Due to the complexity of thermal effects in porous electrodes, the process of temperature rise in supercapacitors is difficult to be quantified by some simple but physically meaningful formulas. Here, the stack-electrode model is applied to investigate this issue both analytically and numerically. The numerical results show the process has three relaxation times, which divide that into four stages controlled by heat generation (HG) or heat transfer (HT). Temperature rise is first controlled by HG in the bulk phase, then by HG in both porous electrodes and bulk phase, then mainly by HT, and finally all by HT. The analytical formulas of three relaxation times and temperature rise under different structural parameters and intensity of heat dissipation are obtained. These formulas are expected to indicate the contribution of the different stages to total temperature rise, thus to guide the design of cooling methods of supercapacitors during the different stages.

中文翻译：

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多孔电极充电过程中与离子电荷传输耦合的四个阶段的热效应

由于多孔电极中热效应的复杂性，超级电容器的温升过程很难通过一些简单但具有物理意义的公式来量化。在这里，堆叠电极模型用于分析和数值研究这个问题。数值结果表明，该过程具有三个弛豫时间，分为四个阶段，分别由产热 (HG) 或传热 (HT) 控制。温升首先由体相中的 HG 控制，然后由多孔电极和体相中的 HG 控制，然后主要由 HT 控制，最后全部由 HT 控制。得到了不同结构参数和散热强度下三种弛豫时间和温升的解析公式。