A solid cylinder of length 30cm and radius 1.5cm. When the cylinder is immersed

Question

A solid cylinder of length 30cm and radius 1.5cm. When the cylinder is immersed in a large container of 25C water, where the heat transfer coefficient is 550, the cylinder begins to generate energy uniformly.

A solid cylinder of length 30 cm and radius 1.5 cm lias a density, specific heat and thermal conductivity of p= 11,000 kg/m3, cp = 120 J/kg.K and k = 54 W/m.K, respectively. When the cylinder is immersed in a large container of 25degree C water, where the heat transfer coefficient is 550 W/m2K, the cylinder begins to generate energy uniformly within it at a rate of 0.6 MW/m3. If The initial temperature of the cylinder is equal to that of the water, how much time passes before the temperature of the cylinder reaches 400degree C?

Explanation / Answer

total surface area of cylinder = 2*3.14*0.015^2 +2*3.14*0.015*0.3 =0.0297 m^2

volume =3.14*0.015^2*0.3 =2.12*10^-4 m^3

hence here

het generated per unit time =heat transfered per unit time + heat for temperature rise per unit time

hence 0.6*10^6 *2.12*10^-4 =550*0.0297*(T-25) +11000*2.12*10^-4 *120* dT/dt

hence we get t =3500 sec

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