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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 h₁ = 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 Heater 25 W/m 7 8 Thermal symmetry line 6 K 9 Outer surface Glass 0.2 cm 1 cm Thermal symmetry line 1) Determine the temperature at node 3, 15 min after the strip heaters are turned on. 2) Determine the temperature at node 3 when steady conditions are reached.

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 h₁ = 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 Heater 25 W/m 7 8 Thermal symmetry line 6 K 9 Outer surface Glass 0.2 cm 1 cm Thermal symmetry line 1) Determine the temperature at node 3, 15 min after the strip heaters are turned on. 2) Determine the temperature at node 3 when steady conditions are reached.

Elements Of Electromagnetics
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) Determine the temperature at node 3, 15 min after the strip heaters are turned on. 2) Determine the temperature at node 3 when steady conditions are reached.
Transcribed Image Text: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) Determine the temperature at node 3, 15 min after the strip heaters are turned on. 2) Determine the temperature at node 3 when steady conditions are reached.
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