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patriot [66]
3 years ago
5

A cartridge electrical heater is shaped as a cylinder of length L=200mm and outer diameter D=20 mm. Under normal operating condi

tions the heater dissipates 2kW while submerged in a water flow that is 20℃ and provides a convection heat transfer coefficient of ℎ = 5000 W/m2K. Neglecting heat transfer from the ends of the heater, determine its surface temperature T???? . If the water flow is in advertently terminated while the heater continues to operate, the heater surface is exposed to air that is also at 20℃ but for which ℎ = 50 W/m2K. What is the corresponding surface temperature?
Engineering
1 answer:
lara31 [8.8K]3 years ago
3 0

Answer:

T(water)=50.32℃

T(air)=3052.6℃

Explanation:

Hello!

To solve this problem we must use the equation that defines the transfer of heat by convection, which consists of the transport of heat through fluids in this case water and air.

The equation is as follows!

Q=ha(Ts-T\alpha )

Q = heat

h = heat transfer coefficient

Ts = surface temperature

T = fluid temperature

a = heat transfer area

The surface area of ​​a cylinder is calculated as follows

a=\pi D(\frac{D}{2} +L)

Where

D=diameter=20mm=0.02m

L=leght=200mm)0.2m

solving

a=\pi (0.02)(\frac{0.02}{2} +0.2)=0.01319m^2

For water

Q=2Kw=2000W

h=5000W/m2K

a=0.01319m^2

Tα=20C

Q=ha(Ts-T\alpha )

solving for ts

Ts=T\alpha +\frac{Q}{ha}

Ts=20+\frac{2000}{(0.01319)(5000)} =50.32C

for air

Q=2Kw=2000W

h=50W/m2K

a=0.01319m^2

Tα=20C

Ts=20+\frac{2000}{(0.01319)(50)}=3052.6C

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#include <iostream>

using namespace std;

//function prototype declaration

void MilitaryTime(int, int, char, int &, int &);

int main()

{

    //declare required variables

    int SHour, SMin, MHour, MMin;

    char AorP;

    //promt and read the hours from the user

    cout<<"Enter hours in standard time : ";

    cin>>SHour;

    //check the hours are valid are not

    while(SHour<0 || SHour>12)

    {

         cout<<"Invalid hours for standard time. "

             <<"Try again..."<<endl;

         cout<<"Enter hours in standard time : ";

         cin>>SHour;

    }

    //promt and read the minutes from the user

    cout<<"Enter minutes in standard time : ";

    cin>>SMin;

    //check the minutes are valid are not

    while(SMin<0 || SMin>59)

    {

         cout<<"Invalid minutes for standard time. "

             <<"Try again..."<<endl;

         cout<<"Enter minutes in standard time : ";

         cin>>SMin;

    }

    //promt and read the am or pm from the user

    cout<<"Enter standard time meridiem (a for AM p for PM): ";

    cin>>AorP;

    //check the meridiem is valid are not

    while(!(AorP=='a' || AorP=='p' || AorP=='A' || AorP=='P'))

    {

         cout<<"Invalid meridiem for standard time. "

             <<"Try again..."<<endl;

         cout<<"Enter standard time meridiem (a for AM p for PM): ";

         cin>>AorP;

    }

    //call function to calculate the military time

    MilitaryTime(SHour, SMin, AorP, MHour, MMin);

    //fill zeros and display standard time

    cout.width(2);

    cout.fill('0');

    cout<<SHour<<":";

    cout.width(2);

    cout.fill('0');

    cout<<SMin;

    if(AorP=='a' || AorP=='A')

         cout<<" am = ";

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    //fill zeros and display military time

    cout.width(2);

    cout.fill('0');

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    cout.width(2);

    cout.fill('0');

    cout<<MMin<<endl;

    system("PAUSE");

    return 0;

}

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void MilitaryTime(int SHour, int SMin, char AorP, int &MHour, int &MMin)

{

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             MHour = SHour;

    }

    else

         MHour = SHour+12;

    MMin = SMin;

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