### OverviewA common issue in cars during winter is fog accumulation on the glass surfaces, obstructing visibility. A practical solution is to use hot air or electric resistance heaters on the inner surfaces. Consider a car's rear window composed of a 0.4-cm-thick glass with thermal conductivity \( k = 0.84 \, \text{W/m} \cdot \text{K} \) and thermal diffusivity \( \alpha = 0.39 \times 10^{-6} \, \text{m}^2/\text{s} \). Strip heaters, with negligible thickness, are attached 4 cm apart on the inner surface, each producing heat at 25 W/m length. Initially, the whole car, including windows, is at an outdoor temperature of \( T_0 = -3^\circ \text{C} \).The heat transfer coefficients on the inner and outer glass surfaces are \( h_i = 6 \, \text{W/m}^2 \cdot \text{K} \) and \( h_o = 20 \, \text{W/m}^2 \cdot \text{K} \), respectively. The implicit method is used with a time step of 1 minute, a mesh size of \( \Delta x = 0.2 \, \text{cm} \) along the thickness, and \( \Delta y = 1 \, \text{cm} \) in the direction normal to the heater wires.### Diagram ExplanationThe diagram illustrates the setup with these features:- **Glass Layers:** The glass is labeled with nodes 1 to 9, showing the arrangement of the strip heaters and indicating the inner and outer surfaces.- **Heater Wires:** Positioned at specific intervals on the inner surface, generating 25 W/m.- **Mesh Size Indication:** The glass is divided into sections with a thickness of 0.2 cm and intervals of 1 cm between heaters.- **Thermal Symmetry Lines:** Indicate symmetry in the distribution of heat across the window.### TaskDetermine the temperature at node 4, 15 minutes after the strip heaters are activated.

Answered: Image /qna-images/answer/525e6086-2da8-4c5d-ac83-3b9c8ddfff39.jpg

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

See similar textbooks

Similar questions

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)…
Consider steady heat transfer between two large parallel plates at constant temperatures of T1 = 500 K and T2 = 300 K that are L = 2.5 cm apart. The emissivity of the surfaces, ɛ = 0.95. Calculate the total rate of heat transfer and the percentage by thermal radiation between the plates per unit surface area assuming the gap between the plates is (a) filled with atmospheric air (k = 0.02 W/m.°C), (b) evacuated. %3D %3D %3D O = 5.67 x 10-8 W/m².K4
A household oven door of 0.4 m height and 0.6 m width reaches an average surface temperature of 50°C during operation. Estimate the total heat loss to the room with ambient air at 22°C and convective heat transfer coefficient 5 W/m².K, if the door has an emissivity of 0.83 and the surroundings are also at 22°C.
1. (a) Consider a room with a 1.8-m-high and 2.0-m-wide double-pane window consisting of two 4-mm-thick layers of glass separated by a 10-mm-wide stagnant air space. The convection heat transfer coefficients on the inner and outer surfaces of the window are 12 W/m2 K and 25 W/m2 K, respectively, while the average thermal conductivity of glass is 0.78 W/m K; and the air, 0.026 W/m K. If the room is maintained at 22 oC, the outside temperature is -4 oC and heat transfer due to radiation can be neglected, determine: (i) Draw the sketch and thermal resistance network; (ii) the total thermal resistance; (iii) the steady rate of heat transfer through this double-pane window; (iv) the temperature of the inner surface of the window.…
How does a fin enhance heat transfer at a surface?
The wall of an oven in an industrial plant, made of fire brick (k = 0.71 W/m/K) has thickness of L = 15 cm. The oven is exposed to air at 28oC and the surfaces of the far surroundings are at 20oC. If the temperature of the outer surface of the wall is 92oC and the heat transfer coefficient and emissivity are 20 W/(m^2*K) and 0.8 respectively, determine the temperature of the inner surface of the wall.
Radioactive material is stored in a spherical vessel with a diameter of 3.7 m, and the center of the vessel is 11 m below the ground. The vessel is surrounded by a 10.2 cm thick layer of rigid foam insulation (k = 0.026 W/m-K). The radioactive material releases heat at a rate of 1000 W/m³. The surface of the soil it's buried in (k = 2 W/m- K) is exposed to wind with a temperature of 20°C and a convection coefficient of 17 W/m²-K. What is the temperature of the surface of the tank?
A thin board of 0.5 cm thickness is exposed to a fluid of T, = 22°C and h = 30 W/m².K from one side with an emissivity of 0.7 where it faces a surrounding whose temperature is Tsur = 30°C. A heat flux of q" = 3500 W/m? is applied to the other side. Each side has an area of 12cm×12cm. Tsur (a) If the board has the following properties: k = 15.1 W/m.K, c, = 480 J/kg.K and p = 8055 kg/m², express an equation for the variation of temperature with respect to time. (b) Find the initial time rate of change of the board temperature if the initial board temperature is q" h 50°C.
Please check attach file
The wall of a house is 4-meter-high and 15 -meter- wide. The wall is constructed with a 9-cm thick outer layer of brick and a 5-cm inner layer of insulating material. On a cold day, the outer surface temperature of the wall is -5°C while the inner surface temperature is 24°C. The thermal conductivity of the brick is 0.80 W/m-K, while the thermal conductivity of the insulation is 0.03 W/m-K . both inner and outer and outer has transfeer coefficeint of 20 W/m2- K a. What is the total thermal resistance of the wal? b. What is the rate of heat loss through the wal
One side of a 2-m-high and 3-m-wide vertical plate at 80°C is to be cooled by attaching aluminum fins (k= 237 W/m-K) of rectangular profile in an environment at 35°C. The fins are 2 cm long, 0.3 cm thick, and 0.4 cm apart. The heat transfer coefficient between the fins and the surrounding air for combined convection and radiation is estimated to be 30 W/m2-K. Assume steady one-dimensional heat transfer along the fin and take the nodal spacing to be 0.5 cm. (Note: Round off all the numerical answers up to 2 decimal places.) T. = 35°C 0.4 cm 0.5 cm ´ 0.3 cm 3 m -2 cm What is the temperature of nodes 1 and 4? (You must provide an answer before moving to the next part.) T = 200.8 8 °C T4 = 235.4 O °C
A furnace wall comprises three layers of thickness 250 mm, 100 mm, and 150 mm with thermal conductivities of 1.65, k and 9. W/m K respectively. The inside is exposed to gases at 1250 ˚C with convection of 25 W/m2K, and the inside surface is at 1100 ˚C, the outside surface air at 25 ˚C with convection of 12 W/m2K. Determine the temperatures of the mid-inner surface in 0C to 1 d.p.?