Fig depicts the effects of M and on

Fig. 3 depicts the effects of M and λ on the horizontal velocity profile. It is noted that BLZ945 the increasing values of magnetic parameter reduce the horizontal velocity profile. The figure clearly indicates that the transverse magnetic field opposes the transport phenomena. This is due to the fact that variation of M leads to the variation of the Lorentz force induced by the magnetic field, and the Lorentz force produces more resistance to transport phenomena. With the increasing λ, the horizontal velocity is found to increase the buoyancy-induced flow (λ>0) but decreases for the buoyancy-opposed flow (λ<0). For λ>0, there is a favorable pressure gradient due to the buoyancy forces, which results in the flow being accelerated. The effects of C and A on the dimensionless temperature profile are shown in Fig. 4. It can be seen that the effect of increasing values of the curvature parameter enhances the thermal boundary-layer thickness. The temperature profile increases with the increase of the slip parameter. This is because an increase in the slip parameter leads to the thickening of the thermal boundary layer. Fig. 5 demonstrates the effects of λ and M on the temperature profile. With increasing λ, the temperature is found to decrease in the buoyancy induced flow and to increase with λ in the buoyancy-opposed flow. The thermal boundary-layer thickness decreases with the increasing values of the mixed convection parameter. The temperature profile enhances with the increase of the magnetic parameter. Thus the presence of the magnetic field leads to increase the thermal boundary-layer thickness. The effects of Pr and γ on the dimensionless temperature profile are elucidated in Fig. 6. It is clear that the increasing values of Pr reduce the temperature profile. Fluids with lower Prandtl numbers have higher thermal conductivities (and thicker thermal boundary-layer structures) so that heat can diffuse from the sheet faster than for higher Pr fluids (thinner boundary-layers). Hence the Prandtl number can be used to increase the rate of cooling in conductive fluids. It is also seen that the temperature profile enhances with the surface convection parameter. The parameter γ is directly proportional to the heat transfer coefficient associated with the hot fluid . The thermal resistance on the hot fluid side is inversely proportional to . Thus as γ increases, the hot fluid side convection resistance decreases and consequently, the temperature profile increases. Physically, the negative sign of F ″(0) implies that the surface exerts a dragging force on the fluid and the positive sign implies the opposite. This is consistent with the present case as a stretching cylinder which induces the flow that is considered here. Fig. 7 shows the variation of the skin friction coefficient. It is clear that the skin friction coefficient F ″(0) increases with the increase of λ and A and decreases with increasing C and M. The variation of the Nusselt number is shown in Fig. 8. It is observed that the Nusselt number increases with the increasing values of C, λ and γ and decreases with M and A.
Conclusion The steady axi-symmetric laminar boundary-layer slip flow of a viscous incompressible fluid and heat transfer towards a vertical stretching cylinder in the presence of the uniform magnetic field has been investigated. Using a similarity transformation, the governing system of partial differential equations is first transformed into coupled non-linear ordinary differential equations and then solved with the help of the numerical shooting method. The parameters involved in this study significantly affect the flow and heat transfer. The following conclusions can be drawn as a result of the computations:
Introduction The task of developing effective semiconductor sources of terahertz radiation (the wavelength range of electromagnetic radiation is 30–300µm) is rather important at present as these devices can be used in diverse areas of science and technology, such as medicine, environmental monitoring, security systems, and computer science (see, for example, Refs. [1–3]). One of the most promising mechanisms for generating terahertz radiation is based on optical transitions of nonequilibrium charge carriers involving impurity states in semiconductors and semiconductor nanostructures. This mechanism is an alternative to the quantum cascade laser [4], since fabricating the latter requires very sophisticated techniques of high-quality growth of semiconductor nanostructures.