**1. Introduction**

In various fields of science and technology rapid progress has urged the researchers to extend their study towards the regime of boundary layer flow over a stretching sheet. The boundary layer flow behavior towards a linearly or nonlinearly stretching sheet plays a significant role for solving engineering problems and possess vast applications in manufacturing and production processes including metal spinning, rubber sheet manufacturing, production of glass fibers, wire drawing, extrusion of polymer sheets, petroleum industries, polymer processing etc. In these cases, the final product of desired characteristics depends on the rate of cooling in the process and the process of stretching. The dynamics of the boundary layer fluid flow over a stretching surface originated from the pioneering work of Crane [1] and he examined the incompressible steady boundary layer fluid flow caused by stretching sheet which moves in its own plane with linear velocity due to the uniform stress applications. This problem is particularly interesting as Crane [1] obtained the exact solution of 2D Navier–Stokes equations. Afterthat, Gupta and Gupta [2] extend Crane [1] work over different mathematical geometries. Yoon et al. [3] studied the theoretical and experimental results using Coulomb friction model by considering punch-sheet interface. Also, Sarma and Rao [4] examined the viscoelastic fluid flow by considering stretched sheet. In view of this, Vajravelu [5]

studied flow and heat transfer in a viscous fluid over a nonlinear stretching sheet without using the impact of viscous dissipation. Cortell [6] examined heat and fluid flow transportation over a nonlinear stretching sheet for two different types of thermal boundary conditions, prescribed surface temperature (PST) and constant surface temperature (CST). The influence of heat transfer on the stagnation point flow of a third-order fluid over a shrinking surface has been studied by Nadeem et al. [7]. Recently, Prasad et al. [8] examined the mixed convection heat transfer aspects with variable fluid flow properties over a non-linear stretching surface.

coefficient along with the rate of heat transfer. Basir et al. [19] examined the consequences of Peclet and Schmidt number in existence of partial slip towards a stretching surface. After that, rate of heat transfer along with partial slip condition was generalized by Pandey and Kumar [20]. Recently, Vinita and Poply [21] discussed MHD slip fluid flow of nanofluid in the existence of free stream velocity or outer velocity towards a stretching surface. Vinita et al. [22] studied MHD fluid flow with variable slip conditions over non-linear stretching surface. Furthermore, non-linearity effect towards the stretching surface under different physical circumstances has been

The outcomes of current study reveal that the results obtained is very significant in the formation of quality object in various manufacturing processes like polymer engineering, paper technology, wire and plastic industries. This study holds important industrial application, particularly in the field of extrusion where the fluid dispersed with particles is used to augment the strength and durability of the material.

In present analysis, 2-D incompressible fluid flow in MHD nanofluid over linear stretching sheet has been considered. Linear behavior generates flow and sheet is stretched in both direction of *x* axis with stretching velocity *uw* ¼ *ax*, where *a* and *x* denotes a constant and stretching surface coordinate respectively. *Tw* <sup>¼</sup> *<sup>T</sup>*<sup>∞</sup> <sup>þ</sup> *<sup>T</sup>*0*xm* at *y* ¼ 0, where *T*<sup>0</sup> refers to the positive constant, *T*<sup>∞</sup> refers to the ambient temperature attained and m refers to the physical parameter known as surface temperature parameter. Also, by introducing *m* ¼ 0, we have a special case of constant surface temperature (CST). **Figure 1** represents the physical model of the current study.

> *∂*2 *u <sup>∂</sup>y*<sup>2</sup> � *<sup>σ</sup>B*<sup>2</sup> *ρ*

*<sup>∂</sup><sup>y</sup>* <sup>¼</sup> <sup>0</sup> (1)

*u* (2)

The continuity, momentum, energy and concentration equations of the incompressible nanofluid boundary layer flow are as follows [10]

> *∂u ∂x* þ *∂u*

*u ∂u ∂x* þ *v ∂u <sup>∂</sup><sup>y</sup>* <sup>¼</sup> *<sup>ν</sup>*

examined by researchers in [6, 23–25].

*Heat Transfer in a MHD Nanofluid Over a Stretching Sheet*

*DOI: http://dx.doi.org/10.5772/intechopen.95387*

**2. Materials and methods**

**Figure 1.**

**215**

*Physical model and coordinate system.*

Fluid heating and cooling are important in many industries such as power, manufacturing and transportation. Effective cooling techniques are greatly needed for cooling any sort of high energy device. Common heat transfer fluids such as water, ethylene glycol, and engine oil have limited heat transfer capabilities due to their low heat transfer properties. In contrast, metals have thermal conductivities up to three times higher than these fluids, so it is naturally desirable to combine the two substances to produce a heat transfer medium that behaves like a fluid, but has the thermal of a metal. Since last two decades, study of nanofluid has urged the researcher's attention due to their heat transportation rate. Nanofluid comes in existence when we add a small quantity of nano-sized 10<sup>9</sup> <sup>10</sup><sup>7</sup> particles to the base fluids. Low heat transportation fluids like fluorocarbons, glycol, deionized water, etc. have badly thermal conductivity and therefore deliberated necessary for heat transfer coefficient surrounded by heat transfer medium and surface. The nanoparticles are typically made up of metals (*Al*,*Cu*), nitrides (*AlN*, *SiN*), carbides (*Sic*), oxides (*Al*2*O*3), or nonmetals (carbon nanotubes, Graphite, etc.) and the base fluid (conductive fluid) is usually water or ethylene glycol. Also, it has been experimentally proved that rate of heat conduction of nanofluids is more than rate of heat conduction of the base fluids. The concept of nanofluid was initially proposed by Choi and Eastman [9] to indicate engineered colloids composed of nanoparticles dispersed in a base fluid. An MIT based comprehensive survey has been done by Buongiorno [10] for convective transportation in nanofluids by considering seven slip conditions that may produce a relative velocity within the base fluid and nanoparticles. Only two (Brownian motion and thermophoresis) out of these seven slip mechanisms were found to be important mechanisms. By adopting Buogiorno's model, Kuznetsov and Nield [11] explored the nanofluid boundary layer uniform convecting fluid flow.

In recent years, MHD fluid flow has gained researchers attention due to its controllable heat transfer rate. Magnetohydrodynamics (MHD) effect also play and influential role in controlling the rate of cooling as well as segregation of molten metal's from various non-metallic impurities. Magnetohydrodynamic (MHD) fluid flow has enormous utilization in manufacturing processes, even in the industrial areas as well. The terminology "Magnetohydrodynamic" is combination of three elementary terms magneto that stands for magnetic field, hydro that stands for fluid/liquid and dynamics that stands for evolution of particles. The existence of external magnetic field gives rise to Lorentz drag force which acts on the fluid, so potentially altering the characteristics of fluid flow especially velocity, temperature and concentration. Grouping of electromagnetism Maxwell's equation and fluid mechanics Navier's stokes equations therefore provides Magnetohydrodynamic (MHD) relation [12, 13]. Hayat et al. [14] studied the MHD fluid flow transportation over stretching surfaces. Later, the influence of viscous and Ohmic dissipation (i.e. joule heating) in nanofluid has been presented by Hussain et al. [15]. Vajravelu and Canon [16] studied the flow behavior of fluid towards a non-linear stretching sheet. Further, Matin et al. [17] analyzed the entropy effect in MHD nanofluid flow over stretching surface. Shawky et al. [18] studied the Williamson nanofluid flow in porous medium and he acknowledged that enhancement in non-Newtonian parameter escalates skin friction

*Heat Transfer in a MHD Nanofluid Over a Stretching Sheet DOI: http://dx.doi.org/10.5772/intechopen.95387*

coefficient along with the rate of heat transfer. Basir et al. [19] examined the consequences of Peclet and Schmidt number in existence of partial slip towards a stretching surface. After that, rate of heat transfer along with partial slip condition was generalized by Pandey and Kumar [20]. Recently, Vinita and Poply [21] discussed MHD slip fluid flow of nanofluid in the existence of free stream velocity or outer velocity towards a stretching surface. Vinita et al. [22] studied MHD fluid flow with variable slip conditions over non-linear stretching surface. Furthermore, non-linearity effect towards the stretching surface under different physical circumstances has been examined by researchers in [6, 23–25].

The outcomes of current study reveal that the results obtained is very significant in the formation of quality object in various manufacturing processes like polymer engineering, paper technology, wire and plastic industries. This study holds important industrial application, particularly in the field of extrusion where the fluid dispersed with particles is used to augment the strength and durability of the material.
