Extra credit 1 Fall 2023

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School

University of Houston *

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Course

4364

Subject

Aerospace Engineering

Date

Oct 30, 2023

Type

pdf

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Uploaded by ibrahimmriaz

1 Extra Credit 1. Consider 1D, steady-state conduction in a composite wall. The wall consists of two layers, A and B, with thickness of ࠵? ! = 0.1 ࠵? and ࠵? " = 0.2 ࠵? . The thermal conductivities are ࠵? ! = 20 W/mK and ࠵? " = 5 W/mK. The left surface has a temperature of 120℃ and is exposed to air at T ∞ = 20°C. The convection coefficient is h = 50 W/m 2 K. The right surface is well insulated. Inside wall B, there is a uniform heat generation ࠵?̇ . For these conditions, the temperature distribution in B has the form: ࠵?(࠵?) = ࠵? + ࠵?࠵? + ࠵?࠵? # a. Applying an overall energy balance to the wall, calculate the volumetric energy generation rate ࠵?̇. b. Calculate the temperature ࠵? # at the interface between A and B (at ࠵? = 0) . c. Calculate the coefficients a , b and c by applying the boundary conditions to the prescribed temperature distribution. d. Calculate ࠵? $ the temperature at ࠵? = ࠵? " . e. Plot the temperature distribution in the composite wall. f. Plot the heat flux distribution in the composite wall. x B A !̇ # ! = 120℃ # " = 20℃ ℎ = 50 ,/. # / 0 $ = 0.2 . 0 % = 0.1 . # # # &

2 2. Consider a wall sandwiched between two thin metal sheets. The thermal conductivity of the wall material is ࠵? = 0.05 W/mK. The left wall surface receives a solar irradiation heat flux of ࠵? %&’ (( = 100 ࠵?/࠵? # . Hot air of a temperature T ∞,1 = 300°C is blowing on the left side of the wall, and the corresponding convection coefficient is h 1 = 30 W/m 2 K. Cold air of a temperature T ∞,2 = 25°C is blowing on the right side of the wall, and the corresponding convection coefficient is h 2 = 10 W/m 2 K. a. Draw the thermal network for the wall and label all temperatures, thermal resistances, and heat transfer rate through each thermal resistance. b. If the right wall surface temperature is ࠵? # = 40°C, what is the convection heat flux from the hot air entering the wall? c. Following part b, what is the convection heat flux from wall entering the cold air? d. Following part c, calculate the left wall surface temperature ࠵? ) ? e. To maintain a right wall surface temperature ࠵? # of 40°C, what should the thickness of the wall be? ! !"# $$ = 100 &/( % ) &,( = 300℃ ℎ ( = 30 &/( % - . ) ( ) % ) &,% = 25℃ ℎ % = 10 &/( % -

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