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 0.019/m.

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Chapter8: Natural Convection
Section: Chapter Questions
Problem 8.36P
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a)

b) Find the time constant associated with this transient analysis.  Enter only a numeric value (with no units entered) and express your answer in units of seconds. 

c) 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. Enter only a numeric value (with no units entered) and express your answer in units of seconds. 

Select the appropriate energy balance for this transient analysis:
dT
-kA, -h(T-T) A₁ + Ég = mc₂
Oh (T-T) A, = mcp de
-h (T-Tx) As + Ėg = 0
dT
Oh (T-T) A, + Ég = mc₂
Transcribed Image Text:Select the appropriate energy balance for this transient analysis: dT -kA, -h(T-T) A₁ + Ég = mc₂ Oh (T-T) A, = mcp de -h (T-Tx) As + Ėg = 0 dT Oh (T-T) A, + Ég = mc₂
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.
Transcribed Image Text: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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