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Tham khảo tài liệu 'a heat transfer textbook - third edition episode 2 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 264 Chapter 5 Transient and multidimensional heat conduction a. Show that eqn. 1.20 leads to d T TC de dt T T dF T where the time constant T is defined as usual. b. If the initial temperature of the object is Ti use either an integrating factor or a Laplace transform to show that T t is T t T t Ti T 0 e t T e t T es TdT s ds. 0 ds 5.53 Use the result of Problem 5.52 to verify eqn. 5.13 . 5.54 Suppose that a thermocouple with an initial temperature Ti is placed into an airflow for which its Bi 1 and its time constant is T. Suppose also that the temperature of the airflow varies harmonically as T t Ti AT cos wt . a. Use the result of Problem 5.52 to find the temperature of the thermocouple Ttc t for t 0. If you wish note that the real part of eiwt is Re Ieiwtj cos wt and use complex variables to do the integration. b. Approximate your result for t T. Then determine the value of Ttc t for wT 1 and for wT 1. Explain in physical terms the relevance of these limits to the frequency response of the thermocouple. c. If the thermocouple has a time constant of T 0.1 sec estimate the highest frequency temperature variation that it will measure accurately. 5.55 A particular tungsten lamp filament has a diameter of 100 ụm and sits inside a glass bulb filled with inert gas. The effective heat transfer coefficient for conduction and radiation is 750 W m-K and the electrical current is at 60 Hz. How much does the filament s surface temperature fluctuate if the gas temperature is 200 C and the average wire temperature is 2900 C 5.56 The consider the parameter p in eqn. 5.41 . a. If the timescale for heat to diffuse a distance Ô is Ô2 a explain the physical significance of p and the consequence of large or small values of p. References 265 b. Show that the timescale for the thermal response of a wire with Bi 1 is pcpô 2h . Then explain the meaning of the new parameter l pcpw5 4nh . c. When Bi 1 is l or p a more relevant parameter References 5.1 H. D. Baehr and K. Stephan. Heat and .