This work is devoted to investigating weakly nonlinear hyperbolic waves arising from the action of small-amplitude, high-frequency boundary disturbances. By directly introducing a nonlinear phase variable corresponding to the leading wavefront and specifying a single-wave-mode boundary disturbance, we are able to construct an asymptotic solution. Furthermore, our result shows that, by properly arranging the relation of small amplitude to high frequency, a systematic procedure can be provided for constructing weakly nonlinear wave solutions with interior shocks and determining the shock initiation position (and time) when there is a local linear degeneracy at the leading wavefront.

Summary In the paper, we analyzed internal thermal transmission characteristics of water‐heating photovoltaic/thermal (PV/T) solar collector covered by photovoltaic (PV) cell, established photothermal conversion model of PV/T solar system, and analyzed the influence of PV cell coverage to photothermal characteristics of PV/T solar system. Results show that the thermal efficiency of PV/T solar system by optimizing PV cells coverage can reach 68%. In addition, by designing four water‐heating PV/T solar system prototypes with PV cell coverage of 0.4, 0.56, 0.7, and 0.82, respectively, we conducted experimental researches for the four prototypes and found that the four prototypes can achieve thermal efficiencies of 58%, 51%, 64%, and 67%, respectively, in heating 250 L of water to 50°C. The experiment results are consistent with theoretical analysis results, indicating that it is feasible to improve thermal characteristics of PV/T solar system by optimizing PV cell coverage. Copyright © 2017 John Wiley & Sons, Ltd.

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