Abstract: A refractory tile has a body formed from a refractory material. The body has a front side that defines a front plane, and a rear side that defines a rear plane that is opposite the front plane. A concave portion is formed in the rear side and is contoured to a wall of boiler tubes. The body also has an inclined portion extending from the front plane to the rear plane. The inclined portion is formed at an acute angle with respect to the rear plane. The inclined portion defines an edge at an intersection with the rear plane. The edge directly contacts the wall without a backfill material. The tiles form an array of upper refractory tiles located only on an uppermost row of the array above lower refractory, against the bare wall of boiler tubes.