The heat flows in positive x-direction but the slope dT/dx is negative because the heat flows from high temperature to low temperature.

As we can see from the signs of each term above if the negative sign is not added we get heat transfer in the negative x-direction. So, the negative sign makes the heat transfer value positive in the x-direction.

Fourier's law in differential form is given by,

Where,

k = thermal conductivity in W/m^2.K

A = area normal to the heat flow in m^2

dT/dx = temperature gradient

The heat flows in positive x-direction but the slope dT/dx is negative because the heat flows from high temperature to low temperature.

As we can see from the signs of each term above if the negative sign is not added we get heat transfer in the negative x-direction. So, the negative sign makes the heat transfer value positive in the x-direction.