Transport Phenomena and Rate Processes · Heat transfer · 2 marks · Numerical answer
Steady radial conduction in an infinitely long hollow zirconia cylinder obeys $d^2T/dr^2+(1/r)dT/dr=0$. Inner and outer radii are 0.05 and 0.07 m, at 1473 and 973 K respectively. Conductivity is 2 W/(m K). Find heat loss per unit length in W/m (nearest integer).
Integrating the cylindrical conduction equation gives T=A ln r+B. The resulting outward heat rate per length is $q/L=2\pi k(T_i-T_o)/\ln(r_o/r_i)$. Substitute to obtain $2\pi(2)(500)/\ln(1.4)=18674$ W/m approximately. The logarithm accounts for changing radial heat-flow area.
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