Answer to Question #204834 in Mechanical Engineering for Jaafar Kadi

Question #204834

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


1
Expert's answer
2021-06-10T03:46:45-0400

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



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