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Linearization of the source term of the diffusion equation

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October 27, 2022, 02:43	Linearization of the source term of the diffusion equation	#1
M.L.QU New Member Zhejiang Join Date: Oct 2022 Posts: 2 Rep Power: 0	Hi guys, I want to solve a convection-diffusion equation with an absorption source term (Liner Driving Force model and Langmuir-Freundlich isothermals), but I don't know how to linearise this source term. Please see the following equations: $\frac{\partial c}{\partial t}+u \frac{\partial c}{\partial z} -D_{z}\frac{\partial^{2} c}{\partial z^{2}}+\rho_{p} \frac{\partial q}{\partial t} =0$ $\frac{\partial q}{\partial t} =k^{}_{LDF} (q^{}-q)$ $q^{}=\frac{q_{max} (bcRT)^{\frac{1}{n}}}{1+(bcRT)^{\frac{1}{n}}}$ where c is the variable, and others are constant. I wonder how to linearise this $q^{}$ . Please give me some advice, and I really appreciate your time and patience.

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absorptivity, diffusion equation, linearize, source terms

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