The heater wire of Example 2-7 is submerged in a fluid maintained at $93^{\circ} \mathrm{C}$. The convection heat-transfer coefficient is $5.7 \mathrm{~kW} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$. Calculate the center temperature of the wire.

A hot-wire anemometer consists of a 5-mm-long, 5- $\mu \mathrm{m}$ diameter platinum wire. The probe is operated at a constant current of $0.03 \mathrm{~A}$. The electrical resistivity of platinum is $17 \mu \Omega \mathrm{cm}$ at $20^{\circ} \mathrm{C}$ and increases by $0.385 \%$ per ${ }^{\circ} \mathrm{C}$. (a) If the voltage across the wire is $1.75 \mathrm{~V}$, determine the velocity of the air flowing across it and the wire temperature if the free-stream air temperature is $20^{\circ} \mathrm{C}$. (b) What are the wire temperature and voltage if the air velocity is $10 \mathrm{~m} / \mathrm{s}$ ? Neglect radiation and conduction heat transfer from the wire.

For the cantilever steel beam $[E=200 \mathrm{GPa} ; I=129 \times$ $\left.10^6 \mathrm{~mm}^4\right]$ shown in Figure P10.12, use the double-integration method to determine the deflection at $A$. Assume that $L=2.5 \mathrm{~m}$, $P=50 \mathrm{kN}$, and $w=30 \mathrm{kN} / \mathrm{m}$.

A cantilever beam carries a trapezoidal distributed load. Let $w_g=2.5\ \mathrm{kN} / \mathrm{m}$, $w_A=5.0\ \mathrm{kN} / \mathrm{m}$, and $L=2.5 \mathrm{~m}$. The beam has a modulus $E=45\ \mathrm{GPa}$ and a rectangular cross sec. tion with width $b=200 \mathrm{~mm}$ and depth $h=300 \mathrm{~mm}$. Use the method of superposition and Cases as discussed in table to calculate the deflection and rotation at $B$.

In tensile test the sample with 172 mm length is subjected to load of $35 KN$ and the deformation is $0.5 mm$, knowing that the specimen diameter is $1.2 cm$, determine The modulus of elasticity:- A. 212 Gpa B. $106 Mpa$ C. $212 Mpa$ D. $106 Gpa$

For the cantilever steel beam $[E=200 \mathrm{GPa} ; I=129 \times$ $10^6 \mathrm{~mm}^4$ ] shown in Figure P10.13, use the double-integration method to determine the deflection at $B$. Assume that $L=3 \mathrm{~m}, M_0=70 \mathrm{kN}-\mathrm{m}$, and $w=15 \mathrm{kN} / \mathrm{m}$.

For the simply supported steel beam $[E=200 \mathrm{GPa}$; $I=129 \times 10^6 \mathrm{~mm}^4$ ] shown in Figure Pl0.11, use the doubleintegration method to determine the deflection at $B$. Assume that $L=4 \mathrm{~m}, P=60 \mathrm{kN}$, and $w=40 \mathrm{kN} / \mathrm{m}$.

For the cantilever steel beam $[E=200 \mathrm{GPa} ; I=129 \times$ $10^6 \mathrm{~mm}^4$ ] shown in Figure P10.14, use the double-integration method to determine the deflection at $A$. Assume that $L=2.5 \mathrm{~m}, P=50 \mathrm{kN}$, and $w_0=90 \mathrm{kN} / \mathrm{m}$.

A 3.2-mm-diameter stainless-steel wire $30 \mathrm{~cm}$ long has a voltage of $10 \mathrm{~V}$ impressed on it. The outer surface temperature of the wire is maintained at $93^{\circ} \mathrm{C}$. Calculate the center temperature of the wire. Take the resistivity of the wire as $70 \mu \Omega \cdot \mathrm{cm}$ and the thermal conductivity as $22.5 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$.

A plate having a thickness of $4.0 \mathrm{~mm}$ has an internal heat generation of $200 \mathrm{MW} / \mathrm{m}^3$ and a thermal conductivity of $25 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$. One side of the plate is insulated and the other side is maintained at $100^{\circ} \mathrm{C}$. Calculate the maximum temperature in the plate.

A house has an electric heating system that consists of a 300-W fan and an electric resistance heating element placed in a duct. Air flows steadily through the duct at a rate of 0.6 kg/s and experiences a temperature rise of $7^{\circ} \mathrm{C}.$ The rate of heat loss from the air in the duct is estimated to be 300 W. Determine the power rating of the electric resistance heating element.

Heat is generated uniformly in a stainless steel plate having $k=20 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$. The thickness of the plate is $1.0 \mathrm{~cm}$ and the heat-generation rate is $500 \mathrm{MW} / \mathrm{m}^3$. If the two sides of the plate are maintained at 100 and $200^{\circ} \mathrm{C}$, respectively, calculate the temperature at the center of the plate.

A 3.0-cm-thick plate has heat generated uniformly at the rate of $5 \times 10^5 \mathrm{~W} / \mathrm{m}^3$. One side of the plate is maintained at $200^{\circ} \mathrm{C}$ and the other side at $45^{\circ} \mathrm{C}$. Calculate the temperature at the center of the plate for $k=16 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$.

Two 5.0-cm-diameter aluminum bars, $2 \mathrm{~cm}$ long, have ground surfaces and are joined in compression with a $0.025-\mathrm{mm}$ brass shim at a pressure exceeding $20 \mathrm{~atm}$. The combination is subjected to an overall temperature difference of $200^{\circ} \mathrm{C}$. Calculate the temperature drop across the contact join.