text: The G equation has an exact expression for a simple slot burner. Consider a two-dimensional planar slot burner of slot width  with a premixed reactant mixture is fed through the slot with constant velocity , where the coordinate  is chosen such that  lies at the center of the slot and  lies at the location of the mouth of the slot. When the mixture is ignited, a flame develops from the mouth of the slot to certain height  with a planar conical shape with cone angle . In the steady case, the G equation reduces to
  If a separation of the form  is introduced, the equation becomes
  which upon integration gives
  Without loss of generality choose the flame location to be at . Since the flame is attached to the mouth of the slot , the boundary condition is , which can be used to evaluate the constant . Thus the scalar field is
  At the flame tip, we have , the flame height is easily determined as
  and the flame angle  is given by
  Using the trigonometric identity , we have