Analytical studies on the temperature distribution in spiral plate heat exchangers: Straightforward design formulae for efficiency and mean temperature difference

The temperature distribution in spiral plate heat exchangers has been calculated numerically to obtain the efficiency and the logarithmic mean temperature difference (LMTD) correction factors F as a function of the number of transfer units N, the number of turns n, and the heat capacity rate ratio C. It has been found that the LMTD correction factors, when plotted against the number of transfer units per turn N/n, fall approximately on a single curve. That curve for balanced countercurrent operation (C = −1) can be very closely represented by the simple formula F = (n/N)tanh(N/n). From that simple analytic representation of our numerical results it was concluded that a simpler physical model might exist to represent the overall behaviour of a spiral plate heat exchanger equally well. In fact, a countercurrent cascade of n cocurrent heat exchangers does result exactly in the above-mentioned formula for the LMTD correction factor. From that model the F-factors for other heat capacity rate ratios C (−1 < C ⩽ 0) can also be calculated and they are in sufficient agreement with the numerical results.