a) First, let's start with the steady-state analysis for the cable. 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? Enter only a numeric value (with no units entered) and express your answer in ∘C.b) Now, let's think about the transient case. 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. Enter only a numeric value (your answer should be unitless). c) From this Biot number and your simplifications of the geometry, select the appropriate assumptions:There is no heat generation in the cable.We must account for heat transfer from the circular ends of the cable.We will neglect radiative heat transfer from the cable.The properties in this scenario will remain constant (independent of temperature).The cable must not be treated as lumped (a 1D or higher order analysis is warranted).The cable can now be assumed to be in steady-state.The cable can be treated as lumped (OD). A submarine power cable is a cable that is run underwater to carry electrical power across oceansand seas.PETROLEUM JELLYPOLYCARBONATESTRANDED METAL(STEEL) WIES1-OPTICAL FIRERS9-POLYETHYLENESTRANDED METAL(STEEL) WIRES-8-MILAN+2-COPPER ORALUMAVUM-ALUMUM WATEN BAR(Image: Wind Systems Magazine)(Image: US Patent #4278835)Usually these cables are very thick and surrounded by protective material but you work for acompany whose R&D is focused on developing a new material for submarine cables that allows themto be both electrically conductive and durable enough to withstand the harsh conditions of theocean. Assume the cable being analyzed is made up of one core material with uniform propertiesthroughout. 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 writtenwork). The water through which this cable runs is flowing very fast and has a convection coefficientof 450W/m² K and temperature of 25° C. You can assume that this water is touching the entirelength of the cable you are analyzing on its entire surface. The special cable material has a density of7500kg/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 is0.010/m.

Given Data: Radius of wire r = 0.5 mmh = 450 W/m2KT∞ = 25°Cp = 7500 kg/m3cp=500 J/kgKK = 20…

Answered: Usually these cables are very thick and…

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) First, let's start with the steady-state analysis for the cable. 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? Enter only a numeric value (with no units entered) and express your answer in ∘C.

b) Now, let's think about the transient case. 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. Enter only a numeric value (your answer should be unitless).

From this Biot number and your simplifications of the geometry, select the appropriate assumptions:
There is no heat generation in the cable.
We must account for heat transfer from the circular ends of the cable.
We will neglect radiative heat transfer from the cable.
The properties in this scenario will remain constant (independent of temperature).
The cable must not be treated as lumped (a 1D or higher order analysis is warranted).
The cable can now be assumed to be in steady-state.
The cable can be treated as lumped (OD).

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) WIES
1-OPTICAL FIRERS
9-POLYETHYLENE
STRANDED METAL
(STEEL) WIRES
-8-MILAN
+2-COPPER OR
ALUMAVUM
-ALUMUM WATEN BAR
(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
0.010/m.

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