Heat is produced in a long resistance wire q.u= 1.5 W/cm3. The radius of the wire is given as r1=0.3 cm and the thermal conductivity coefficient as ksteel=18 W/m.K. In addition, the wire is covered with a 0.4 cm thick plastic layer with a thermal conductivity coefficient of kplastic = 1.8 W/m.K. The outer surface of the plastic layer loses heat with an average heat transfer coefficient of h=14/W/m2K and by convection to the ambient air at T∞ =250 C. Considering the interface temperature as T1 and accepting the heat transfer as one-dimensional; a) Find the expression for the temperature distribution for the resistance wire, using the1 ddifferential equation r dr("ar)k and applying the necessary boundary conditions.b) Find the expression for the temperature distribution for the plastic layer, using thedTdifferential equation drc) The temperature at the centre of the resistance wire under continuous conditions, andand applying the necessary boundary conditions.d) Calculate the temperature at the wire-plastic interface (T1)T00hTelPlastik

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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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Heat is produced in a long resistance wire q^._u= 1.5 W/cm³. The radius of the wire is given as r₁=0.3 cm and the thermal conductivity coefficient as k_steel=18 W/m.K. In addition, the wire is covered with a 0.4 cm thick plastic layer with a thermal conductivity coefficient of k_plastic = 1.8 W/m.K. The outer surface of the plastic layer loses heat with an average heat transfer coefficient of h=14/W/m²K and by convection to the ambient air at T∞ =25⁰ C. Considering the interface temperature as T₁ and accepting the heat transfer as one-dimensional;

a) Find the expression for the temperature distribution for the resistance wire, using the
1 d
differential equation r dr
("ar)
k and applying the necessary boundary conditions.
b) Find the expression for the temperature distribution for the plastic layer, using the
dT
differential equation dr
c) The temperature at the centre of the resistance wire under continuous conditions, and
and applying the necessary boundary conditions.
d) Calculate the temperature at the wire-plastic interface (T1)
T
00
h
Tel
Plastik

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