Thermodynamics HW Solutions 489

Thermodynamics HW Solutions 489 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-92 The formation of fog on the glass surfaces of a car is to be prevented by attaching electric resistance heaters to the inner surfaces. The temperature distribution throughout the glass 15 min after the strip heaters are turned on and also when steady conditions are reached are to be determined using the implicit method with a time step of Δ t = 1 min. Thermal symmetry line Heater 10 W/m Thermal symmetry line 0.2 cm 1 cm Outer surface 1 2 3 Glass Inner surface Assumptions 1 Heat transfer through the glass is given to be transient and two-dimensional. 2 Thermal conductivity is constant. 3 There is heat generation only at the inner surface, which will be treated as prescribed heat flux. Properties The conductivity and diffusivity are given to be k = 0.84 W/m °C and . α 039 10 6 . m 2 / s Analysis The nodal spacing is given to be Δ x = 0.2 cm and Δ y = 1 cm. The implicit finite difference equations are determined on the
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