# Magnetohydrodynamic Nanoliquid Thin Film Sprayed on a Stretching Cylinder with Heat Transfer
## 1 Introduction
[6]. It is very necessary to know more about heat transfer properties of fluids due to the different speculated applications. It is a fact that the study of heat transfer techniques can enhance the comprehensive understanding of physical phenomena like convection and boiling. The effective thermal conductivity is one of the most controversial topics in nanofluids. In addition, the physical nature is still far from being well understood due to its complexity and diversity. After detailed analysis, Brownian motion induced convection and effective conduction through percolating nanoparticle paths are taken to be the two most probable mechanisms that yield the improved heat conduction in nanofluids. Through a mechanistic point of view, although the effects of some parameters such as the average size of nanoparticles and nanoparticles concentration have been discussed in literatures [1; 2; 3; 4], yet an overall mechanistic description is not available. It is a problem to investigate the effective thermal conductivity of nanofluids analytically due to the extremely complicated mechanisms of heat transfer and the interrelationship between thermal conductivity and the size of nanoparticles and the nanoparticles concentration. Therefore the clear mechanism of heat transfer is still not known in nanofluids. To fill this gap [PERSON] et al. [7] attempted to derive the analytical expressions for effective thermal conductivity of nanofluids while taking into account the effect of heat convection due to the Brownian motion of nanoparticles based on the fractal theory. Similarly [PERSON] et al. [8] investigated the advances of nanoparticles researches by introducing the fractal theory presenting the fractal model of thermal conductivity of nanofluids under the consideration of fractal distribution of nanoparticles sizes and heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, in which the nanoparticles are assumed to be dispersed. [PERSON] [9] considered a detailed discussion about the nanofluid. [PERSON] [10] explored the effects of MHD and temperature dependent viscosity on the flow of a non-Newtonian nanofluid in a pipe. [PERSON] and [PERSON] [11] elaborated the motion of a nanofluid passing a stretching surface. The effects of wall behavior for the peristaltic flow of a nanofluid were described by [PERSON] et al. [12]. [PERSON] and [PERSON] [13] investigated the endoscopic exploration of peristaltic flow of a nanofluid. [PERSON] [14] solved the problem of peristaltic flow of a nanofluid in the regime of Hall current and porous medium. A vast study exploring different aspects of nanofluid may be consulted in the references [15; 16; 17; 18; 19; 20; 21; 22; 23]. A magnetic nanofluid is a special substance having the combined features of fluid and magnetic characteristics. These fluids are practiced resulting in numerous distinguished utilizations like magneto-optic wavelength filters, and other substances related to optic like nonlinear materials and tunable fiber filters, gratings and switches. Several types of physical characteristics of such fluids are changed by the help of varying the intensity of magnetic field. Nanofluids related to magnetism assume presently a broad application in several departments such as biomedicine, medicine and in sink float isolation. Too many biomedical uses that contains nanofluids, like drug supply, magnetic cell separation and negative growth in magnetic resonance imaging are most important. Magnetohydrodynamic (MHD) motions are significant due to their use in power generators, MHD accelerators, refrigerations coils, transmissions lines, electric transformers and heating elements. Due to the scope of this notion, several researchers have done their work on magnetohydrodynamic motions. It is a proved statement that energy transfer is possible due to composition (concentration) gradient and mass transportation is occurred due to temperature gradient.