After a long period of slow growth, the large New York City banks expect to experience extremely brisk business loan demand through the end of 1978, the head of Chase Manhattan Bank's corporate banking department said yesterday.

"Between now and the end of this year, you are going to have a hell of a six months in loan volume," James Carey predicted yesterday.

The reason for the belated increase is that the large corporations, which are the traditional customers of the New York City money center banks, finally are finding themselves with financing needs they no longer can supply internally or at attractive rates through the commercial paper market, where they borrow directly from each other.

Regional banks have been experiencing a lending surge for about a year, but the New York City banks only have begun to participate recently. These key banks, however, are now an important reservoir of liquidity for the banking system as a whole, Carey indicated.

In a session with reporters, Carey dismissed concern about a liquidity squeeze and said he did not "see any problem accomodating a very healthy increase in loan demand of just about any nature." He said the increase in demand would be accompanied by a "reasonable increase" in interest rates, though he declined to be specific. But he predicted that rates should "peak in the fourth quarter."

His remarks came amidst expectations by many money market analysts that short-term rates will continue to rise sharply for the remainder of the year, and some predictions that another quarter-point increase in the commercial bank prime lending rate may be in the offing.

The last increase - to 8 1/2 percent - was initiated 10 days ago, less than a month after the previous rise.

"It's going to 8 3/4 shortly," said Lawrence Kudlow, a money market economist with Paine Webber. "But whether it will be this week, I'm not sure."

Kudlow predicted the prime would reach 9 1/4 percent to 9 1/2 percent by the end of the year, with no interest rate peak in sight before the early part of 1979.

In its most recent credit market commentary, Salomon Brother said "credit demands, which are being fueled by sharp increase in real growth and a high rate of inflation, are soaring in key sectors."