## 2 Model Formulation  
The radiative and dissipative colloidal suspension of water and ethylene glycol suspended by cobalt ferrite and Mn-Zn ferrite is under consideration over a non-static wedge. The flow obeys the characteristics of incompressible flow. The flow configuration is taken in the Cartesian coordinatesystem. \(U_{w}=U_{\infty}x^{m}\) and \(u_{w}=U_{w}x^{m}\) denote the main stream and wedge velocities, respectively. Furthermore, \(\lambda=2m(m+1)^{-1}\) represents the Hartree pressure corresponding to \(\lambda=(\pi)^{-1}\Omega\). Moreover, the temperature of the wedge wall is a function of x and is \(T_{w}(x)=T_{\infty}+\frac{A}{x^{-2m}}\), where \(T_{\infty}\) shows the free stream temperature. Figure 1 depicts the flow configuration with coordinate axes:  
In the light of aforesaid assumptions, the following set of PDE's govern the flow of H\({}_{2}\)O and C\({}_{2}\)H\({}_{6}\)O\({}_{2}\) suspended by cobalt ferrite and Mn-Zn ferrite nanoparticles [47; 48]:  
\[\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0, \tag{1}\]  
\[u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=U(x)\frac{dU(x )}{dx}+\frac{\mu_{nf}}{\rho_{nf}}\left(\frac{\partial^{2}u}{\partial y^{2}} \right), \tag{2}\]  
\[u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}=\frac{k_{nf}}{ \left(\rho c_{p}\right)_{nf}}\left(\frac{\partial^{2}T}{\partial y^{2}} \right)+\frac{1}{\left(\rho c_{p}\right)_{nf}}\left(\frac{\partial u}{ \partial y}\right)^{2}-\frac{16\alpha^{*}T_{\infty}^{3}}{3k\left(\rho C_{p} \right)_{nf}}\frac{\left(\frac{\partial^{2}T}{\partial y^{2}}\right)}{\partial y ^{2}}. \tag{3}\]  
Here, Equation (1) shows the conservation law for mass and Equation (2) represents the momentum equation. Furthermore, velocity components in horizontal and vertical directions are denoted by \(u\) and \(v\), respectively. Additionally, \(U(x)\) shows main stream velocity, Temperature \(T\), heat capacity \(\left(\rho C_{p}\right)_{nf}\) dynamic viscosity \(\mu_{nf}\), effective thermal conductivity \(k_{nf}\), and mean adsorption coefficient is \(k\):  
For our flow model, the following are the feasible boundary conditions [48]:  
\[u_{y=0}=u_{w}(x),\ v_{y=0}=0,\ T_{y=0}=T_{\infty}+\frac{A}{x^{-2m}}, \tag{4}\]  
\[u_{y\rightarrow\infty}\to U(x),\ T_{y\rightarrow\infty}\to T_{\infty}. \tag{5}\]  
The set of self-similar transformations are as under [49]:  
\[u=\frac{\partial\psi}{\partial y},\ v=-\frac{\partial\psi}{\partial x},\ \psi=\sqrt{\frac{2\
u_{f}xU(x)}{(m+1)}}\ F(\eta),\ \eta=\sqrt{\frac{(m+1)U(x)}{2\
u_{f}x}}\ y,\ \beta(\eta)=\frac{T-T_{\infty}}{T_{w}-T_{ \infty}}. \tag{6}\]  
The following nanofluid characteristics are utilized [50]:  
\[\rho_{nf}=(1-\phi)\rho_{f}+\phi\rho_{s}, \tag{7}\]  
Figure 1: Flow Configuration and Coordinates. \[\left(\rho C_{p}\right)_{nf}=(1-\phi)\left(\rho C_{p}\right)_{f}+\phi\left(\rho C _{p}\right)_{g}, \tag{8}\]  
\[k_{nf}=k_{s}\left[\frac{\left(k_{s}+2k_{f}\right)-2\phi\left(k_{f}-k_{s}\right) }{\left(k_{s}+2k_{f}\right)+\phi\left(k_{f}-k_{s}\right)}\right], \tag{9}\]  
In Equations (7)-(9), \(\phi\) is volume fraction, \(\left(\rho C_{p}\right)_{f}\) is heat capacity of carrier fluids, \(k_{s}\) shows nanoparticles thermal conductivity, \(k_{f}\) is base liquid thermal conductivity, and \(\rho_{s}\) and \(\rho_{f}\) are the dynamic viscosities of nanoparticles and base liquid, respectively. Table 1 excircles the thermal and physical characteristics for base liquids and nanoparticles.