Algorithm 1. Proposed method’s algorithm for thermal conductivity estimation (for each hybrid nanofluid)
Input: T, TC1, TC2, ρ, and hybrid1_datas Output: pTC, MAE, MSE, MAPE, R2
1	size ← Load(hybrid1_datas)
2	i ← 0
3	if i < 30 then
3.1	${w_i}_1={\displaystyle \frac{{\rho }_1}{{\rho }_1+{\rho }_2}}$, wi2$={\displaystyle \frac{{\rho }_2}{{\rho }_1+{\rho }_2}}$, hTCi = $w_{i1}\ast {TC}_{i1}+w_{i2}\ast {TC}_{i2}$
3.2	inputDatas(Ti, TCi1, TCi2)
3.3	outputDatas(hTCi)
3.4	i = i + 1, go to step 3
4	trainRatio = 0.8 trainIndex = randperm(size, round(trainRatio * size)) XTrain = inputDatas(trainIndex, :)’, YTrain = outputDatas(trainIndex, :)’ testIndex = setdiff(1:size, trainIndex) XTest = inputDatas(testIndex, :)’, YTest = outputDatas(testIndex, :)’ net = feedforwardnet([10 10]) net.trainFcn = ‘trainbr’ net.layers{1}.transferFcn = ‘tansig’ net.layers{2}.transferFcn = ‘tansig’ net.layers{3}.transferFcn = ‘purelin’ net.trainParam.epochs = 1000 net.trainParam.goal = 10−1000
5	net = train(net, XTrain, YTrain)
6	pTC = net(XTest)
7	MAE = mean(abs(pTC − YTest)) MSE = mean((pTC − YTest).^2); MAPE = mean(abs((pTC − YTest)/YTest)) * 100 R2 = 1 − mean(((pTC-YTest).^2)/(YTest.^2))
8	returnpTC, MAE, MSE, MAPE, R2