# Heat

## Heat

Heat ( \(q\) ) is a form of energy that causes physical change in what is being heated. The lack of heat is cold. This physical change comes from total amount of internal energy (kinetic energy and potential energy) possessed by an object or substance. There is a basic difference between temperature and heat, heat is the amount of energy in a system. The transfer of heat from higher or lower is because of the movement of molecules colliding, rotating, and vibrating into each other within a body. When two objects come in contact with each other the thermal energy of the hotter object will be transfered to the colder object until both objects have the same thermal energy or temperature.

The Zeroth law of thermodynamics states when two thermal systems are in equilibrium and they with a third, then all are equal to each other.

## Convective Heat Transfer

Convective heat transfer ( \(\dot {Q}\) ) is the transfer of heat by bulk movement and mixing from one place to another of liquids or gasses.

### Convective Heat Transfer Formula

\(\dot {Q} = h_c A \left( T_s \; - \; T_a \right) \) \(heat \; transfer \;=\; heat \; transfer \; coefficient \;\;x\;\; hear \; transfer \; area \; \left( \; surface \; temperature \; - \; air \;temperature \; \right) \)

Where:

\(\dot {Q} \) = heat transfer per unit time

\(A \) = heat transfer area of the surface

\( h_c\) = heat transfer coefficient

\(T_a \) = air temperature

\(T_s \) = surface temperature

## Convective Heat Transfer Coefficient

Convective heat transfer coefficient ( \(h_c\) ) (also called film coefficient or film effectiveness) is a porportional constant between heat flux and force from the flow of heat, this also depends on the type of fluid and fluid velocity.

### Convective Heat Transfer Coefficient Formula

\(h_c = \frac { Q } { \Delta T } \) \(heat \; transfer \; coefficient \;=\; \frac { amount \; of \; heat \; transfered \; area } { temperature \; differential } \)

Where:

\(h_c \) = heat transfer coefficient

\(Q \) = amount of heat transfered area of the surface

\( \Delta T \) = temperature differential between solid surface and surrounding fluid area

## Heat Capacity

Heat capacity ( \(C\) ) (also called thermal capacity) is the ratio of heat transferred to raise the temperature of an object. The heat gain or loss results in a change in temperature and the state and performance of work.

### Heat Capacity Formula

\(C = \frac {\Delta Q} { \Delta T } \) \( heat \; capacity \;=\; \frac { amount \; of \; heat \; transfered } { temperature \; differential } \)

Where:

\(C \) = heat capacity

\(\Delta Q \) = amount of heat transfered

\(\Delta T \) = temperature differential

## Heat Capacity at Constant Pressure

At constant pressure ( \(C_p\) ) some of the heat goes to doing work. The value of heat capacity depends on whether the heat is added at constant volume, constant pressure, etc.

### Heat Capacity at Constant Pressure Formula

\( Q = n C_p \Delta T \) \( heat \; transfer \;=\; number \; heat \; constant \; pressure \;\;x\;\; temperature \; differential \)

Where:

\( Q \) = heat transfer

\(C_p\) = heat constant pressure

\(\Delta T\) = temperature differential

## Heat Capacity at Constant Volume

At a constant volume ( \(C_v\) ) all the heat added goes into raising the temperature. The value of heat capacity depends on whether the heat is added at constant volume, constant pressure, etc.

### Heat Capacity at Constant Volume Formula

\( Q = n C_v \Delta T \) \( heat \; transfer \;=\; number \; heat \; constant \; volume \;\;x\;\; temperature \; differential \)

Where:

\( Q \) = heat transfer

\(C_v\) = heat constant volume

\(\Delta T\) = temperature differential

## Heat Energy

Heat energy (also called thermal energy) is the exertion of power that is created by heat, or the increase in temperature by the transfer of particles bouncing into each other by means of kinetic energy. Here are a few examples of heat energy: fire, geothermal, lightening, oven, steam, the sun, etc.

## Heat Flow Rate

Heat flow rate ( \(Q_f\) ) is the rate at which heat moves from an area of higher temperature to an area of lower temperature. Btu/hr (W/hr). Heat flow is generally used to quantify the rate of total heat gain or heat loss of a system.

### Heat Flow Rate FORMULA

\(Q_f = -\lambda \left( \frac {A} {l} \right) \Delta T \) \(heat \; flow \; rate \;=\; -\; thermal \; conductivity \;\; \left( \; \frac { area \; of \; body } { length \; of \; material } \; \right) \;\; temperature \; differential \)

Where:

\(Q_f\) = heat flow rate

\(\lambda\) (Greek symbol lambda) = thermal conductivity

\(A\) = area of the emitting body

\(l\) = length of the material

\(\Delta T\) = temperature differential

## Heat Flux

Heat flux ( \(Q"\) ) (also called thermal flux) is the heat flow rate transfer through a given surface, per unit surface.

### Heat Flux Formula

\(Q" = \frac { Q_f } { A } \) \( heat \; flux \;=\; \frac { heat \; flow \; rate } { area } \)

Where:

\(Q"\) = heat flux

\(Q_f\) = heat flow rate

\(A\) = area

## Heat Transfer

Heat transfer ( \(Q\) ) (also called thermal energy) is the exertion of power that is created by heat, or the increase in temperature. There are three ways to transfer heat: conduction, convection and radiation.

### Heat Transfer Formula

\(q = mc \Delta T \) \( heat \; content \;=\; mass \;\;x\;\; specific \; heat \;\;x\;\; change \; in \; temperature \)

Where:

\(q\) = heat content

\(m\) = mass

\(c\) = specific heat

\(\Delta T\) = change in temperature

## Heat Transfer by Conduction

Heat transfer by conduction ( \(Q_c\) ) (also called heat conduction, heat radiation, or heat transfer) is the flow of heat between two objects having different temperatures that are in contact with each other.

### Heat Transfer by Conduction Formula

\(Q_c = \frac { kA \Delta T t } {d} \) \( heat \; transfer \; by \; conduction \;=\; \frac { thermal \; conductivity \;\;x\;\; area \; cross \; section \;\;x\;\; temperature \; differential \;\;x\;\; time \; taken } { thickness \; of \; material } \)

\(Q_c = \frac { kA \left( T_h \;-\; T_c \right) t } {d} \) \( heat \; transfer \; by \; conduction \;=\; \frac { thermal \; conductivity \;\;x\;\; area \; cross \; section \; \left( \; higher \; temperature \;-\; cooler \; temperature \; \right) \; time \; taken } { thickness \; of \; material } \)

Where:

\(Q_c\) = heat transfer by conduction

\(k\) = thermal conductivity

\(A\) = area cross section

\(\Delta T\) = temperature differential

\(T_h\) = higher temperature

\(T_c\) = cooler temperature

\(t\) = time taken

\(d\) = thickness of the material

## Heat Transfer by Conduction Through a Cylindrical Wall

### Heat Transfer by Conduction Through a Cylindrical Wall Formula

\(Q_c = \frac { 2\pi kl \left( T_1 \;-\; T_2 \right) } { ln \left( \frac {r_2 } { r_1 } \right) } \) \( heat \; transfer \; by \; conduction \;=\; \frac { 2 \;\;x\;\; \pi \;\;x\;\; thermal \; conductivity \;\;x\;\; length \; of \; material \; \left(\; temperature \; surface \; 1 \;-\; temperature \; surface \; 2 \;\right) } { natural \; logarithm \; \left( \; \frac { radius \; outside \; wall } { radius \; inside \; wall } \;\right) } \)

Where:

\(Q_c\) = heat transfer by conduction

\(ln\) = natural logarithm

\(\pi\) = Pi

\(k\) = thermal conductivity

\(l\) = length of the material

\(T_1\) = temperature of one surface of the wall

\(T_2\) = temperature of the other surface of the wall

\(r_1\) = radius to inside wall

\(r_2\) = radius to outside wall

## Heat Transfer by Conduction Through a Plane Wall

### Heat Transfer by Conduction Through a Plane Wall Formula

\(Q_c = \frac {- kA \left( T_2 \;-\; T_1 \right) } { l } \) \( heat \; transfer \; by \; conduction \;=\; \frac { - \; thermal \; conductivity \;\;x\;\; area \; cross \; section \; \left(\; temperature \; surface \; 2 \;-\; temperature \; surface \; 1 \;\right) } { thickness \; of \; material } \)

Where:

\(Q_c\) = heat transfer by conduction

\(k\) = thermal conductivity

\(A\) = area cross section

\(T_1\) = temperature of one surface of the wall

\(T_2\) = temperature of the other surface of the wall

\(l\) = thickness of the material

## Heat Transfer by Conduction resistance Through a Cylindrical Wall

### Heat Transfer by Conduction resistance Through a Cylindrical Wall Formula

\(R_t = \frac { ln \left( \frac {r_2 } { r_1 } \right) } { 2\pi kl } \) \( thermal \; resistance \;=\; \frac { natural \; logarithm \; \left( \; \frac { radius \; outside \; wall } { radius \; inside \; wall } \;\right) } { 2 \;\;x\;\; \pi \;\;x\;\; thermal \; conductivity \;\;x\;\; length \; of \; material } \)

Where:

\(R_t\) = thermal resistance

\(ln\) = natural logarithm

\(\pi\) = Pi

\(k\) = thermal conductivity

\(l\) = length of the material

\(r_1\) = radius to inside wall

\(r_2\) = radius to outside wall

## Heat Transfer by Covection

Heat transfer by convection ( \(Q_c\) ) (also called convection heat transfer or convective heat transfer) is the flow of heat from one place to another by the movement of fluids (liquids or gasses).

### Heat Transfer by Convection Formula

\(Q_c = \frac { kA \Delta T t } {d} \) \(heat \; transfer \; by \; convection \;=\; \frac { thermal \; conductivity \;\;x\;\; area \; cross \; section \;\;x\;\; temperature \; differential \;\;x\;\; time \; taken } { thickness \; of \; the \; material } \)

\(Q_c = \frac { kA \left( T_h \;-\; T_c \right) t } {d} \) \(heat \; transfer \; by \; convection \;=\; \frac { thermal \; conductivity \;\;x\;\; area \; cross \; section \; \left( \; higher \; temperature \;-\; cooler \; temperature \; \right) \; time \; taken } { thickness \; of \; the \; material } \)

Where:

\(Q_c\) = heat transfer by convection

\(k\) = thermal conductivity

\(A\) = area cross section

\(\Delta T\) = temperature differential

\(T_h\) = higher temperature

\(T_c\) = cooler temperature

\(t\) = time taken

\(d\) = thickness of the material

## Heat Transfer by Radiation

Heat transfer by radiation ( \(Q_r\) or \(\phi\) (Greek symbol phi) ) is the flow of energy through electromagnetic waves such as infrared, light, microwaves, etc.

### Heat Transfer by Radiation formula

\(Q_r = \epsilon \sigma A \Delta T ^4 \) \(heat \; transfer \; by \; radiation \;=\; emissivity \; of \; the \; particular \; body \;\;x\;\; Stefan-Boltzmann \; constant \;\;x\;\; cross \; sectional \; area \;\;x\;\; change \; in \; absolute \; temperature^4 \)

\(Q_r = \epsilon \sigma A \left( T_o \;-\; T_e \right)^4 \)

\(Q_r = \epsilon \sigma A \left( T_o^4 \;-\; T_e^4 \right) \)

Where:

\(Q_r\) = heat transfer by radiation

\(\epsilon\) (Greek symbol epsilon) = emissivity of the particular body (a number between 0 and 1)

\(\sigma\) (Greek symbol sigma) = Stefan-Boltzmann constant

\(A\) = cross sectional area

\(\Delta T\) = change in absolute temperature \( \left( T_o \;-\; T_e \right)^4 \)

\(T_o\) = absolute temperature of the object emitting

\(T_e\) = absolute temperature of the environment

## Heat Transfer Coefficient

Heat transfer coefficient ( \(h\) ) (also known as film coefficient or film effectiveness) is the convective heat transfer between a solid surface and the fluid around it.

## Heat Transfer Coefficient of a Pipe Wall

The resistance to the flow of heat by the pipe wall material can be expressed by the heat transfer coefficient of the pipe wall.

### Heat Transfer Coefficient of Pipe Wall FormulA

\(p_{wall} = \frac { 2k } { d_i \; \cdot \; ln \left( \frac { p_o } { P_i } \right) } \) \( heat \; transfer \; coefficient \; of \; wall \;=\; \frac { \; 2 \;\;x\;\; thermal \; conductivity } { pipe \; ID \;\;x\;\; natural \; logarithm \; \left( \frac { pipe \; OD } { pipe \; ID } \; \right) } \)

Where:

\(h_{wall}\) = heat transfer coefficient of wall

\(k\) = thermal conductivity

\(p_i\) = pipe ID

\(p_o\) = pipe OD

\(ln\) = natural logarithm

## Heat Transfer Rate

### Heat Transfer Rate FormulA

\(Q_t = k_t \frac { \Delta T}{l} \) \( heat \; transfer \; rate \;=\; thermal \; conductivity \; constant \; \; \frac { temperature \; differential } { distance } \)

Where:

\(Q_t\) = heat transfer rate

\(k_t\) = thermal conductivity constant

\( \Delta T\) = temperature differential

\(l\) = distance or length

Solve for:

\(k_t = \frac { {Q_t} l } {\Delta T } \)

\(\Delta T = \frac { {Q_t} l } {k_t } \)

\( l = k_t \frac {\Delta T} {Q_t} \)

## Latent Heat

Latent heat ( \(L\) ) is the energy absorbed or released by a substance during a constant temperature or phase change from a solid to liquid, liquid to gas or vise versa.

### Latent Heat Formula

\(L = \frac{Q}{m}\) \( latent \; heat \;=\; \frac { energy \; transfered } { mass \; of \; the \; substance }\)

Where:

\(L \) = latent heat of a substance

\(Q\) = amount of energy transferred for the phase change

\(m\) = mass of the substance

Solve for:

\(Q = mL\)

## Overall Heat Transfer Coefficient

Overall heat transfer coefficient ( \(U\) ) is the heat transfer between items like walls in buildings or across heat exchangers for the conduction within materials.

### Overall Heat Transfer Coefficient Formula

\( \frac{ 1 } { U \;\dot\;\; A } \;=\; \frac{ 1 } { h_1 \;\dot\;\; A_1 } \;+\; \frac{ dx } { k \;\dot\;\; A } \;+\; \frac{ 1 } { h_2 \;\dot\;\; A_2 } \)

Where:

\( U \) = overall heat transfer coefficient

\( A \) = contact area for each fluid side

\( h_1 \) = individual heat transfer convection coefficient for one of the fluids

\( h_2 \) = individual heat transfer convection coefficient for the other fluid

\( A_1 \) = contact area for one of the fluids

\( A_1 \) = contact area for the other fluid

\( k \) = thermal conductivity of the material

\( dx \) = wall thickness

## Sensible Heat

The heat added to a substance which increases its temperature but not the phase is called sensible heat. The sensible heat added to a substance can be readily calculated. The quantity of heat in a body or the amount of heat energy which a body gains or loses in passing through a temperature range is measured in thermal units.

### Sensible Heat Formula

\(Q = mc \Delta T\) \( specific \; heat \;=\; mass \;\;x\;\; specific \; heat \;\;x\;\; change \; in \; temperature \)

Where:

\(Q\) = sensible heat

\(c\) = specific heat

\(m\) = mass

\(\Delta T\) = change in temperature

## Specific Heat

Specific heat ( \(c\) ) (also called specific heat capacity) is the amount of heat required to raise the temperature of a material 1 degree.

### Specific Heat Formula

\(c = \frac {Q } {m \Delta T}\) \( specific \; heat \;=\; \frac { thermal \; energy } { mass \;\;x\;\; change \; in \; temperature }\)

Where:

\(c\) = specific heat

\(Q\) = thermal energy or heat transfer

\(m\) = mass

\(\Delta T\) = change in temperature

## Specific Heat Capacity

Specific heat capacity ( \(Q\) ) (also called specific heat) is the amount of energy required to increase the temperature of the substance by 1°C.

## Specific Heat Capacity at Constant Pressure

Specific heat ratio ( \(C_p\) ) is the ratio of two specific heats. If we specify any two properties of the system, then the state of the system is fully specific.

### Specific Heat Capacity at Constant Pressure Formula

\(C_p = \left(\frac{ \partial H }{ \partial T }\right)_p\)

Where:

\(C_p\) = heat constant pressure

\(\partial H\) = rate of change enthalpy

\(\partial T\) = rate of change temperature

\(p\) = pressure

\(\partial\) = designates heat as a path function

## Specific Heat Capacity at Constant Volume

Specific heat ratio ( \(C_v\) ) is the ratio of two specific heats. If we specify any two properties of the system, then the state of the system is fully specific.

### Specific Heat Capacity at Constant Volume Formula

\(C_v = \left(\frac{ \partial U }{ \partial T }\right)_v\)

\(dU = C_v \partial T\)

Where:

\(C_v\) = heat constant volume

\(\partial U\) = rate of change internal energy

\(\partial T\) = rate of change temperature

\(v\) = volume

\(\partial\) = designates heat as a path function

## Specific Heat Ratio

Specific heat ratio ( \(\gamma\) ) (dimensionless number) (also called heat capacity ratio, adiabatic index, isentropic expansion factor) is the ratio of two specific heats or the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

### Specific Heat Ratio Formula

\(\gamma = \frac {C_p } {C_v}\) \(specific \; heat \; ratio \;=\; \frac { specific \; heat \; constant \; pressure } { specific \; heat \; constant \; volume }\)

Where:

\(\gamma\) (Greek symbol gamma) or \(\kappa\) (Greek symbol kappa) = specific heat ratio

\(C_p\) = specific heat constant pressure

\(C_v\) = specific heat constant volume

## Total Heat Transfer

### Total Heat Transfer Formula

\(Q = hA \; \left( T_s \;-\; T_{\infty} \right) \) \( total \; heat \; transfer \;=\; heat \; transfer \; coefficient \;\;x\;\; surface \; area \; where \; heat \; is \; transfered \; \left( \; surface \; temperature \;-\; approach \; fluid \; temperature \; \right)\)

Where:

\(Q\) = total heat transfer (heat put into system or heat lost)

\(h\) = heat transfer coefficient

\(A\) = surface area where heat is transfered

\(T_s\) = surface temperature

\(T_{\infty}\) = approach fluid temperature