A common annoyance in cars during winter is the formation of fog on the glass surfaces that blocks the view. A practical way of solving this problem is to blow hot air or to attach electric resistance heaters to the inner surfaces. Consider the rear window of a car that consists of a 0.4-cm-thick glass (k = 0.84 W/m-K and a = 0.39 x 10-6 m²/s). Strip heater wires of negligible thickness are attached to the inner surface of the glass, 4 cm apart. Each wire generates heat at a rate of 25 W/m length. Initially, the entire car, including its windows, is at the outdoor temperature of To= -3°C. The heat transfer coefficients at the inner and outer surfaces of the glass can be taken to be h;= 6 and ho= 20 W/m².K, respectively. Use the implicit method with a time step of 1 min with a mesh size of Ax=0.2 cm along the thickness and Ay=1 cm in the direction normal to the heater wires. Inner surface Heater 25 W/m 7 Thermal symmetry line Outer surface Glass 0.2 cm 1 cm Thermal symmetry line Determine the temperature at node 4, 15 min after the strip heaters are turned on.

A common annoyance in cars during winter is the formation of fog on the glass surfaces that blocks the view. A practical way of solving this problem is to blow hot air or to attach electric resistance heaters to the inner surfaces. Consider the rear window of a car that consists of a 0.4-cm-thick glass (k = 0.84 W/m-K and a = 0.39 x 10-6 m²/s). Strip heater wires of negligible thickness are attached to the inner surface of the glass, 4 cm apart. Each wire generates heat at a rate of 25 W/m length. Initially, the entire car, including its windows, is at the outdoor temperature of To= -3°C. The heat transfer coefficients at the inner and outer surfaces of the glass can be taken to be h;= 6 and ho= 20 W/m².K, respectively. Use the implicit method with a time step of 1 min with a mesh size of Ax=0.2 cm along the thickness and Ay=1 cm in the direction normal to the heater wires. Inner surface Heater 25 W/m 7 Thermal symmetry line Outer surface Glass 0.2 cm 1 cm Thermal symmetry line Determine the temperature at node 4, 15 min after the strip heaters are turned on.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A common annoyance in cars during winter is the formation of fog on the glass surfaces that blocks the view. A practical way of solving this problem is to blow hot air or to attach electric resistance heaters to the inner surfaces. Consider the rear window of a car that consists of a 0.4-cm-thick glass (k = 0.84 W/m-K and a = 0.39 x 10-6 m2/s). Strip heater wires of negligible thickness are attached to the inner surface of the glass, 4 cm apart. Each wire generates heat at a rate of 25 W/m length. Initially, the entire car, including its windows, is at the outdoor temperature of To= -3°C. The heat transfer coefficients at the inner and outer surfaces of the glass can be taken to be h;= 6 and ho= 20 W/m².K, respectively. Use the explicit finite difference method with a mesh size of Ax = 0.2 cm along the thickness and Ay=1 cm in the direction normal to the heater wires. Inner surface Thermal -symmetry line 5 6 Heater 25 W/m 7 8 9 Outer surface Glass 0.2 cm 1 cm Thermal symmetry line 1)…
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