Heat and Thermodynamics

11.2 Rectilinear Flow of Heat

Let us consider a metal rod of area of cross section A whose one end is heated at a furnace (Fig. 11.1). Heat will be conducted towards the free end. The temperature at any section of the rod perpendicular to its length increases and after some time it becomes steady; before this state, it was variable state when the temperature varied with time.

 

 

Fig. 11.1 Rectilinear flow of heat

 

Let θ be the steady temperature at a distance x and θ + dθ be the steady temperature at a distance x + dx. The quantity of heat flowing through the layer x per second is

 

 

and the quantity of heat flowing through the layer x + ...