# Heat Transfer by Conduction

on . Posted in Thermodynamics

Heat transfer by conduction, abbreviated as Qc, also called heat conduction or conduction heat transfer, is a process of thermal energy transfer through a substance or between two objects in physical contact, where heat flows from a higher temperature region to a lower temperature region.  This transfer occurs due to the temperature gradient or difference between the two regions, which causes the molecules in the higher temperature region to transfer some of their thermal energy to the neighboring molecules in the lower temperature region.

The rate of heat transfer by conduction depends on the thermal conductivity of the material, the thickness of the material, and the temperature difference between the two regions.  The transfer of thermal energy can occur through three modes of heat transfer: conduction, convection, and radiation.

Common thermal conductivity constants for non-metallic construction materials can be found here.

### Heat transfer by conduction formula

$$Q_c \;=\; k \; A_c \; (T_h - T_c) \;/\; d$$     (Heat Transfer by Conduction)

$$k \;=\; Q_c \; d \;/\; A_c \; (T_h - T_c)$$

$$A_c \;=\; Q_c \; d \;/\; k \; (T_h - T_c)$$

$$T_h \;=\; (Q_c \; d \;/\; k \; A_c) + T_c$$

$$T_c \;=\; T_h - (Q_c \; d \;/\; k \; A_c)$$

$$d \;=\; k \; A_c \; (T_h - T_c) \;/\; Q_c$$

Symbol English Metric
$$\large{ Q_c }$$ = heat transfer by conduction $$Btu\;/\;hr$$  $$W$$
$$\large{ k }$$ = thermal conductivity of the material $$Btu-ft\;/\;hr-ft^2-F$$ $$W\;/\;m-K$$
$$\large{ A_c }$$ = area cross-section $$in^2$$ $$mm^2$$
$$\large{ T_h }$$ = higher temperature $$F$$ $$K$$
$$\large{ T_c }$$ = cooler temperature $$F$$ $$K$$
$$\large{ d }$$ = thickness of the material $$in$$ $$mm$$

### Heat transfer by conduction formula

$$Q_c \;=\; k \; A \; ( \frac{dT}{dx} ) \;/\; \Delta t$$     (Heat Transfer by Conduction)

$$k \;=\; Q_c \; \Delta t \;/\; A \; ( \frac{dT}{dx} )$$

$$A \;=\; Q_c \; \Delta t \;/\; k \; ( \frac{dT}{dx} )$$

$$\frac{dT}{dx} \;=\; Q_c \; \Delta t \;/\; k \; A$$

$$\Delta t \;=\; k \; A \; ( \frac{dT}{dx} ) \;/\; Q_c$$

Symbol English Metric
$$\large{ Q_c }$$ = heat transfer by conduction $$Btu\;/\;hr$$  $$W$$
$$\large{ k }$$ = thermal conductivity of the material $$Btu-ft\;/\;hr-ft^2-F$$

$$W\;/\;m-K$$

$$\large{ A }$$ = area of the surface $$in^2$$ $$mm^2$$
$$\large{ \frac{dT}{dx} }$$ = temperature gradient $$F$$  $$K$$
$$\large{ \Delta t }$$ = time interval $$sec$$ $$s$$

Tags: Heat Transfer Heat