The exact solution of a class of boundary value problems with polynomial coefficients and its applications on nanofluids

Usually, the temperature distribution of nanofluids and the nanoparticles' concentration are finally governed by second-order ordinary differential equations with polynomial coefficients. In this work, a class of second-order boundary value problems with applications on nanofluids has been theoretically solved in terms of the Kummer function. Several lemmas have been presented to relate the Kummer function with the generalized incomplete gamma function. Accordingly, the current solutions reduce to those in the literature at certain values of the coefficients as special cases. Furthermore, the present results are very useful in obtaining the solutions for any future similar problems without any need to perform further calculations.