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HW2 - Hint general solution for a differential equation of...

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CHE 303-Problem Set 2 Due October 12, 2011, 4 PM 1) Consider a shielding wall for a nuclear reactor. The wall receives a gamma-ray flux such that the heat is generated within the wall according to the relation e -ax Where, is the heat generation at the inner face of the wall exposed to the gamma-ray flux and a is a constant. Derive an expression for the temperature distribution in a wall of thickness L, where the inside and outside temperatures are maintained at T i and T 0 respectively. You can assume 1-D heat conduction and steady state. Also, obtain an expression for the maximum temperature in the wall. 2) Derive an expression for the temperature distribution in a plane wall in which distributed heat sources vary according to the linear relation Where is a constant. Both sides of the plate are maintained at temperature
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Unformatted text preview: Hint: general solution for a differential equation of the form ¿ À Á ¿Â À ¸ ÃÁ ² Ä´Å ´ÆÇÈÉȴôÊË´Ì´ÍÎÏËÐÌÏÐ is Á ² Ñ Ò ÑÎË´ÓÔà ÂÕ ¸ Ñ À ÖÊÏ´ºÔà ½ 3) Electric heater wires are installed in a solid wall having a thickness of 8 cm and k =2.5 W/m. o C. The right face is exposed to an environment with h =50 W/m 2 o C and » × =30 o C, while the left face is exposed to h =75 W/m 2 o C and » × =50 o C. What is the maximum allowable heat generation rate such that the maximum temperature in the solid does not exceed 300 o C? 4) Derive an expression for the temperature distribution in a hollow cylinder with heat sources that vary according to the following relation ± ² Ì ¸ ØÉ a and b are constants. The inside and outside temperatures are T=T i at r=r i and T=T 0 at r=r 0 Assume steady state and 1-D conduction...
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