Norfolk & Western Railway said today that strong demand for coal offset declines in other goods that the railroad transports, and the big carrier reported record net income of $93.5 million ($2.86 a share) during the fourth quarter of 1981.

N&W, which plans to merge with Washington-based Southern Railway later this year, said fourth-quarter earnings were 15 percent higher than those for the fourth quarter of 1980, when the company earned $81.4 million ($2.55) on revenues of $423 million. In the fourth quarter of 1981, N&W revenues were $495.6 million.

For the full year of 1981, Norfolk and Western earned $291.1 million ($8.94) on revenues of $1.8 billion. In 1980, earnings were $232.4 million ($7.36) on revenues of $1.58 billion.

Robert B. Claytor, president and chief executive officer, told securities analysts today that not only is N&W bucking the recession but a strong challenge from the new CSX railroad--an amalgam of the Chessie System and the Seaboard Coast Line--that can provide direct routes to and from the South to the Middle West, which Norfolk and Western cannot do.

It is the competitive challenge from CSX that in part impelled the merger between Southern and N&W. The Interstate Commerce Commission must rule on the proposed marriage of the two lines by April 28. Norfolk and Western's routes extend from Virginia through the Midwest to Omaha and Kansas City. Southern's trackage would link Norfolk & Western directly to the South.

N&W traditionally has been the most profitable railroad in the industry, while Southern usually has performed well, too. Analysts say that while CSX has a head start on N&W and Southern, the combined NWS, as the company will be called, will be a financially formidable competitor for CSX.

During the fourth quarter, N&W's coal business was sharply higher than the year before, although its merchandise traffic--from grain to chemicals to paper products--was down markedly.

The volume of coal that N&W picked up from mines for the export market grew from 6.8 million tons in the fourth quarter of 1980 to 9.2 million tons last year. The volume of coal carried to U.S. utilities increased from 6.9 million tons to 7.5 million tons, while the volume of metallurgical coal carried to steel companies totaled 5.3 million tons compared with 5.1 million tons in the 1980 quarter.

Merchandise traffic, on the other hand, declined to 11.8 million tons from 12.5 million tons.

Claytor said that N&W is optimistic that its coal shipments will be strong in 1982, but said the continued recession and competition from CSX will hold down N&W's merchandise business.