Answer to Question #204834 in Mechanical Engineering for Jaafar Kadi

Question

A body having a cylindrical shape of length equals to 1.9 m and diameter equals to 400 mm is inside a room where the ambient temperature is equal to 300 K. The initial temperature of the body is equal to 350 K. If the heat convective coefficient is equal to 1.3 W/m^2.K. What condition should the thermal conductivity k verify in order to apply the lumped capacitance method

Answer 1

Convective heat transfer coefficient, $h=1.3 w/m^2=k$

Thermal conductivity, $k=?$

$B_i=\frac{hLc}k$

characteristic length, $L_c=\frac{volume}{surface \space area}, L_c=\frac{v}{A_s}$

$L_c=\frac{\pi R^2L}{2 \pi R(R+L)}=\frac{RL}{2(R+L)}$

$L_c= \frac{0.2 *1.9}{2(0.2+1.9)}=0.090476m$

For lumped heat capacity method, is valid,

$Bi \le 0.1$

$\frac{hLc}k \le 0.1$

$\frac{1.3*0.090476}k \le 0.1,k \le1.176 w/m-k$

$k \ge 1.176 w/m-k$

k is greater than 1.176 w/m-k