This investigation derives formulas to predict the mixed convective surface conductance of a flat isotropic surface roughness having a convex perimeter in a Newtonian fluid with a steady forced flow in the plane of that roughness. Heat transfer measurements of a 30.5 cm square rough plate with forced air velocities between 0.1 m/s and 2.5 m/s were made by the present apparatus in two inclined and all five orthogonal orientations. The present work’s formulas are compared with 104 measurements in twelve data-sets. The twelve data-sets have root-mean-square relative error (RMSRE) values between 1.3% and 4% relative to the present theory. The present work’sformulas are also compared with 78 measurements in 28 data-sets on five vertical rough surfaces in horizontal flow from prior work. The five stucco data-sets have RMSRE values between 2.5% and 6.5%; the other data-sets have RMSRE values between 0.2% and 5%. 

Hybrid nanofluids have several potential applications in various industries, including electronics cooling, automotive cooling systems, aerospace engineering, and biomedical applications. The primary goal of the study is to provide more information about the characteristics of a steady and incompressible stream of a hybrid nanofluid flowing over a thin, inclined needle. This fluid consists of two types of nanoparticles: non-magnetic nanoparticles (aluminium oxide) and magnetic nanoparticles (ferrous oxide). The base fluid for this nanofluid is a mixture of water and ethylene glycol in a 50:50 ratio. The effects of inclined magnetic fields and joule heating on the hybrid nanofluid flow are considered. The Runge-Kutta fourth-order method is used to numerically solve the partial differential equations and governing equations, which are then converted into ordinary differential equations using similarity transformations. Natural convection refers to the fluid flow that arises due to buoyancy forces caused by temperature differences in a fluid. In the context of an inclined needle, the shape and orientation of the needle have significantly affected the flow patterns and heat transfer characteristics of the nanofluid. These analyses protest that raising the magnetic parameter results in an increase in the hybrid nanofluid thermal profile under slip circumstances. Utilizing the potential of hybrid nanofluids in a variety of technical applications, such as energy systems, biomedicine, and thermal management, requires an understanding of and ability to manipulate these effects.