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A motor draws electric power Pelec P_{\text {elec }} from a supply line and delivers mechanical power Pmech P_{\text {mech }} to a pump through a rotating copper shaft of thermal conductivity ksk_{s}, length L, and diameter D. The motor is mounted on a square pad of width W, thickness t, and thermal conductivity kpk_{p}. The surface of the housing exposed to ambient air at TT_{\infty} is of area AhA_{h}, and the corresponding convection coefficient is hhh_{h}. Opposite ends of the shaft are at temperatures of ThT_{h} and TT_{\infty}, and heat transfer from the shaft to the ambient air is characterized by the convection coefficient hsh_{s}. The base of the pad is at TT_{\infty}. (a) Expressing your result in terms of Pelec ,Pmech ,ksP_{\text {elec }}, P_{\text {mech }}, k_{s}, L, D, W, t, kp,Ah,hhk_{p}, A_{h}, h_{h}, and hsh_{s}, obtain an expression for (ThT)\left(T_{h}-T_{\infty}\right). (b) What is the value of ThT_{h} if Pelec=25kW,Pmech=15kW,ks=400W/mKP_{\mathrm{elec}}=25 \mathrm{kW}, P_{\mathrm{mech}}=15 \mathrm{kW}, k_{s}=400 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}, L=0.5 m, D=0.05 m, W=0.7 m, t=0.05 m, kp=0.5W/mK,Ah=2m2,hh=10W/m2K,hs=300W/m2Kk_{p}=0.5 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}, A_{h}=2 \mathrm{m}^{2}, h_{h}=10 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}, h_{s}=300 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}, and T=25CT_{\infty}=25^{\circ} \mathrm{C}?


A certain semiconductor material has a conductivity of 0.0124 W/cmC0.0124 \mathrm{~W} / \mathrm{cm} \cdot{ }^{\circ} \mathrm{C}. A rectangular bar of the material has a cross-sectional area of 1 cm21 \mathrm{~cm}^2 and a length of 3 cm3 \mathrm{~cm}. One end is maintained at 300C300^{\circ} \mathrm{C} and the other end at 100C100^{\circ} \mathrm{C}, and the bar carries a current of 50 A50 \mathrm{~A}. Assuming the longitudinal surface is insulated, calculate the midpoint temperature in the bar. Take the resistivity as 1.5×103Ωcm1.5 \times 10^{-3} \Omega \cdot \mathrm{cm}.


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-A certain semi conductor material

-The thermal conductivity of material K=0.0124 W/cm.° CK=0.0124\ \mathrm{W/cm.\text{\textdegree} \ \mathrm{C}}

-A rectangular bar of material has cross sectional area A=1 cm2A=1\ \mathrm{cm^{2}} and length of L=3 cmL=3\ \mathrm{cm}

-One end is maintained at temperature T1=300° CT_1=300\text{\textdegree} \ \mathrm{C}

-The other end is maintained at temperature T2=100° CT_2=100\text{\textdegree} \ \mathrm{C}

-The bar carries a current of I=50 AI=50\ \mathrm{A}

-The longitudinal surface is insulated

-The resistivity ρ=1.5×103 Ω.cm\rho=1.5\times 10^{-3}\ \mathrm{\}


-The mid point temperature in the bar


-Steady state condition

-One dimensional conduction

-Constant properties

-Negligible constant resistance

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