A submarine power cable is a cable that is run underwater to carry electrical power across oceans and seas. PETROLEUM JELLY POLYCARBONATE STRANDED METAL (STEEL) WIRES 1-OPTICAL FIBERS -9-POLYETHYLENE 7-STRANDED METAL (STEEL) WIRES 8-"MYLAR" TAPE 5-ALUMINUM WATER BARRIER 2-COPPER OR ALUMINUM TUBE (Image: Wind Systems Magazine) (Image: US Patent #4278835) Usually these cables are very thick and surrounded by protective material but you work for a company whose R&D is focused on developing a new material for submarine cables that allows them to be both electrically conductive and durable enough to withstand the harsh conditions of the ocean. Assume the cable being analyzed is made up of one core material with uniform properties throughout. These cables have a radius of only 0.5mm and some unknown but very long length L (keep your analysis in terms of this unknown length - don't assume a value for it in your written work). The water through which this cable runs is flowing very fast and has a convection coefficient of 450W/m² K and temperature of 25° C. You can assume that this water is touching the entire length of the cable you are analyzing on its entire surface. The special cable material has a density of 7500kg/m³, specific heat capacity of 500J/kgK, and a thermal conductivity of 20W/mK. Electric current flows through the cable at 220A, and its electrical resistance per unit length is 0.01N/m.

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) What is the steady-state temperature of the wire surface if this current has been passing through the cable for a long period of time in these underwater conditions?

b) Assume that the cable starts at the same uniform temperature as the water and then the electrical current is passed through the cable. We're now interested in the amount of time it takes to heat up. Start by calculating the Biot number for this scenario.

c) Derive the appropriate energy balance for this transient analysis.

A submarine power cable is a cable that is run underwater to carry electrical power across
oceans and seas.
PETROLEUM JELLY
POLYCARBONATE
STRANDED METAL
(STEEL) WIRES
1-OPTICAL FIBERS
-9-POLYETHYLENE
7-STRANDED METAL
(STEEL) WIRES
+8-"MYLAR"
TAPE
+2-COPPER OR
ALUMINUM
TUBE
5-ALUMINUM WATER BARRIER
(Image: Wind Systems Magazine)
(Image: US Patent #4278835)
Usually these cables are very thick and surrounded by protective material but you work for a
company whose R&D is focused on developing a new material for submarine cables that
allows them to be both electrically conductive and durable enough to withstand the harsh
conditions of the ocean. Assume the cable being analyzed is made up of one core material
with uniform properties throughout. These cables have a radius of only 0.5mm and some
unknown but very long length L (keep your analysis in terms of this unknown length - don't
assume a value for it in your written work). The water through which this cable runs is flowing
very fast and has a convection coefficient of 450W/m² K and temperature of 25° C. You
can assume that this water is touching the entire length of the cable you are analyzing on its
entire surface. The special cable material has a density of 7500kg/m³, specific heat capacity
of 500J/kgK, and a thermal conductivity of 20W/mK. Electric current flows through the
cable at 220A, and its electrical resistance per unit length is 0.01N/m.

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d) Find the time constant associated with this transient analysis.

e) Find the time it takes for the temperature of the wire surface to reach a temperature that is within 2∘C of the steady-state temperature of the wire.

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