Lecture 7 : Heat transfer I Flashcards
DEFINITION
What is specific heat capacity and its units?
quantity of heat gained/lost by a unit mass product to accomplish a unit change in temperature, without change in state.
units: kJ /(kg.K) or kJ/(kg.°C)
DEFINITION
What is thermal conductivity, k?
What is its units?
The amount of heat that will be conducted through a unit thickness of object per unit time, if a unit temperature gradient exists.
- per unit time : because Watt = joules/second
Units: W/(m.k) = W/(m.°C)
DEFINITION
What is thermal diffusivity, α ?
Thermal diffusivity is the ratio of heat conducted by a material relative to the heat it absorbs/stores.
What is the equation for thermal diffusivity, α and its units?
α = k / (ρ.c_p) , units = m^2/s
ρ : density
c_p : specific heat capacity
[MODES OF HEAT TRANSFER]
How is heat transferred through conduction?
Is there physical movement of object undergoing heat transfer?
In conduction, when a molecule gets heated up, it gains kinetic energy and vibrates, and this energy is passed onto the neighboring molecule.
No physical movement, movement occurs at a molecular level
[MODES OF HEAT TRANSFER]
Heat transfer through conduction occurs between which 2 medium?
Solid to solid
[MODES OF HEAT TRANSFER]
What is the equation for rate of heat transfer, q, through conduction? What law is it called? State units for each component.
Fourier’s law : q = -kA (dT/dx)
where
q : rate of heat flow in direction of heat transfer by conduction
k : thermal conductivity (W/m.K or W/m.°C)
A: surface area normal/perpendicular to direction of heat transfer (m^2)
dT : temperature difference (K/°C)
x : thickness (length) of wall (m)
[MODES OF HEAT TRANSFER]
How is heat transferred through convection?
Is there physical movement of object undergoing heat transfer?
In convection, exchange of heat occurs through a moving fluid (liquid/gas)
There is physical movement of fluid.
[MODES OF HEAT TRANSFER]
Heat transfer through convection occurs between which 2 medium?
Solid and fluid
(solid transfers heat to fluid for the lecture content)
[MODES OF HEAT TRANSFER]
What are the 2 types of convection and their definition?
- Forced convection: convection that occurs due to the use of mechanical means such as a pump or fan to induce movement of fluid
- Free convection : convection that occurs due to density differences caused by temperature gradients within the system.
[MODES OF HEAT TRANSFER]
What is the equation for rate of heat transfer, q, through convection? What is the law called? State units for each component.
Newton’s law of cooling : q = hA(T_s - T_∞)
q: rate of heat transfer (W)
h: convective heat transfer coefficient (W/m.K or W/m.°C)
A: surface area (m^2)
T_s : temperature at solid surface (K/°C)
T_∞: ambient temperature (K/°C)
- stabilised temperature far away from heated solid surface
T_s - T_∞ : temperature gradient
[MODES OF HEAT TRANSFER]
In convective heat transfer, a high value of h indicates?
High value of convective coefficient indicates high rate of heat transfer
[MODES OF HEAT TRANSFER]
How is heat transferred through radiation?
Transfer of heat occurs between 2 surfaces by emission and absorption of electromagnetic waves (of light), also known as photons
[MODES OF HEAT TRANSFER]
A physical medium is required for heat transfer through radiation. True or False?
False, no physical medium is required, and can occur in perfect vacuum.
[MODES OF HEAT TRANSFER]
Are
(i) Solid
(ii) Liquid
(iii) Gas
good absorbers of radiation?
Solid : opaque to thermal radiation, meaning that they dont allow the electromagnetic waves to pass through. But whether it is a good absorbers depends on the colour of surface
- black : perfect absorbers (black body)
- shiny surfaces : poor absorbers (reflect all the light and thus, electromagnetic waves off)
Liquid : good absorbers of radiation
Gas : transparent to radiation, meaning they allow electromagnetic waves to pass through and are poorest absorbers of radiation out of solid, liquid and gas.
[MODES OF HEAT TRANSFER]
What is the equation for the rate of heat transfer (q) via radiation? State the values of parameters if applicable and units
q = σεA(T_A)^4
q = rate of heat transfer by radiation
σ : stefan-Boltzmann constant = 5.669 x 10-8 W/(m^2.K^4)
ε : emissivity (no units)
T_A : absolute temperature (must be in K!)
A = area (m^2)
[MODES OF HEAT TRANSFER]
What is the definition of emissivity, ε?
Emissivity, ε, is the extent to which the surface is similar to a black body (perfect absorber of radiation).
(like a ratio, values ranges between 0-1)
[MODES OF HEAT TRANSFER]
What is the value of emissivity, ε of a black body?
1
What is the difference between steady heat transfer and unsteady heat transfer?
Steady heat transfer is when temperature may vary at different locations, but temperature does not change with time.
Unsteady heat transfer is when temperature varies with both location and time.
[STEADY STATE HEAT TRANSFER: CONDUCTION]
What is the equation of temperature at location X in a rectangular slab?
Given:
q_x: rate of heat transfer through conduction
k: coefficient
x = x1 ; x = x2
T = T1, T = T2
and heat flows through from x1 to x2
[Write down workings if needed.]
T = T_1 - [(q_x/KA)(x-x1)]
[CONCEPT OF THERMAL RESISTANCE]
What is an analogy for calculating thermal resistance?
Electricity
I = EV/R
where I : electrical current
EV : voltage difference (forward driving force of electricity flow)
R : resistance (opposing force slowing electricity flow)
[CONCEPT OF THERMAL RESISTANCE]
Rearranging the equation for rate of heat transfer ,q, through conduction, how can q be expressed in terms of resistance?
What is resistance equal to?
q = (T_1-T_2) / Rt
Where Rt (resistance) = (x1-x2)/KA
X1-X2 : thickness of wall (length that heat flows through)
K : thermal conduction coefficient
A: surface area
What is the equation for rate of heat flow by conduction through a multilayer slab?
Refer to notes
[STEADY STATE HEAT TRANSFER: CONDUCTION]
According to Fourier’s law, what is the rate of conductive heat transfer, q_r, through a tubular pipe?
q_r = -kA [(T_2-T_1)/(R_2-R_1)]
just replace x with r
[STEADY STATE HEAT TRANSFER: CONDUCTION]
What is the rate of heat transfer, q_r, expressed in terms of resistance?
q_r = (T_i - T_O) / [ln(r_O - r_i) / (2πLk)
T_i : temp inside the pipe
T_O : temp outside the pipe
R_i : inner radius of pipe
R_O : outer radius of pipe
