For the following problems for heat conduction in solids, state the 1) different

Question

For the following problems for heat conduction in solids, state the 1) differential equation, 2) initial condition and/or boundary conditions, 3) solution method you would use to obtain answers to the questions below State and justify any assumptions that you make at arriving at your conclusions. Note: You do not need to solve the problems a) A membrane is cured by heating a thin polymer film to a temperature of T1 throughout the entire thickness of the membrane. Curing is accomplished by sandwiching the membrane between two heated plates, which are brought to a temperature of T1 at a given time. You are interested in determining how long it will take to heat the entire thickness of the membrane to the temperature T1 b) A thick ceramic wall of thickness 10 cm is used to prevent heat from being transferred from a flash photolysis reactor to the surrounding room. If the thermal diffusivity of the ceramic is 3 x 10-7 m2ls, answer the following 1. 2. 3. Is the ceramic material sufficient to prevent measurable heat from being transferred to the room, if the flash photolysis reactor is operated for 1 s? Is the ceramic material sufficient to prevent measurable heat from being transferred to the room, if the flash photolysis reactor is operated for 100 s? What is the heat flux into the room if the flash photolysis reactor is operated continuously for several days?

Explanation / Answer

using result of one dimensional differentia lequation for heat transfer it is clear heat transfer decreases rapidly with time as resistance of ceramic material is so high in order of 106 so for 1 sec heat loss is negligible but for 100 sec resistance offered by ceramic material and heat utilization in curing which is proptional t-1.5 and also changes exponatially on time (from heat Equaltion solution) will be oppsing factor ,but cermaic material will still sufficient but for several days(t is very large) heat transfer to the membrane will be minimum and heat flux into the room will be sufficiently high.

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