Ask question

Ask question

All categories

3 months ago

9

A composite wall separates combustion gases at 2400°C from a liquid coolant at 100°C, with gas and liquid-side convection coeffi

cients of 25 and 1000 W/m2 ⋅ K. The wall is composed of a 12-mm-thick layer of beryllium oxide on the gas side and a 24-mm-thick slab of stainless steel (AISI 304) on the liquid side. The contact resistance between the oxide and the steel is 0.05 m2 ⋅ K/W. What is the rate of heat loss per unit surface area of the composite? Sketch the temperature distribution from the gas to the liquid.

1 answer:

Ostrovityanka [3.2K]3 months ago

3 0

Response:

$\text{heat loss} = 24864.05 \ W/m^2$

Clarification:

If

$T_1$ , $T_2$ represent the temperatures of gases and liquids in Kelvins,

$t_1$ and $t_2$ denote the thicknesses of the gas layer and steel slab in meters,
$h_1$ , $h_2$ are the convection coefficients for gas and liquid in $W/m^2 \cdot K$ ,
$R_c$ represents the contact resistance in $m^2 \cdot K/W$ ,

and $k_1, k_2$ signify thermal conductivities of gas and steel in $W/m \cdot K$ ,

then: part(a):

$\text{heat loss } = \frac{T_1 - T_2} { \frac{1}{h_1} + \frac{t_1}{t_2} + R_c + \frac{t_2}{k_2} + \frac{1}{h_2}}$

by employing known values:

$\text {heat loss} = 2486.05 W/m^2$

part(b): Utilizing the rate equation:

$\text {heat loss} = h_1 (T_1 - T_{s1})$

the surface temperature is $T_{s1} = 1678.438 \ K$

and $T_{c1} = T_{s1} - \frac {t_1 (\text{heat loss})}{k_1} = 1664.560 \ K$

Correspondingly

$T_{c2} = T_{c1} - R_c (\text{heat loss}) = 421.357 \ K$

$T_{s2} = T_{c2} - \frac {t_2 (\text{heat loss})}{ k_2} = 397.864 \ K$

The temperature profile is depicted in the image provided

You might be interested in

Oceanographers use submerged sonar systems, towed by a cable from a ship, to map the ocean floor. In addition to their downward

Yuliya22 [3333]

The tension exerted in the cable amounts to T = 16653.32 N. Parameters: Cross section area A = 1.3 m² Drag coefficient CD = 1.2 Velocity V = 4.3 m/s The angle formed by the cable with the horizontal is 30 degrees. Density defined as follows: The drag force FD is determined by the equation: FD = (1/2) * ρ * V² * A * CD Calculating the drag force yields 14422.2 N acting opposite to motion. Given the cable's angle of 30 degrees with horizontal, the horizontal component contributes to the drag force calculation: T * cos(30) = F_D Thus, T = 16653.32 N.

7 0

2 months ago

A charge of uniform volume density (40 nC/m3) fills a cube with 8.0-cm edges. What is the total electric flux through the surfac

Keith_Richards [3271]

Answer:

The flux across the cube's surface is $2.314\ Nm^{2}/C$ .

Solution:

According to the details provided:

Cube edge length, a = 8.0 cm = $8.0\times 10^{- 2}\ m$ .

Volume charge density, $\rho_{v} = 40 nC/m^{3} = 40\times {- 9}\ C/m^{3}$ .

Now,

To find the electric flux:

$\phi = \frac{q}{\epsilon_{o}}$

where

$\phi$ = electric flux

$\epsilon_{o} = 8.85\times 10^{- 12}\ F/m$ = permittivity of vacuum.

The volume charge density for this scenario is described by:

$\rho_{v} = \frac{Total\ charge, q}{Volume of cube, V}$

Cube volume, $V = a^{3}$ .

Thus,

$V = (8.0\times 10^{- 2})^{3} = 5.12\times 10^{- 4}\ m^{3}$ .

The total charge can be derived from equation (2):

$q = \rho_{v}V = 40\times {- 9}\times 5.12\times 10^{- 4}$ .

$q = 2.048\times 10^{-11}\ F = 20.48\ pF$ .

Now, insert the value of 'q' into equation (1):

$\phi = \frac{2.048\times 10^{-11}}{8.85\times 10^{- 12}} = 2.314\ Nm^{2}/C$ .

5 0

3 months ago

To determine the height of a flagpole, Abby throws a ball straight up and times it. She sees that the ball goes by the top of th

Softa [3030]

Answer:

$H = 10.05 m$

Explanation:

The stone reaches the top of the flagpole at both t = 0.5 s and t = 4.1 s

therefore, the total duration of the upwards motion above the peak of the pole is provided as

$\Delta t = 4.1 - 0.5 = 3.6 s$

now we have

$\Delta t = \frac{2v}{g}$

$3.6 = \frac{2v}{9.8}$

$v = 17.64 m/s$

this indicates the speed at the flagpole's top

at this point we have

$v_f - v_i = at$

$17.64 - v_i = (-9.8)(0.5)$

$v_i = 22.5 m/s$

the height of the flagpole is stated as

$H = \frac{v_f + v_i}{2}t$

$H = \frac{22.5 + 17.64}{2} (0.5)$

$H = 10.05 m$

5 0

4 months ago

A boat is floating in a small pond. the boat then sinks so that it is completely submerged. what happens to the level of the pon

ValentinkaMS [3465]

When the boat submerges completely in the pond, the water level of the pond rises.

4 0

2 months ago

Starting with only the Balmer series light (visible light), how could we ensure that the solar panels generate a current that Ma

ValentinkaMS [3465]

The right answer is (a).

Solar panels create electric current through the photoelectric effect, which describes how photons strike certain material surfaces, resulting in the release of electrons when light with the correct frequency hits them. A photon will interact with an electron on the panel, causing it to be ejected from the panel's surface.

As the illumination on the panel becomes brighter, the intensity of the light rises, indicating an increase in the number of photons. Each photon has the potential to liberate an electron; thus, as the number of incoming photons rises, so does the quantity of freed electrons. Given that the photoelectric current reflects the rate at which these electrons flow, an increase in light intensity leads to a corresponding rise in the photoelectric current.

If the frequency of the light is increased without a change in brightness, the photoelectric current remains the same because the total number of photons does not increase. Yet, the electrons that are ejected do escape with higher kinetic energy. However, since the total number of electrons liberated stays unchanged, the current remains constant regardless of the electrons' increased energy. Thus, option b is incorrect.

Increasing the wavelength of the light means the energy of the photons decreases. This would cause the emitted electrons to have lower energy. However, if the brightness is consistent, the number of electrons remains the same, and as a result, there would be no change in the photoelectric current. Therefore, choice (c) is also incorrect.

The correct answer is (a). To generate the needed current, the brightness of the incident light must be increased.

8 0

3 months ago

Read 2 more answers