The boundary layer flow of nanofluids is usually described by a system of nonlinear differential equations with infinity boundary conditions. These boundary conditions at infinity are transformed into classical boundary conditions via two different transformations. Accordingly, the original heat transfer equation is changed into a new one which is expressed in terms of the new variable. The exact solutions have been obtained in terms of the exponential function for the stream function and in terms of the incomplete Gamma function for the temperature distribution. Furthermore, it is found in this project that a certain transformation reduces the computational work required to obtain the exact solution of the heat transfer equation. Hence, such transformation is recommended for future analysis of similar physical problems. Besides, the other published exact solution was expressed in terms of the WhittakerM function which is more complicated than the generalized incomplete Gamma function of the current analysis. It is important to refer to the fact that the analytical procedure followed in our project is easier and more direct than the one considered in a previous published work.

Nanofluids are a relatively new area of research which attracted attention in recent years because of their applications in engineering and applied sciences. The flow and heat transfer of such nanofluids are usually described by a system of nonlinear differential equations. Such system can be solved using numerical methods [

Equations (

Suppose the following transformation:

Suppose the following transformation:

Inserting this value of

which in terms of

In the previous sections, we have obtained the exact solution of the heat transfer differential equation described by (

The current exact solution is expressed in terms of the generalized incomplete Gamma function, while the other published solution was expressed in terms of two special functions, namely, the WhittakerM and the Hypergeometric functions. The properties of these two latest functions are more difficult than the properties of the generalized incomplete Gamma function. Furthermore, our exact solution agrees with the exact solution obtained very recently by Ebaid et al. [

Our exact solution is expressed in the form of a very simple expression if compared with the complex published solution obtained in [

Our simple exact solution can be easily verified by inserting only one expression into the heat transfer equation (

The verification of the boundary conditions can be checked in a very simple way through our exact solution.

Our exact solution can be easily plotted when compared with the other published solution. With a very simple programme using Mathematica, we have plotted two figures for the purpose of comparisons between the current results and those obtained in [

Effect of

Effect of

The nonlinear differential equations governing the flow and heat transfer of nanofluids in the presence of a magnetic field have been solved exactly. Two transformations have been suggested to change the domain from unbounded domain into a bounded one. It was observed that one of the two transformations is easier than the other where few steps were required in getting the exact solution. Moreover, the obtained exact solution for the heat transfer equation agreed with the results in literature at a special case. Furthermore, the other previous exact solution published in [

The authors declare that there is no conflict of interests regarding the publication of this paper.

_{2}-water nanofluids in the presence of a magnetic field