A common annoyance in cars in winter months 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/mK and α = 0.39 × 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 hi = 6 and ho = 20 W/m² K, respectively. Using 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, determine the temperature distribution throughout the glass 15 min after the strip heaters are turned on. Also, determine the temperature distribution when steady conditions are reached (5th Ed, prob. 5.116). - Thermal symmetry line Inner Outer surface surface Glass Heater 25 W/m -0.2 cm 1 cm -Thermal symmetry line

A common annoyance in cars in winter months 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/mK and α = 0.39 × 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 hi = 6 and ho = 20 W/m² K, respectively. Using 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, determine the temperature distribution throughout the glass 15 min after the strip heaters are turned on. Also, determine the temperature distribution when steady conditions are reached (5th Ed, prob. 5.116). - Thermal symmetry line Inner Outer surface surface Glass Heater 25 W/m -0.2 cm 1 cm -Thermal symmetry line

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.48P: A horizontal, 3-mm-thick flat-copper plate, 1-m long and 0.5-m wide, is exposed in air at 27C to...

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Heat transfer
heat
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)…