Luikov’s equations of heat and mass transfer with pressure gradient have significant applications especially in the case of intensive drying in porous media. The established analytical solution of Luikov’s equations including pressure gradient effect in a complete form is presented in this work. The existence of complex roots in the analytical solution describing intensive drying with pressure gradient was overlooked in literature. A Matlab function capable of searching and sorting out the complex eigenvalues is also showcased. Three test cases are analyzed and compared with numerical solutions: one theoretical case to emphasize the importance of complex roots in analytical solution while two cases of drying process in ceramic and barley kernel to ensure practical applicability. Excellent matching between analytical and numerical results is noticed when complex eigenvalues are included.

中文翻译：

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Luikov 在强化干燥中具有复特征值的解析解

Luikov 的具有压力梯度的传热和传质方程具有重要的应用，特别是在多孔介质中的密集干燥的情况下。本文给出了包含压力梯度效应的 Luikov 方程的完整解析解。文献中忽略了描述压力梯度强化干燥的解析解中复根的存在。还展示了能够搜索和整理复杂特征值的 Matlab 函数。分析了三个测试案例并与数值解进行了比较：一个理论案例强调了复根在解析解中的重要性，而两个案例是陶瓷和大麦仁的干燥过程，以确保实际适用性。