Unsteady Free Convection of Nanofluid Past an Infinite Vertical Sheet Under the Effects of Inclined Magnetic Field and Cogley Radiation
Authors: Gupta Piyush Kumar , Prakash Om , Tinker Seema 
Published: October 2024

Background:
An infinite vertical sheet is the medium of inquiry for studying the copper-
water nanofluid behavior with an inclined magnetic field and Cogley radiation. The research
contains significant aspects. The use of this nanofluid is of great practical importance, especially
in the areas of energy efficiency, thermal management, radiative cooling for space technology, environmental
impact reduction, and improving heat transfer efficiency in electronic device cooling
operations. Moreover, the research enhances the understanding and manipulation of sophisticated
materials. The uttermost significance of this resides in its capacity to uncover issues inherent in
the stages of planning, developing, analyzing, and improving manufacturing processes, possibly
securing new solutions via patent protection.

Objective:
This research aims to provide a comprehensive analysis of the unsteady natural convection
of a nanofluid along an infinite vertical sheet. The study focuses on understanding how an inclined
magnetic field, Cogley radiation, heat source, and varying nanoparticle volume concentrations
impact the velocity, thermal, and concentration profiles of the nanofluid. Additionally, the investigation
seeks to evaluate the Nusselt number, Sherwood number, and skin friction coefficient
across different concentration profiles to derive meaningful insights.

Methods:
The Laplace transform (L.T.) method, in combination with the MATLAB symbolic
computing program, is used to develop numerical solutions for the main boundary value issues.
The Laplace transform technique is used to clarify dimensionless partial differential equations
(PDEs) and their limiting situations. An in-depth study is conducted on the profiles of momentum,
energy, and concentration for various kinds of nanofluids with changing volume concentrations of
nanoparticles. This research provides a comprehensive examination and also identifies prospective
prospects in this field that might be protected by patents.

Result:
The work provides an in-depth understanding of how inclined magnetic fields, Cogley radiation,
heat generation, and nanoparticle volume concentration affect the velocity, energy, and
mass profiles of the nanofluid. Graphical representations depict these effects, offering a visual
comprehension of the system's behavior. The Nusselt number and skin friction coefficient are determined
by analytical and numerical methods. These findings demonstrate that the Nusselt number
and skin friction coefficient have an inverse relationship with changes in concentration profiles.

Conclusion:
The work improves our comprehension of the fluctuating natural convection of
nanofluids across an unbounded vertical surface, taking into account variables such as an inclined
magnetic field, heat source, Cogley radiation, and nanoparticle volume concentration. The practical
implications of the discoveries, together with the analytical and numerical results, enhance our
comprehension of the dynamics of nanofluid systems. Ensuring the protection and widespread distribution
of patented technology is essential for promoting sustainable advancements.