The importance of heat transfer in nanoliquids cannot avoided because it playing crucial role in the applied research fields. The potential area of applications included but restricted to applied thermal, biomedical, mechanical and chemical engineering. Therefore, it is the need of time to introduce new efficient way to enhance the heat transport rate in common fluids. The major aim of this research is to develop a new heat transport BHNF (Biohybrid Nanofluid Model) model in a channel having expanding/contracting walls up to Newtonian regimes of blood. The two sort of nanomaterials (Graphene + CuO) along with blood as base solvent are taken for the formation of working fluid. After that, the model analyzed via VIM (Variational Iteration Method) to examine the influence of involved physical parameters on the behavior of bionanofluids. The model results revealed that the bionanofluids velocity rises towards the lower and upper channel end when the expanding/contracting of the walls in the range of 0.1–1.6 (expanding case) and\documentclass[12pt]{minimal}
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				\begin{document}$$- \, 0.1$$\end{document}-0.1to\documentclass[12pt]{minimal}
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				\begin{document}$$1.6$$\end{document}1.6(contraction case). The working fluid attained high velocity in the neighboring of center portion of the channel. By increasing the walls permeability (\documentclass[12pt]{minimal}
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				\begin{document}$${A}_{1}=\text{0.1,0.2,0.3,0.4}$$\end{document}A1=0.1,0.2,0.3,0.4), the fluid movement can be reduced and optimum decrement observed about\documentclass[12pt]{minimal}
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				\begin{document}$$\eta =0.0$$\end{document}η=0.0. Further, inclusion of thermal radiation (Rd) and temperature coefficient (\documentclass[12pt]{minimal}
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				\begin{document}$${\theta }_{r}$$\end{document}θr) observed good to enhance thermal mechanism in both hybrid and simple bionanofluids. The present ranges of Rdand\documentclass[12pt]{minimal}
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				\begin{document}$${\theta }_{r}$$\end{document}θrconsidered from\documentclass[12pt]{minimal}
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				\begin{document}$$0.9$$\end{document}0.9and\documentclass[12pt]{minimal}
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				\begin{document}$$1.4$$\end{document}1.4, respectively. Thermal boundary layer reduced in the case of simple bionanoliquid keeping\documentclass[12pt]{minimal}
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				\begin{document}$${P}_{r}=21.0$$\end{document}Pr=21.0.