Problem-solving strategies for the methods of heat transfer
Examine the situation to determine what type of heat transfer is involved.
Identify the type(s) of heat transfer—conduction, convection, or radiation.
Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is very useful.
Make a list of what is given or can be inferred from the problem as stated (identify the knowns).
Solve the appropriate equation for the quantity to be determined (the unknown).
For conduction, equation
$\frac{Q}{t}=\frac{\text{kA}({T}_{2}-{T}_{1})}{d}$ is appropriate.
[link] lists thermal conductivities. For convection, determine the amount of matter moved and use equation
$Q=\text{mc}\text{\Delta}T$ , to calculate the heat transfer involved in the temperature change of the fluid. If a phase change accompanies convection, equation
$Q={\text{mL}}_{\text{f}}$ or
$Q={\text{mL}}_{\text{v}}$ is appropriate to find the heat transfer involved in the phase change.
[link] lists information relevant to phase change. For radiation, equation
$\frac{{Q}_{\text{net}}}{t}=\sigma eA\left({T}_{2}^{4}-{T}_{1}^{4}\right)$ gives the net heat transfer rate.
Insert the knowns along with their units into the appropriate equation and obtain numerical solutions complete with units.
Check the answer to see if it is reasonable. Does it make sense?
Summary
Radiation is the rate of heat transfer through the emission or absorption of electromagnetic waves.
The rate of heat transfer depends on the surface area and the fourth power of the absolute temperature:
$\frac{Q}{t}=\sigma eA{T}^{4}\text{,}$
where
$\sigma =5\text{.67}\times {\text{10}}^{-8}\phantom{\rule{0.25em}{0ex}}\text{J/s}\cdot {\text{m}}^{2}\cdot {\text{K}}^{4}$ is the Stefan-Boltzmann constant and
$e$ is the emissivity of the body. For a black body,
$e=1$ whereas a shiny white or perfect reflector has
$e=0$ , with real objects having values of
$e$ between 1 and 0. The net rate of heat transfer by radiation is
where
${T}_{1}$ is the temperature of an object surrounded by an environment with uniform temperature
${T}_{2}$ and
$e$ is the emissivity of the
object .
Conceptual questions
When watching a daytime circus in a large, dark-colored tent, you sense significant heat transfer from the tent. Explain why this occurs.
Satellites designed to observe the radiation from cold (3 K) dark space have sensors that are shaded from the Sun, Earth, and Moon and that are cooled to very low temperatures. Why must the sensors be at low temperature?
Why are thermometers that are used in weather stations shielded from the sunshine? What does a thermometer measure if it is shielded from the sunshine and also if it is not?
At what net rate does heat radiate from a
$\text{275}{\text{-m}}^{2}$ black roof on a night when the roof’s temperature is
$\text{30.}\mathrm{0\xba}\text{C}$ and the surrounding temperature is
$\text{15.}\mathrm{0\xba}\text{C}$ ? The emissivity of the roof is 0.900.
$-\text{21}\text{.}7\text{kW}$ Note that the negative answer implies heat loss to the surroundings.
(a) Cherry-red embers in a fireplace are at
$\text{850\xba}\text{C}$ and have an exposed area of
$0\text{.}\text{200}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ and an emissivity of 0.980. The surrounding room has a temperature of
$\text{18}\text{.}\mathrm{0\xba}\text{C}$ . If 50% of the radiant energy enters the room, what is the net rate of radiant heat transfer in kilowatts? (b) Does your answer support the contention that most of the heat transfer into a room by a fireplace comes from infrared radiation?
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?