• Dr. Pradeep Kashyap

The advection-diffusion equation plays a pivotal role in modeling transport phenomena in diverse scientific and engineering disciplines, encompassing fluid dynamics, environmental science, and heat transfer. This study explores a novel analytical approach to solving the advection-diffusion equation using the Elzaki transform, a robust integral transform method known for its efficiency in handling linear partial differential equations. By leveraging the Elzaki transform, the solution process is significantly simplified, transforming the governing equation into an algebraic form, which facilitates the derivation of exact solutions. The method is applied to specific initial and boundary conditions, and the resulting analytical solutions are validated through illustrative examples. Furthermore, the behavior of the solution over time and space is visualized using graphical representations, highlighting the efficiency of the Elzaki transform in addressing complex transport problems. This work demonstrates the potential of the Elzaki transform as a powerful tool for solving advection-diffusion equations, offering insights into its application for real-world scenarios.

Advection-diffusion equation, Elzaki transform, analytical solutions, integral transform, transport phenomena, fluid dynamics, heat transfer, boundary conditions, initial conditions, transport modeling

"Elzaki Transform Approach to Solving the Advection-Diffusion Equation: A Novel Perspective", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 3, page no.a78-a85, March-2025, Available :http://www.jetir.org/papers/JETIR2503009.pdf

"Elzaki Transform Approach to Solving the Advection-Diffusion Equation: A Novel Perspective", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 3, page no. ppa78-a85, March-2025, Available at : http://www.jetir.org/papers/JETIR2503009.pdf