The influences of recycle on a double-pass laminar counterflow concentric-tube heat exchangers with sinusoidal wall fluxes

The effects of external recycle at the ends on double-pass laminar countercurrent heat exchangers with sinusoidal heat flux distribution are investigated analytically by setting a general solution to separate the original boundary value problem into a partial differential equation, which is solved by Frobenius method, and an ordinary differential equation. Analytical results show that recycle effects enhance the heat-transfer efficiency due to that the desirable effect of forced-convection increment has more influence than the undesirable effect of the heat-transfer driving-force decrement, and hence the forced-convection increment by increasing the recycle ratio leads to improved device performance in heat-transfer rate as compared with that in the single-pass operation (without an impermeable sheet inserted).