Hot water flows through a PVC $(k=0.092 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ pipe whose inner diameter is $2 \mathrm{~cm}$ and whose outer diameter is $2.5 \mathrm{~cm}$. The temperature of the interior surface of this pipe is $35^{\circ} \mathrm{C}$, and the temperature of the exterior surface is $20^{\circ} \mathrm{C}$. The rate of heat transfer per unit of pipe length is (a) $22.8 \mathrm{~W} / \mathrm{m}$ (b) $38.9 \mathrm{~W} / \mathrm{m}$ $(c)$ $48.7 \mathrm{~W} / \mathrm{m}$ (d) $63.6 \mathrm{~W} / \mathrm{m}$ (e) $72.6 \mathrm{~W} / \mathrm{m}$

The variation of temperature in a plane wall is determined to be T(x) = 110 - 60x where x is in m and T is in $^\circ C.$ If the thickness of the wall is 0.75 m, the temperature difference between the inner and outer surfaces of the wall is (a) $30^\circ C$ (b) $45^\circ C$ (c) $60^\circ C$ (d) $75^\circ C$ (e) $84^\circ C$

The variation of temperature in a plane wall is determined to be $T(x)=65 x+25$ where $x$ is in $\mathrm{m}$ and $T$ is in ${ }^{\circ} \mathrm{C}$. If the temperature at one surface is $38^{\circ} \mathrm{C}$, the thickness of the wall is

$$\begin{array}{ll}\text { (a) } 2 \mathrm{~m} & \text { (b) } 0.4 \mathrm{~m}\end{array}$$

$(c)$ $0.2 \mathrm{~m}$ (d) $0.1 \mathrm{~m}$ (e) $0.05 \mathrm{~m}$

Hot water flows through a $PVC (k= 0.092 W/m \cdot K)$ pipe whose inner diameter is 2 cm and outer diameter is 2.5 cm. The temperature of the interior surface of this pipe is $50^\circ C$ and the temperature of the exterior surface is $20^\circ C.$ The rate of heat transfer per unit of pipe length is (a) 77.7 W/m (b) 89.5 W/m (c) 98.0 W/m (d) 112 W/m (e) 168 W/m

Identify the constants $b$ and $m$ in the expression $b+m t$ for the linear functions.

$$f(t)=200+14 t$$

The conduction equation boundary condition for an adiabatic surface with direction n being normal to the surface is

(a) $T =0$

(b) $dT/dn = 0$

(c) $d^{2} T / d n^{2}=0$

(d) $d^{3} T / d n^{3}=0$

(e) $-k d T / d n=1$

Consider steady one-dimensional heat conduction through a plane wall, a cylindrical shell, and a spherical shell of uniform thickness with constant thermophysical properties and no thermal energy generation. The geometry in which the variation of temperature in the direction of heat transfer will be linear is(a) plane wall(b) cylindrical shell(c) spherical shell(d) all of them(e) none of them

A large plane wall has a thickness $L=50 \mathrm{~cm}$ and thermal conductivity $k=25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. On the left surface $(x=0)$, it is subjected to a uniform heat flux $\dot{q}_0$ while the surface temperature $T_0$ is constant. On the right surface, it experiences convection and radiation heat transfer while the surface temperature is $T_L=225^{\circ} \mathrm{C}$ and the surrounding temperature is $25^{\circ} \mathrm{C}$. The emissivity and the convection heat transfer coefficient on the right surface are $0.7$ and $15 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$, respectively. $(a)$ Show that the variation of temperature in the wall can be expressed as $T(x)=\left(\dot{q}_0 / k\right)(L-x)+T_L,(b)$ Find the heat flux $\dot{q}_0$ on the left face of the wall, and $(c)$ Find the temperature of the left surface of the wall at $x=0$.

Can the transient temperature charts for a plane wall exposed to convection on both sides be used for a plane wall with one side exposed to convection while the other side is insulated? Explain.

The variation of temperature in a plane wall is determined to be $T(x)=110 x-48 x$ where $x$ is in $\mathrm{m}$ and $T$ is in ${ }^{\circ} \mathrm{C}$. If the thickness of the wall is $0.75 \mathrm{~m}$, the temperature difference between the inner and outer surfaces of the wall is (a) $110^{\circ} \mathrm{C}$ (b) $74^{\circ} \mathrm{C}$ $(c)$ $55^{\circ} \mathrm{C}$ (d) $36^{\circ} \mathrm{C}$ (e) $18^{\circ} \mathrm{C}$

Consider a medium in which the heat conduction equation is given in its simplest forms as $\frac{1}{r^{2}} \frac{\partial}{\partial r}\left(r^{2} \frac{\partial T}{\partial r}\right)=\frac{1}{\alpha} \frac{\partial T}{\partial t}$ (a) Is heat transfer steady or transient?(b) Is heat transfer one-, two-, or three-dimensional?(c) Is there heat generation in the medium?(d) Is the thermal conductivity of the medium constant or variable?(e) Is the medium a plane wall, a cylinder, or a sphere?(f) Is this differential equation for heat conduction linear or nonlinear?

Consider a medium in which the heat conduction equation is given in its simplest form as $\frac{\partial^{2} T}{\partial x^{2}}=\frac{1}{\alpha} \frac{\partial T}{\partial t}$ (a) Is heat transfer steady or transient? (b) Is heat transfer one-, two-, or three-dimensional? (c) Is there heat generation in the medium? (d) Is the thermal conductivity of the medium constant or variable?

Consider a medium in which the heat conduction equation is given in its simplest form as $r \frac{d^{2} T}{d r^{2}}+2 \frac{d T}{d r}=0$ (a) Is heat transfer steady or transient? (b) Is heat transfer one-, two-, or three-dimensional? (c) Is there heat generation in the medium? (d) Is the thermal conductivity of the medium constant or. variable?

The heat conduction equation in a medium is given in its simplest form as

$$\begin{array}{l}{1 d} \\ {r d r}\end{array} \left( \begin{array}{c}{d T} \\ {d r}\end{array}\right)+\dot{e}_{\mathrm{gen}}=0$$

Select the wrong statement below. (a) The medium is of cylindrical shape. (b) The thermal conductivity of the medium is constant. (c) Heat transfer through the medium is steady. (d) There is heat generation within the medium. (e) Heat conduction through the medium is one-dimensional.