A series of experiments were conducted by passing $40^\circ C$ air over a long 25 mm diameter cylinder with an embedded electrical heater. The objective of these experiments was to determine the power per unit length required (Ẇ/L) to maintain the surface temperature of the cylinder at $300^\circ C$ for different air velocities (V). The results of these experiments are given in the following table:

$$\begin{matrix} \text{V(m/s) } & \text{1} & \text{2} & \text{4} & \text{8} & \text{12}\\ \text{W/L(W/m)} & \text{450} & \text{658} & \text{983} & \text{1507} & \text{1963}\\ \end{matrix}$$

(a) Assuming a uniform temperature over the cylinder, negligible radiation between the cylinder surface and surroundings, and steady state conditions, determine the convection heat transfer coefficient (h) for each velocity (V). Plot the results in terms of $h(W/m^2 \cdot K)$ vs. V (m/s). Provide a computer generated graph for the display of your results and tabulate the data used for the graph.(b) Assume that the heat transfer coefficient and velocity can be expressed in the form of $h = CV^n.$ Determine the values of the constants C and n from the results of part (a) by plotting h vs. V on log-log coordinates and choosing a C value that assures a match at V = 1 m/s and then varying n to get the best fit.

Carbon dioxide and hydrogen as ideal gases at 1 atm and $-20^\circ C$ flow in parallel over a flat plate. The flow velocity of each gas is 1 m/s and the surface temperature of the 3-m-long plate is maintained at $20^\circ C.$ Using the EES (or other) software, evaluate the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient along the plate for each gas. By varying the location along the plate for $0.2 \leq x \leq 3 \mathrm{m},$ plot the local Reynolds number, the local Nusselt number, and the local convection heat transfer coefficient for each gas as functions of x. Discuss which gas has higher local Nusselt number and which gas has higher convection heat transfer coefficient along the plate. Assume flow is laminar but make sure to verify this assumption.

In a power plant, pipes transporting superheated vapor are very common. Superheated vapor is flowing at a rate of 0.3J kg/s inside a pipe with 5cm in diameter and 10m in length. The pipe is located in a power plant at $20^\circ C,$ and has a uniform pipe surface temperature of $100^\circ C.$ If the temperature drop between the inlet and exit of the pipe is $30^\circ C,$ and the specific heat of the vapor is $2190 J/kg \cdot K,$ determine the heat transfer coefficient as a result of convection between the pipe surface and the surrounding.

A 25-cm-diameter black ball at $130^\circ C$ is suspended in air, and is losing heat to the surrounding air at $25^\circ C$ by convection with a heat transfer coefficient of $12 W/m^2 \cdot K,$ and by radiation to the surrounding surfaces at. $15^\circ C.$ The total rate of heat transfer from the black ball is (a) 217W (b) 247 W (c) 251 W (d) 465 W (e) 2365 W

Air at $20^\circ C$ with a convection heat transfer coefficient of $20 W/m^2 \cdot K$ blows over a pond. The surface temperature of the pond is at $40^\circ C.$ Determine the heat flux between the surface of the pond and the air.

The sun is approximately 93 million miles distant from Earth, and its diameter is 860,000 miles. On a clear day solar irradiation at Earth’s surface has been measured at 360 Btu/h ft2 and an additional 90 Btu/h ft2 are absorbed by Earth’s atmosphere. With this information, estimate the sun’s effective surface temperature.

Air at $40^{\circ} \mathrm{C}$ flows over a long, 25-mm-diameter cylinder with an embedded electrical heater. In a series of tests, measurements were made of the power per unit length, $P^{\prime}$, required to maintain the cylinder surface temperature at $300^{\circ} \mathrm{C}$ for different free stream velocities V of the air. The results are as follows:

$$\begin{matrix} \text{Air velocity, V(m/s)} & \text{1} & \text{2} & \text{4} & \text{8} & \text{12}\\ \text{Power, }{P^{\prime}(\mathrm{W} / \mathrm{m})} & \text{450} & \text{658} & \text{983} & \text{1507} & \text{1963}\\ \end{matrix}$$

(a) Determine the convection coefficient for each velocity, and display your results graphically. (b) Assuming the dependence of the convection coefficient on the velocity to be of the form $h=C V^{n}$, determine the parameters C and n from the results of part (a).

Can all three modes of heat transfer occur simultaneously (in parallel) in a medium?

Consider three equally spaced sources of strength m placed at (x, y) = (–a, 0), (0, 0), and (a, 0). Sketch the resulting streamline pattern. Are there any stagnation points?

The velocity profile in fully developed laminar flow in a circular pipe of inner radius R = 10 cm, in m/s, is given by $u(r) = 4(1 − r^2/R^2).$ Determine the mean and maximum velocities in the pipe, and the volume flow rate.

Silicon wafer is susceptible to warping when the wafer is subjected to temperature difference across its thickness. Thus, steps needed to be taken to prevent the temperature gradient across the wafer thickness from getting large. As an engineer in a semiconductor company, your task is to determine the maximum allowable heat flux on the bottom surface of the wafer, while maintaining the upper surface temperature at $27^\circ C.$ To prevent the wafer from warping, the temperature difference across its thickness of $500 \mu \mathrm{m}$ cannot exceed $1^\circ C.$

Steam at $250^{\circ} \mathrm{C}$ flows in a stainless steel pipe $(k=15 \mathrm{W} / \mathrm{m} \cdot \mathrm{K})$ whose inner and outer diameters are 4 cm and 4.6 cm, respectively. The pipe is covered with 3.5-cm-thick glass wool insulation $(k = 0.038 W/m \cdot K)$ whose outer surface has an emissivity of 0.3. Heat is lost to the surrounding air and surfaces at $3^{\circ} \mathrm{C}$ by convection and radiation. Taking the heat transfer coefficient inside the pipe to be $80 W/m^2 \cdot K,$ determine the rate of heat loss from the steam per unit length of the pipe when air is flowing across the pipe at 4 m/s. Evaluate the air properties at a film temperature of $10^\circ C$ and 1 atm.

A plane wall of thickness L is subjected to convection at both surfaces with ambient temperature $T_{\infty 1}$ and heat transfer coefficient $h_1$ at inner surface, and corresponding $T_{\infty 2}$ and $h_2$ values at the outer surface. Taking the positive direction of x to be from the inner surface to the outer surface, the correct expression for the convection boundary condition is

(a)

$$k \frac{d T(0)}{d x}=h_{1}\left[T(0)-T_{\infty 1}\right) ]$$

(b)

$$k \frac{d T(L)}{d x}=h_{2}\left[T(L)-T_{\infty 2}\right) ]$$

(c)

$$-k \frac{d T(0)}{d x}=h_{1}\left[T_{\infty 1}-T_{\infty 2}\right) ]$$

(d)

$$-k \frac{d T(L)}{d x}=h_{2}\left[T_{\infty 1}-T_{\infty 2}\right) ]$$

(e) None of them

How does surface roughness affect the pressure drop in a tube if the flow is turbulent? What would your response be if the flow were laminar?