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[T(1,t)-T(1,0)]/[Q"/pcl)] The figure on the right side shows the measured temperature transients of T(l,t) using the flash method to measure the thermal diffusivity of a sample with a thickness of 4 mm. a) Estimate the value of t1/2 from this figure? How to determine the thermal diffusivity based on 11/2? What is the thermal diffusivity of the sample based on t1/2? Check the unit of the diffusivity. Does the determined value of the thermal diffusivity make sense, considering that the majority component in tissue is water? b) You should be able to determine the thermal diffusivity of the sample from any set of values (T(l,te), te), where te is any time instant? For example, t 25 seconds, and the dimensionless temperature is around 0.8. What method are you going to use to determine the thermal diffusivity value? (Hint: once the values of t=te and T(lt.) are substituted into the temperature expression given on page 21 in the notes, the only thing one does not know in the equation is the thermal diffusivity a. Even if on one side of the equation is a summation, one should be able to solve for the value of a.) 0 10 20 30 40 50 60 70 t(s) 1 0.5 c) Can you determine the thermal diffusivity of the sample from all the measured values on this Figure? If yes, how? If no, why? (Hint: think about curve fitting.)

[T(1,t)-T(1,0)]/[Q"/pcl)] The figure on the right side shows the measured temperature transients of T(l,t) using the flash method to measure the thermal diffusivity of a sample with a thickness of 4 mm. a) Estimate the value of t1/2 from this figure? How to determine the thermal diffusivity based on 11/2? What is the thermal diffusivity of the sample based on t1/2? Check the unit of the diffusivity. Does the determined value of the thermal diffusivity make sense, considering that the majority component in tissue is water? b) You should be able to determine the thermal diffusivity of the sample from any set of values (T(l,te), te), where te is any time instant? For example, t 25 seconds, and the dimensionless temperature is around 0.8. What method are you going to use to determine the thermal diffusivity value? (Hint: once the values of t=te and T(lt.) are substituted into the temperature expression given on page 21 in the notes, the only thing one does not know in the equation is the thermal diffusivity a. Even if on one side of the equation is a summation, one should be able to solve for the value of a.) 0 10 20 30 40 50 60 70 t(s) 1 0.5 c) Can you determine the thermal diffusivity of the sample from all the measured values on this Figure? If yes, how? If no, why? (Hint: think about curve fitting.)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The figure shows the measured temperature transients of \( T(l,t) \) using the flash method to assess the thermal diffusivity of a sample with a thickness of 4 mm. ### Questions and Analysis: **a) Estimate the value of \( t_{1/2} \) from this figure. How to determine the thermal diffusivity based on \( t_{1/2} \)? What is the thermal diffusivity of the sample based on \( t_{1/2} \)?** - **Check the unit of the diffusivity:** Does the determined value of the thermal diffusivity make sense, considering that the majority component in tissue is water? **b) Determining the thermal diffusivity from any set of values \( (T(l,t_s), t_s) \):** - For example, \( t_s = 25 \) seconds, with the dimensionless temperature around 0.8. - **Hint:** Once the values of \( t = t_s \) and \( T(l,t_s) \) are substituted into the temperature expression, the only unknown is the thermal diffusivity \( \alpha \). You should be able to solve for \( \alpha \). **c) Can the thermal diffusivity of the sample be determined from all measured values in the figure?** - If yes, how? If no, why? Consider the concept of curve fitting. ### Graph Explanation: The graph presented is a plot of dimensionless temperature \( \frac{T(l,t)-T(l,0)}{(Q/\rho c)} \) on the vertical axis against time \( t(s) \) on the horizontal axis. The curve trends upward, approaching a steady state as time progresses. The \( t_{1/2} \) is the time at which the curve reaches half of its maximum value. This data can be used to determine thermal diffusivity using mathematical modeling or curve fitting techniques.
Transcribed Image Text:The figure shows the measured temperature transients of \( T(l,t) \) using the flash method to assess the thermal diffusivity of a sample with a thickness of 4 mm. ### Questions and Analysis: **a) Estimate the value of \( t_{1/2} \) from this figure. How to determine the thermal diffusivity based on \( t_{1/2} \)? What is the thermal diffusivity of the sample based on \( t_{1/2} \)?** - **Check the unit of the diffusivity:** Does the determined value of the thermal diffusivity make sense, considering that the majority component in tissue is water? **b) Determining the thermal diffusivity from any set of values \( (T(l,t_s), t_s) \):** - For example, \( t_s = 25 \) seconds, with the dimensionless temperature around 0.8. - **Hint:** Once the values of \( t = t_s \) and \( T(l,t_s) \) are substituted into the temperature expression, the only unknown is the thermal diffusivity \( \alpha \). You should be able to solve for \( \alpha \). **c) Can the thermal diffusivity of the sample be determined from all measured values in the figure?** - If yes, how? If no, why? Consider the concept of curve fitting. ### Graph Explanation: The graph presented is a plot of dimensionless temperature \( \frac{T(l,t)-T(l,0)}{(Q/\rho c)} \) on the vertical axis against time \( t(s) \) on the horizontal axis. The curve trends upward, approaching a steady state as time progresses. The \( t_{1/2} \) is the time at which the curve reaches half of its maximum value. This data can be used to determine thermal diffusivity using mathematical modeling or curve fitting techniques.
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