8 9 10110=0x=00=1x=1Fig 2

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Answered: (I) [40 Points] Using centered finite…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.7P

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Solve the preceding problem for the following data: x=190106,y=230106,xy=160106,and=45.
5.19 Suppose that the graph below shows measured values of for air in forced convection over a cylinder of diameter D. plotted on a logarithmic graph of as a function of ReD Pr. Write an appropriate dimensionless correlation for the average Nusselt number for these data and state any limitations to your equation.
5.2 Evaluate the Prandtl number from the following data: , .
A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:).
The drag on an airplane wing in flight is known to be a function of the density of air (), the viscosity of air(), the free-stream velocity (U), a characteristic dimension of the wing (s), and the shear stress on the surface of the wing (s). Show that the dimensionless drag, sU2, can be expressed as a function of the Reynolds number, Us.
To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the material is subjected to a uniform heat flux of 2500 W/m2 while thermocouples embedded in the wall at 2.5 cm. intervals are read over a period of time. After the system had reached equilibrium, an operator recorded the thermocouple readings shown below for two different environmental conditions: Distance from the Surface (cm) Temperature (C) Test 1 0 40 5 65 10 97 15 132 Test 2 0 95 5 130 10 168 15 208 From these data, determine an approximate expression for the thermal conductivity as a function of temperature between 40 and 208C.
Use numerical integration to compute the product of inertia of the region show with respect to the x- and y-axes.
A differential equation is d2ydt2=Ay2+Byt where y represents a distance and t is time. Determine the dimensions of constants A and B for which the equation will be dimensionally homogeneous.
Using the information in Problem 1.22, estimate the ambient air temperature that could cause frostbite on a calm day on the ski slopes. 1.22 In order to prevent frostbite to skiers on chair lifts, the weather report at most ski areas gives both an air temperature and the wind-chill temperature. The air temperature is measured with a thermometer that is not affected by the wind. However, the rate of heat loss from the skier increases with wind velocity, and the wind-chill temperature is the temperature that would result in the same rate of heat loss in still air as occurs at the measured air temperature with the existing wind. Suppose that the inner temperature of a 3-mm-thick layer of skin with a thermal conductivity of 0.35W/mKis35C and the air temperature is 20C. Under calm ambient conditions the heat transfer coefficient at the outer skin surface is about 20W/m2K (see Table 1.4), but in a 40-mph wind it increases to 75W/m2K. If frostbite occurs when the skin temperature drops to about 10C, do you advise the skier to wear a face mask? What is the skin temperature drop due to the wind?
1.22 In order to prevent frostbite to skiers on chair lifts, the weather report at most ski areas gives both an air temperature and the wind-chill temperature. The air temperature is measured with a thermometer that is not affected by the wind. However, the rate of heat loss from the skier increases with wind velocity, and the wind-chill temperature is the temperature that would result in the same rate of heat loss in still air as occurs at the measured air temperature with the existing wind. Suppose that the inner temperature of a 3-mm-thick layer of skin with a thermal conductivity of 0.35 W/m K is and the air temperature is . Under calm ambient conditions the heat transfer coefficient at the outer skin surface is about (see Table 1.4), but in a 40-mph wind it increases to . (a) If frostbite occurs when the skin temperature drops to about , do you advise the skier to wear a face mask? (b) What is the skin temperature drop due to the wind?
If the R-value of a construction material is 2.0, what isits U-value? A. 0.25 B. 0 50 C. 1.0 D. 2.0
Use integration to verify the formula given in Table 9.2 for Ixy of a half parabolic complement.

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