## 5 Concluding Remarks
**Nomenclature**  
**Symbols** **Meaning** **Dimensions**  
\(a\) **Channel's half width** **[L]**  
\(\overline{A}_{m}\) **Revilin Erickson tensor** **[M/LT\({}^{2}\)]**  
\(b\) **Wave amplitude** **[L]**  
\(B_{r}\) **Brinkman number** **[-]**  
\(c\) **Wave speed** **[L/T]**  
\(\overline{C}\) **Dimensional concentration field** **[N/L\({}^{3}\)]**  
\(C_{0}\)**,** \(C_{1}\) **Concentration field at upper and lower wall** **[N/L\({}^{3}\)]**  
\(D\) **Diffusivity of chemical species** **[-]**  
\(D_{m}\) **Mass diffusivity coefficient** **[L\({}^{2}\)/T]**  
\(E_{c}\) **Eckert number** **[-]**  
\(E_{x}\) **Axial electric field** **[ML/AT\({}^{3}\)]**  
\(e\) **Electron charge** **[AT]**  
\(\overline{t}\) **Non-dimensional mean flow rate in moving frame** **[-]**  
\(\overline{h}\) **Dimensional upper wall** **[L]**  
\(h\) **Non-dimensional upper wall** **[-]**  
\(k\) **Thermal conductivity** **[ML/KT\({}^{3}\)]**  
\(k_{t}\) **Ratio of thermal diffusion** **[N/L\({}^{3}\)]**  
\(K_{B}\) **Boltzmaan constant** **[ML\({}^{2}\)/T\({}^{2}\)K]**  
\(m_{e}\) **Electroosmotic parameter** **[-]**  
\(\overline{n}^{*}\) **Positive and negative ions** **[AT]**  
\(n_{0}\) **Bulk concentration** **[AT]**  
\(\overline{p}\) **Dimensional pressure field** **[ML/T\({}^{2}\)]**  
\(p\) **Non-dimensional pressure field** **[-]**  
\(P_{e}\) **Peclet number** **[-]**  
\(P_{r}\) **Prandtl number** **[-]**  
\(\overline{Q}\) **Dimensional volume flow rate in fixed frame** **[L\({}^{3}\)/T]**  
\(R_{e}\) **Reynolds number** **[-]**  
\(\overline{S}\) **Dimensional shear stress** **[M/LT\({}^{2}\)]**  
\(S\) **Non-dimensional shear stress** **[-]**  
\(S_{c}\) **[PERSON] number** **[-]**  
\(S_{r}\) **Soret number** \begin{tabular}{l l l} \(t\) & Dimensional time & [T] \\ \(t\) & Non-dimensional time & [-] \\ \(\overline{T}\) & Dimensional temperature field & [K] \\ \(T_{0}\),\(T_{1}\) & Temperature field at upper and lower wall & [K] \\ \(T_{m}\) & Mean temperature & [K] \\ \(\overline{U}\) & Dimensional velocity along \(\overline{X}\) direction & [L/T] \\ \(u\) & Non-dimensional velocity along \(x\) direction & [-] \\ \(U_{\rm hs}\) & Helmholtz-Smoluchowski velocity & [L/T] \\ \(\overline{V}\) & Dimensional velocity along \(\overline{Y}\) direction & [L/T] \\ \(v\) & Non-dimensional velocity along \(y\) direction & [-] \\ \(\overline{X}\) & Dimensional axial coordinate in fixed frame & [L] \\ \(x\) & Non-dimensional axial coordinate in moving frame & [-] \\ \(\overline{Y}\) & Dimensional transverse coordinate in fixed frame & [L] \\ \(y\) & Non-dimensional transverse coordinate in moving frame & [-] \\ \(Z\) & heat transfer coefficient & [-] \\ \(z_{v}\) & Valence of ions & [-] \\ \(\alpha\) & Peristaltic wave number & [-] \\ \(\alpha_{1}\),\(\alpha_{2}\) & Material constants & [-] \\ \(\beta_{1}\),\(\beta_{2}\),\(\beta_{3}\) & Material constants & [-] \\ \(\gamma_{1}\),\(\gamma_{2}\),\(\gamma_{3}\) & Material coefficients & [-] \\ \(\lambda\) & Wavelength & [L] \\ \(\lambda_{1}\),\(\lambda_{2}\) & Material coefficients & [-] \\ \(\lambda_{D}\) & Debye length & [L] \\ \(\epsilon\) & Dielectric permittivity & [-] \\ \(\rho_{e}\) & Toatl charge density & [AT/L\({}^{3}\)] \\ \(\rho\) & Density of fluid & [M/L\({}^{3}\)] \\ \(\overline{\Phi}\) & Dimensional electric potential & [ML\({}^{2}\)/T\({}^{2}\)] \\ \(\Phi\) & Non-dimensional electric potential & [-] \\ \(\Gamma\) & Non-dimensional Deborah number & [-] \\ \(\epsilon\) & Amplitude ratio & [-] \\ \(\Theta\) & Non-dimensional volume flow rate & [-] \\ \(\theta\) & Non-dimensional temperature field & [-] \\ \(\Omega\) & Non-dimensional concentration field & [-] \\ \(\overline{\psi}\) & Dimensional stream function & [L\({}^{2}\)/T] \\ \(\psi\) & Non-dimensional stream function & [-] \\ \end{tabular}