An element of a certain volume is located at Point P in the figure shown below

An element of a certain volume is located at Point P in the figure shown below. The edges of the element are parallel to the coordinate axes (x, y, and z). The lengths are 2dx, 2dy, and 2dz. At this time, any internal heat production is neglected.

The heat flux density is parallel to the x-axis at Point P and is denoted as qx. The heat flux is entering the element via face A which is perpendicular to the x-axis and its equation is given below:

The heat flux leaving the element via the same face A is the same as the equation above, however, the negative sign is changed to positive. As a result, the sum of the two heat flux entering and leaving is the total heat flux. The equation for the total heat flux in the x-direction is shown below: