Forced Convection in Micropolar Fluid Flow through a Wavy-Wall Channel

ABSTRACT

Forced convection of micropolar fluids through a periodic array of wavy-wall channels has been analyzed by using a simple coordinate transformation method and the spline alternating- direction implicit method. The effects of the wavy amplitude, the micropolar parameter, and the Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging-diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and larger wavy amplitudes. For the micropolar fluids, increasing the vortex viscosity causes an increase in the total viscosity of the fluid, thus the skin friction coefficient increases while the Nusselt number decreases. Also, the influence of vortex viscosity on the minimum cross section of the wavy-wall channel and on a tiny change of the maximum cross section is manifest. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, regardless of whether the fluids are Newtonian or micropolar fluids.     

FORCED CONVECTION IN MICROPOLAR FLUID FLOW OVER A WAVY SURFACE

Forced convection in the boundary layer flow of a micropolar fluid over a wavy surface is studied by the coordinate transformation and the spline alternating direction implicit method. Effects of the vortex viscosity parameter and the wavy geometry on the velocity, the local skin friction coefficient, and the local Nusselt number (Nu) are studied. Results show that the harmonic curves for the local skin friction coefficient and the local Nu have the same frequency as the frequency of the wavy surface. Moreover, the vortex viscosity parameter tends to decrease the heat transfer rate and to increase the skin friction coefficient.     

Mixed convection plume about a line heat source in micropolar fluid

This paper analyses the flow and heat transfer characteristics of the mixed convection in the boundary layer flow of micropolar fluids about a line heat source embedded on the edge of a plate. The dimensionless forms of boundary layer equations and their associated boundary conditions have been derived and investigated numerically in order to characterize the behaviors of the mixed convection wall plume. The numerical results have been obtained using the method of cubic spline collocation and the finite difference scheme. The micropolar parameter reduces the velocity but increases the temperature in the boundary layer, whereas the effects of buoyancy parameter trend conversely. Furthermore, the micropolar parameter decreases the skin friction parameter and the wall couple stress but increases the wall temperature, whereas the effects of buoyancy parameter trend conversely. Finally, the higher the value of Prandtl number, the greater the skin friction parameter, the wall couple stress and the wall temperature.     

Free convection heat and mass transfer from a horizontal cylinder of elliptic cross section in micropolar fluids

This work examines the natural convection heat and mass transfer near a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in a micropolar fluid. The transformed governing equations are then solved by the cubic spline collocation method. Results for local Nusselt and Sherwood numbers are presented as functions of vortex viscosity parameter and aspect ratio. The heat and mass transfer rates of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, the heat and mass transfer rates from an elliptical cylinder in Newtonian fluids are higher than those in micropolar fluids.     

Natural convection of a micropolar fluid from a vertical truncated cone with power-law variation in surface temperature

This work presents a boundary-layer analysis about the natural convection heat transfer near a vertical truncated cone with power-law variation in surface temperature in a micropolar fluid. The transformed boundary layer governing equations are solved by the cubic spline collocation method. Results for local Nusselt numbers are presented as functions of vortex viscosity parameter, the surface temperature exponent, and the Prandtl number. The heat transfer rates of the truncated cones with higher surface temperature exponents are higher than those with lower surface temperature exponents. Moreover, the heat transfer rate from a vertical truncated cone in Newtonian fluids is higher than that in micropolar fluids.     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration

This work examines the natural convection heat and mass transfer near a sphere with constant wall temperature and concentration in a micropolar fluid. A coordinate transformation is used to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. For micropolar fluids, higher viscosity tends to retard the flow and thus decreases the natural convection heat and mass transfer rates from the sphere with constant wall temperature and concentration. Moreover, the natural convection heat and mass transfer rates from a sphere in Newtonian fluids are higher than those in micropolar fluids.     

Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature

This work studies the natural convection boundary layer flow of a micropolar fluid near a vertical permeable cone with variable wall temperature. The transformed boundary layer governing equations are solved by the cubic spline collocation method. The local Nusselt numbers are presented as functions of suction variables for different values of vortex viscosity parameter, surface temperature exponent, and Prandtl number. Results show that the heat transfer rates of the permeable cones with higher suction variables are higher than those with lower suction variables. Moreover, the heat transfer rate from a vertical permeable cone in Newtonian fluids is higher than that in micropolar fluids.     

Fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations

This work examines the effects of the vortex viscosity parameter and the buoyancy ratio on the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. The closed-form analytic solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived. Increasing the vortex viscosity parameter tends to increase the magnitude of microrotation and thus decreases the fluid velocity in the vertical channel. Moreover, the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid for micropolar fluids are lower than those of Newtonian fluids.     

TRANSIENT ANALYSIS OF COMBINED FORCED AND FREE CONVECTION-CONDUCTION ALONG A VERTICAL CIRCULAR FIN IN MICROPOLAR FLUIDS

The conjugate, transient, laminar, combined convection and conduction problem of mi-cropolar fluids along a vertical circular fin has been investigated. The coupled governing equations in dimensionless form are solved numerically using cubic spline collocation formulation. The analyses of heat transfer are divided into constant root temperature and constant heat flux from the root. Numerical results show that the heat transfer rate increases with increasing buoyancy force. A comparison of the heat transfer characteristics between a Newtonian fluid and a micropolar fluid is also discussed.     

Joule heating effects on magnetohydrodynamic free convection flow of a micropolar fluid

An analysis is presented to study the effect of viscous and Joule heating on MHD-free convection flow with a variable plate temperature in a micropolar fluid in the presence of uniform transverse magnetic field. The presence of dissipation increases both the skin friction and the rate of heat transfer at the surface. The friction factor and heat transfer rate decrease with an increase in the magnetic field parameter M and micropolar parameter Δ.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Similarity solution of three‐dimensional MHD radiative Casson nanofluid motion over a stretching surface with chemical and diffusion‐thermo effects

In this study, we analyzed three‐dimensional magnetohydrodynamic non‐Newtonian and Newtonian fluid motion, transfer of heat and mass over a stretching surface with Brownian flow, thermophoresis, and Dufour effects. By Runge‐Kutta based shooting method, the transformed governing equations are solved numerically. With the facilitate of tables and graphs, momentum, energy and mass profiles along with the skin friction coefficient, local Nusselt number, and Sherwood number are analyzed in the influence of nondimensional parameters. It is established that enhance the stretching ratio parameter improves the energy and concentration transfer rate. The transfer of energy and concentration rate in the Newtonian fluid is relatively low while compared with non‐Newtonian fluid.     

Numerical simulation of the natural convection plume about line heat source in micropolar fluid

This paper analyses the flow and heat transfer characteristics of laminar free convection in the boundary layer flow of micropolar fluids about a line heat source embedded on the edge of a plate. The nonlinear formulation governing equations are initially cast into dimensionless form by a local non-similar transformation and the resulting system of equations is then solved by the cubic spline collocation method and the finite difference scheme. Of particular interest are the effects of the micropolar parameter, Δ, and the Prandtl number on the velocity and temperature fields and on the skin friction coefficient, wall couple stress, and wall temperature. Numerical results are obtained for the velocity and temperature profiles for different values of the Prandtl number and micropolar parameter.     

Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet

This paper investigates the magnetohydrodynamic (MHD) flow and heat transfer characteristics in the presence of a uniform applied magnetic field. The boundary layer flow of a third-order fluid is induced due to linear stretching of a non-conducting sheet. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing non-linear differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence of these solutions is discussed. Velocity and temperature distributions are shown graphically. The numerical values for the skin friction coefficient and the Nusselt number are entered in tabular form. Emphasis has been given to the variations of the emerging parameters such as third-order parameter, magnetic parameter, Prandtl number and the Eckert number. It is noted that the skin friction coefficient decreases as the magnetic parameter or the third grade parameter increases.     

Transient mixed radiative convection flow of a micropolar fluid past a moving, semi-infinite vertical porous plate

The flow of viscous incompressible micropolar fluid past a semi-infinite vertical porous plate is investigated with the presence of thermal radiation field, taking into account the progressive wave type of disturbance in the free stream. The effects of flow parameters and thermophysical properties on the flow and temperature fields across the boundary layer are investigated. The Rosseland approximation is used to describe radiative heat transfer in the limit of optically thick fluids. Numerical results of velocity profile of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. It is observed that, when the radiation parameter increases the velocity and temperature decrease in the boundary layer, whereas when Grashof number increases the velocity increases.     

Comprehensive analysis of radiation impact on the transfer of heat and mass micropolar MHD free convective fluid flow across a stretching permeability sheet with suction/injection

As part of our research, we investigate the analysis influence of radiation on heat and mass transfer free convection of micropolar MHD fluids over a stretched porosity sheet involving suction and injection. The governing energy, rotational momentum, and concentration and momentum partial differential equations are transformed into ordinary differential equation ones via a similarity transformation. This system of equations is then solved by using MATLAB's built-in solver. The Sherwood numbers, Nusselt, friction factor, wall couple shear stress, and dimensionless profiles are all influenced by the various physical parameters of the flow. When the material parameter is increased, velocity rises but decreases when the magnetic parameter and surface condition factor are increased.     

Combined heat and mass transfer in natural convection flow from a vertical wavy surface in a power-law fluid saturated porous medium with thermal and mass stratification

This work studies the coupled heat and mass transfer by natural convection near a vertical wavy surface in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the vertical wavy plate is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the important heat and mass transfer characteristics are studied. Results show that an increase in the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the vertical wavy surface. It is shown that an increase in the power-law index, the thermal stratification parameter, or the concentration stratification parameter leads to a smaller fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinate. Moreover, the total heat transfer rate and the total mass transfer rate of vertical wavy surfaces are higher than those of the corresponding smooth surfaces.     

Slip Flow of Casson Rheological Fluid Under Variable Thermal Conductivity with Radiation Effects

This paper investigates the radiation and chemical reaction effects on Casson non‐Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions. The governing boundary layer conservation equations are normalized into nonsimilar form using similarity transformations. A numerical approach is applied to the resultant equations. The behavior of the velocity, temperature, concentration, as well as the skin friction coefficient, Nusselt number, and Sherwood number for various governing physical are discussed. Increasing the radiation parameter decreases the temperature. An increase in the rheological parameter (Casson parameter) induces an elevation in the skin friction coefficient, the heat and mass transfer rates. The larger the β values the closer the fluid is in behavior to a Newtonian fluid and further departs from plastic flow. Temperature of the fluid was found to decrease with increasing values of the Casson rheological parameter. The most important non‐Newtonian fluid possessing a yield value is the rheological Casson fluid, which finds significant applications in polymer processing industries, biomechanics, and chocolate food processing.     

The effect of temperature-dependent viscosity on the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature-dependent viscosity. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of viscosity-variation parameter, aspect ratio, and Prandtl number. The total heat transfer rate and the total skin friction of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, increasing the viscosity-variation parameter tends to enhance the heat transfer rates from a horizontal elliptical cylinder.