A gasifier and incinerator for use in gasifying biomass waste in the form of a sludge having particle size not greater than 1 cm, and having 20% to 100% solids content with the rest being liquid, said gasifier and incinerator comprising: a primary chamber adapted to receive biomass sludge therein for gasification and incineration thereof; a fume transfer vent disposed near the top of said primary chamber, said fume transfer vent being in fluid communication with said primary chamber, to permit the escape of fumes from said primary chamber; a mixing chamber in fluid communication with said fume transfer vent to accept said fumes from said primary chamber; an afterburner chamber in fluid communication with said mixing chamber; a secondary burner member situated in said gasifier so as to produce an initial heating flame within a first vertically disposed portion of said afterburner chamber, said burner member having a fuel inlet and an air inlet to permit the supply of fuel and oxygen gas, respectively, to said burner member, and control means to control the supply of fuel and oxygen to said burner member; a partitioning wall disposed between said mixing chamber and said primary chamber, wherein said partitioning wall defines the bottom limit of said transfer vent; a heat transfer chamber in fluid communication with said afterburner chamber, wherein heated gases flowing from said afterburner chamber cause heating of said heat transfer chamber; wherein said primary chamber has a heat conductive floor and is superimposed on said heat transfer chamber with said heat conductive floor being disposed in separating relation therebetween so as to permit conductive and convective heating of said primary chamber; and an exhaust vent in fluid communication with said heat transfer chamber for venting said fumes into said ambient surroundings; characterized in that said gasifier and incinerator additionally comprises at least one primary auger located crosswise in said primary chamber, and being in communication at a first end with a sludge feed hopper and at a second end with an ash hopper; drive means to rotate said at least one primary auger so as to drive biomass sludge through said primary chamber from said sludge feed hopper to said ash hopper, across said heat conductive floor; and wherein said heat transfer chamber underlies said at least one primary auger near the second end thereof. a primary chamber adapted to receive biomass sludge therein for gasification and incineration thereof; a fume transfer vent disposed near the top of said primary chamber, said fume transfer vent being in fluid communication with said primary chamber, to permit the escape of fumes from said primary chamber; a mixing chamber in fluid communication with said fume transfer vent to accept said fumes from said primary chamber; an afterburner chamber in fluid communication with said mixing chamber; a secondary burner member situated in said gasifier so as to produce an initial heating flame within a first vertically disposed portion of said afterburner chamber, said burner member having a fuel inlet and an air inlet to permit the supply of fuel and oxygen gas, respectively, to said burner member, and control means to control the supply of fuel and oxygen to said burner member; a partitioning wall disposed between said mixing chamber and said primary chamber, wherein said partitioning wall defines the bottom limit of said transfer vent; a heat transfer chamber in fluid communication with said afterburner chamber, wherein heated gases flowing from said afterburner chamber cause heating of said heat transfer chamber; wherein said primary chamber has a heat conductive floor and is superimposed on said heat transfer chamber with said heat conductive floor being disposed in separating relation therebetween so as to permit conductive and convective heating of said primary chamber; and an exhaust vent in fluid communication with said heat transfer chamber for venting said fumes into said ambient surroundings; characterized in that said gasifier and incinerator additionally comprises at least one primary auger located crosswise in said primary chamber, and being in communication at a first end with a sludge feed hopper and at a second end with an ash hopper; drive means to rotate said at least one primary auger so as to drive biomass sludge through said primary chamber from said sludge feed hopper to said ash hopper, across said heat conductive floor; and wherein said heat transfer chamber underlies said at least one primary auger near the second end thereof.