A growing number of shutoffs and rising delinquency in paying utility bills greets the second year of the Washington Area Fuel Fund, which helps needy people pay their gas, electric, fuel oil and wood bills.

This week, an appeal for contributions will be mailed in all Washington Gas bills. In addition the Salvation Army, WMAL Radio and WDVM-TV and other sponsors will begin publicizing the fund. In October, messages will be posted on 100 Metrobuses.

The fund, which helps Washington area residents after government aid has been exhausted, begins taking applications on Jan. 2 in the eight area Salvation Army offices.

The fund raised $522,000 last year, mostly from individuals who added contributions to payments on their utility bills. Washington Gas customers gave $31,500, Pepco customers gave $20,000 and contributions directly to the fund's post office box totaled $49,000. Washington Gas as a corporation gave $125,000 and its employes another $13,000, said Paul Young, a Washington Gas spokesman.

The money was distributed to 2,163 households in the District, Southern Maryland and Northern Virginia. About two out of three households that applied for aid received it, Young said.

Nearly half of the money, 46 percent, was returned to Washington Gas as recipients paid their delinquent bills. Another 39 percent went to Pepco and Vepco, and the rest for wood and coal.

"When we began last fall, we had no idea there were so many people needing help," said Salvation Army Major Tom Jones. To be eligible, a single person's income must be less than $9,110, a couple's less than $12,260 and that of a family of four less than $18,560.

Organizers hope to raise $750,000 this year.Tax-deductible contributions may be sent to Box 1999, Washington, D.C. 20013.