We conducted Computational Fluid Dynamics (CFD) and heat transfer simulations for a cross-flow heat exchanger. Explored thermal interactions between the laminar-flow heated fluid in a linear pipe and the turbulent-flow external water environment. Utilized a RANS model with a k-ε variant to assess various materials under varying turbulence, velocity, pressure, and vorticity conditions. Among Copper, Stainless Steel, Mild Steel, and Aluminum, Aluminum exhibited the most substantial increase in thermal conductivity when graphene-coated. Additionally, we compared inner and outer graphene coatings, finding that outer coatings were both economically preferable and thermally superior for Copper and Mild Steel, while inner coatings improved the performance of Aluminum and Stainless Steel.