Q2 A 2 kW resistance heater wire with thermal conductivity of k = 20 W/m °C, a diameter of D = 5 mm, and a length of L = 0.7 m is used to boil water. If the outer surface temperature of the resistance wire is Ts = 110°C, determine the temperature at the center of the wire.

Elements Of Electromagnetics
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Q2 A 2 kW resistance heater wire with thermal conductivity of k = 20 W/m °C, a
diameter of D = 5 mm, and a length of L= 0.7 m is used to boil water. If the outer
surface temperature of the resistance wire is Ts= 110°C, determine the temperature at the
center of the wire.
Q3: Consider a 20-cm-thick large concrete plane wall (k = 0.77 W/m °C) subjected to
convection on both sides with T1 = 27°C and h₁ = 5 W/m² °C on the inside, and T2 =
8°C and h₂ = 12 W/m² °C on the outside. Assuming constant thermal conductivity with
no heat generation and negligible radiation, (a) express the differential equations and the
boundary conditions for steady one-dimensional heat conduction through the wall, (b)
obtain a relation for the variation of temperature in the wall by solving the differential
equation, and (c) evaluate the temperatures at the inner and outer surfaces of the wall.
Ans: (a)
Ans: 121.4 °C
dT (L)
-k
dx
-=h₂ [T(L)-T₂]
(b) T(x) = 20-45.44x
Q4: A double pane window consists of 3 mm thick layer of glass separated by a 12 mm wide
stagnant air space. for specified indoors and outdoors and outdoors temperatures, determine the
rate of the heat loss through the window and the inner surface temperature of the window.
Take kglass = 0.78 W/m °C and Kair= 0.026 W/m °C
Ans: 114 W, 19.2 °C
(c) 10.9°
34
Air
Transcribed Image Text:Q2 A 2 kW resistance heater wire with thermal conductivity of k = 20 W/m °C, a diameter of D = 5 mm, and a length of L= 0.7 m is used to boil water. If the outer surface temperature of the resistance wire is Ts= 110°C, determine the temperature at the center of the wire. Q3: Consider a 20-cm-thick large concrete plane wall (k = 0.77 W/m °C) subjected to convection on both sides with T1 = 27°C and h₁ = 5 W/m² °C on the inside, and T2 = 8°C and h₂ = 12 W/m² °C on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation, (a) express the differential equations and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperatures at the inner and outer surfaces of the wall. Ans: (a) Ans: 121.4 °C dT (L) -k dx -=h₂ [T(L)-T₂] (b) T(x) = 20-45.44x Q4: A double pane window consists of 3 mm thick layer of glass separated by a 12 mm wide stagnant air space. for specified indoors and outdoors and outdoors temperatures, determine the rate of the heat loss through the window and the inner surface temperature of the window. Take kglass = 0.78 W/m °C and Kair= 0.026 W/m °C Ans: 114 W, 19.2 °C (c) 10.9° 34 Air
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