Inverse Heat Conduction 2nd. Edition by Hamidreza Najafi, Keith A. Woodbury, Filippo de Monte, James V. Beck | 9781119840190 | 1119840198 | Holooly

Inverse Heat Conduction

44 SOLVED PROBLEMS

Question: 3.6

A steel plate (α = 10−5 m²/s), initially at 20 °C, is subject at x = 0 to a surface heat flux as given by Eq. (3.50), starting at time zero, with p = 2 (quadratic-in-time increase) and sq = q0/t²ref = 105 W/m²/s². The plate is insulated on the back side x=L= 5 cm. Calculate the temperature at 1.25 ...

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The current problem can be denoted by X22B30T1, wh...

Question: 3.3

A steel plate (α = 10^−5 m² /s), initially at 20 °C, is subject at x = 0 to a surface temperature as given by Eq. (3.17), starting at time zero, with p = 2 (quadratic-in-time increase) and sT = (T0 − Tin)/t²ref = 2 °C s^−2. The plate is insulated on the back side x = L = 5 cm. Calculate the ...

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The current problem can be denoted by X12B30T1, wh...

Question: 10.5

Consider the same intrinsic thermocouple as in Example 10.4 with β = 1.33. Suppose that “measurements” are made using the thermocouple, and that these measurements are Yi = 20 exp (−0.15t^+) + εi (10.24) where εi is a random number from a Gaussian distribution with zero mean and standard deviation ...

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The measurements Y are computed using the specifie...

Question: 3.9

A steel plate (α = 10^−5 m²/s, k = 40 W/m- °C), initially at 30 °C, is subject at x = 0 to a surface heat flux as q0(y , t) = qy0 (y/W)^py + qt0 (t/tref)^pt = σqy^py + sqt^pt (0 ≤ y ≤ W; t ≥ 0) with py = 1 (linear-in-space increase), a slope of σq = q0/W = 10^6 (W/m²)/m, pt = 1 (linear-in-time ...

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The temperature at the surface point of interest [...

Question: 3.8

Calculate the temperature of the rectangular body of Example 3.7 at three different locations of its heated surface, say 1, 10 and 19 cm, at time 12.5 seconds by using the fdX22By_t10Y22B00T0_pua.m MATLAB function for different space steps. ...

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The temperatures of the rectangle at the surface p...

Question: 3.5

Calculate the temperature at 1 cm inside the steel plate of the X22B20T1 case of Example 3.4 of Section 3.4.1.4 at times 1, 2, and 3 seconds by using Eq. (3.62). Then, compare it with the exact values coming from the exact analytical solution defined in Section 2.3.9 of Chapter 2. ...

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The temperature at the interior point of interest ...

Question: 3.4

A steel plate (α = 10^−5 m²/s, k = 40 W/m/ °C), initially at 30 °C, is subject at x = 0 to a surface heat flux as given by Eq. (3.50), starting at time zero, with p = 1 (linear-in-time increase) and a rate of sq = q0/tref = 106 W/m²/s. The plate is insulated on the back side x=L= 5 cm. Calculate ...

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The temperature at the interior point of interest ...

Question: 3.7

A steel plate (α = 10^−5 m²/s, k = 40 W/m/ °C), initially at 30 °C, is subject at x = 0 to a surface heat flux as given by Eq. (3.80), starting at y = 0, with p = 1 (linear-in-space variation), and ending at y = W, with a slope of σq = qy0/ W = 107 (W/m²)/m. The plate is insulated on the back side ...

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The temperature at the heated surface point of int...

Question: 10.4

Consider an intrinsic thermocouple having β = 1.33. For a step change in substrate temperature, determine the correction kernel H. Use a time step of Δt^+=0.01 and consider 0 ≤ t^+≤ 10. ...

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Eq. (10.19) is used to compute the temperature of ...

Question: 3.2

Calculate the temperature at 1 cm inside the steel plate of Example 3.1 of Section 3.3.1.4 at times 1, 2, and 3 seconds by using Eq. (3.31). Then, compare it with the exact values coming from the exact analytical solution defined in Section 2.3.7. ...

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The temperature at the interior point of interest ...

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