Exact solution of a solar energy model using four different kinds of nanofluids: Advanced application of Laplace transform

Abstract

This paper analyzes the system of partial differential equations (PDEs) describing the absorption of solar energy via a solar collector utilizing nanofluids. Obtaining exact solution of any system of PDEs is a challenge, however, the current system is effectively solved by means of the Laplace transform (LT). To simplify our procedure, some preliminary theoretical aspects are derived for the inverse LT of some complex expressions and then invested to establish the exact solution. Explicit exact forms are obtained for the involved phenomena in terms of the complementary error function. Moreover, the exact solutions at different special cases are evaluated. Four different kinds of nanofluids are considered to extract the numerical results and physically discussed/interpreted.

Keywords

• Partial differential equation
• Error function
• Laplace transform
• Boundary value problem