# CSU MECH 344 - HW3 - Solutions (10 pages)

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## HW3 - Solutions

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- Pages:
- 10
- School:
- Colorado State University- Fort Collins
- Course:
- Mech 344 - Heat and Mass Transfer

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PROBLEM 3 3 KNOWN Temperatures and convection coefficients associated with air at the inner and outer surfaces of a rear window FIND a Inner and outer window surface temperatures Ts i and Ts o and b Ts i and Ts o as a function of the outside air temperature T o and for selected values of outer convection coefficient ho SCHEMATIC ASSUMPTIONS 1 Steady state conditions 2 One dimensional conduction 3 Negligible radiation effects 4 Constant properties PROPERTIES Table A 3 Glass 300 K k 1 4 W m K ANALYSIS a The heat flux may be obtained from Eqs 3 11 and 3 12 q T i T o 1 ho q L k 1 hi 0 004 m 40o C 10o C 1 2 65 W m K 1 4 W m K 50o C 0 0154 0 0029 0 0333 m 2 K W 1 30 W m 2 K 969 W m 2 Hence with q h i T i T o the inner surface temperature is Ts i T i q hi 40o C 969 W m 2 30 W m 2 K 7 7o C Similarly for the outer surface temperature with q h o Ts o T o find Ts o T o q 10o C 969 W m 2 2 4 9o C 65 W m K b Using the same analysis Ts i and Ts o have been computed and plotted as a function of the outside air temperature T o for outer convection coefficients of ho 2 65 and 100 W m2 K As expected Ts i and Ts o are linear with changes in the outside air temperature The difference between Ts i and Ts o increases with increasing convection coefficient since the heat flux through the window likewise increases This difference is larger at lower outside air temperatures for the same reason Note that with ho 2 W m2 K Ts i Ts o is too small to show on the plot ho Continued Surface temperatures Tsi or Tso C PROBLEM 3 3 Cont 40 30 20 10 0 10 20 30 30 25 20 15 10 5 0 Outside air temperature Tinfo C Tsi ho 100 W m 2 K Tso ho 100 W m 2 K Tsi ho 65 W m 2 K Tso ho 65 W m 2 K Tsi or Tso ho 2 W m K COMMENTS 1 The largest resistance is that associated with convection at the inner surface The values of Ts i and Ts o could be increased by increasing the value of hi 2 The IHT Thermal Resistance Network Model was used to create a model of the window and generate the above plot The Workspace is shown below Thermal Resistance Network Model The Network Heat rates into node j qij through thermal resistance Rij q21 T2 T1 R21 q32 T3 T2 R32 q43 T4 T3 R43 Nodal energy balances q1 q21 0 q2 q21 q32 0 q3 q32 q43

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