Abstract
Boundary value problems arise in many real applications such as nanofluids and other areas of applied sciences. The temperature/nanoparticles concentration are usually expressed as singular 2ndorder ODEs. So, it is a challenge to obtain the exact solution of these problems due to the difficulty of the singularity encountered in the governing equations. By means of a suitable transformation, a direct approach is introduced to solve a general class of 2nd-order ODEs. The efficiency of the obtained results is validated through selected problems in the literature. It is found that several existing solutions can be deduced as special cases of our generalized one. Moreover, the present results may be invested for similar future problems in fluid mechanics, especially nanofluids.
Highlights
The field of nanofluid is of great importance in industry, engineering, and physics
Boundary value problems arise in many real applications such as nanofluids and other areas of applied sciences
It is a challenge to obtain the exact solution of these problems due to the difficulty of the singularity encountered in the governing equations
Summary
The distributions of temperature and nanoparticles concentration of such fluids are originally governed by PDEs which can be transformed into ODEs [1,2,3,4,5,6,7,8,9] Such ODEs are, basically, subjected to boundary conditions (BCs) given at infinity. The present generalized results will be invested to construct several exact solutions for some published nanofluids problems as special cases. Since b is neither a negative integer nor zero, the series (3.20) is defined and its general term vi(x) is given by (3.21). 1F1(a, b, −Qδ) is convergent because δ is finite and the solution given by Eqs. 1F1(a, b, −Qδ) is convergent because δ is finite and the solution given by Eqs. (3.16-3.17) or its equivalent form (3.24-3.25) converges
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