The heat flux that is applied to one face of a plane wall is q″ = 20 W/m2. The opposite face is exposed to air at temperature 30°C, with a convection heat transfer coefficient of 20 W/m2 · K. The surface temperature of the wall exposed to air is measured and found to be 50°C. Do steady-state conditions exist? If not, is the temperature of the wall increasing or decreasing with time?

400 W/m^2 and 31℃

Explanation:

The output heat flux q"= 20 W/m^2 (geven)

The output heat flux from.the wall to the air by convection

q"conv = h(ts - t∞)

q"conv = 20(50-30) = 400 W/m^2

Therefor, this case is unsteady and the wall temperature changes with time till the energy balance exist.

ENERGY BALANCE

The input energy must be equal to the output energy for steady state condition. If not the state will be unstaidy or transient.

2. Its noticed that the output heat flux is not that the I put heat flux, therefore the wall tempers will be decreased till the output heat flux is reduced to the value of the given input heat flux

T steady = T∞ +q"/h

= 30 + 20/20 = 31℃

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.