**3. Solution Methodology**

The TLM-BANN coupled with PDEs representing TD-PNFM are converted into system of ODEs by applying suitable transformation. Adam numerical method is used to compute the reference dataset for all the six scenarios of TD-PNFM. The MATLAB command 'nftool' is used to execute the technique of Levenberg Marquardt with backpropagated artificial neural network (TLM-BANN) for the study of TD-PNFM.

The neural network figure for LMT-BANN is given below as Figure 2 and the flow chart is shown in Figure 3.

**Figure 2.** Neural Network diagram for TD-PNFM.

The current model is discussed for six scenarios and the scenarios consist of the variations of Prandtl fluid number, flexible number, ratio parameter, Prandtl number, Biot number and thermophoresis parameter. Each scenario has further four cases and the values for all the cases are written below in Table 1. With *Ha*= 0.4, *Nb*= 0.9 and *Sc* = 1.0. We can easily see the impact of variations of physical parameters on temperature profile and concentration profile. There are 10 hidden neurons with the input lies between 0 and 8 and the step size is 0.08. The dataset is computed for 101 points in which 81 points are for training, 10 points for testing and 10 points for validation.

**Figure 3.** Flow chart for TD-PNFM.


**Table 1.** Variation of parameters of TD-PNFM.
