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A cartridge electrical heater is shaped as a cylinder of length L = 200 mm and outer diameter D = 20 mm. Under normal operating conditions the heater dissipates 2 kW while submerged in a water flow that is at 20°C and provides a convection heat transfer coefficient of h = 5000 W/m2 · K. Neglecting heat transfer from the ends of the heater, determine its surface temperature Ts. If the water flow is inadvertently terminated while the heater continues to operate, the ____

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fabianb4235

Answer:

Ts=51.83C

Explanation:

First we calculate the surface area of ​​the cylinder, neglecting the top and bottom covers as indicated by the question

Cilinder Area= A=Ï€DL

L=200mm=0.2m

D=20mm=0.02m

A=Ï€(0.02m)(0.2m)=0.012566m^2

we use the equation for heat transfer by convection

q=ha(Ts-T)

q= heat=2Kw=2000W

A=Area=0.012566m^2

Ts=surface temperature

T=water temperature=20C

Solving for ts

Ts=q/(ha)+T

Ts=2000/(5000*0.012566m^2)+20=51.83C

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