Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

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.     

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.     

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.     

Entropy minimized MHD microrotations of Cross nanomaterials with cubic autocatalytic chemical reaction

The Cross viscosity model is a generalized non-Newtonian nanofluid model that has widespread engineering and industrial applications like in the synthesis of polymeric solutions, polymeric latex spheres, animal blood, biological fluids, and polyacrylamides. To analyze the micromotion of such nanofluids, a micropolar flow model is introduced. Entropy generation (EG) minimization is important in thermal fluid systems undergoing heat transportation to achieve improved thermohydraulic execution. Homogeneous and heterogeneous reactions involve complex interactions involving the production and consumption of reactant species. Nonlinear thermal radiation plays a vital role in thermal systems undergoing a drastic change in the temperature gradient. The main focus of this study is the investigation of MHD microrotation in Cross nanofluids subject to nonlinear thermal radiation and autocatalytic chemical reactions. The findings from this study show that amplifying the Weissenberg number and power-law index leads to augmentation in axial and transverse fluid velocity components and emaciation in microrotations. Strengthening the magnetic field yields enfeeblement of fluid velocities. In addition, increasing the micropolar parameter leads to the growth of flow velocity, microrotation, and fluid temperature. An increase in Brinkman number contributes to the thicker thermal boundary layer. EG number grows with a rise in Reynolds number.     

Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation

An analysis is carried out to study the effect of suction and injection on the flow and heat transfer characteristics for a continuous moving plate in a micropolar fluid in the presence of radiation. The boundary layer equations are transformed to non-linear ordinary differential equations. Numerical results are presented for the distribution of velocity, microrotation and temperature profiles within the boundary layer. The effects of varying the Prandtl number, Pr, the radiation parameter, N and porosity parameter, F_w, are determined.     

Heat transfer in micropolar fluid along an inclined permeable plate with variable fluid properties

This paper studies the heat transfer process in a two-dimensional steady hydromagnetic natural convective flow of a micropolar fluid over an inclined permeable plate subjected to a constant heat flux condition. The analysis accounts for both temperature dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim–Swigert iteration procedure. Results for the dimensionless velocity and temperature profiles and the local rate of heat transfer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that in modeling the thermal boundary layer flow when both the viscosity and thermal conductivity are temperature dependent, the Prandtl number must be treated as a variable to obtain realistic results. As the thermal conductivity parameter increases, it promotes higher velocities and higher temperatures in the respective boundary layers. The wall shear stress increases with the increase of thermal conductivity parameter. This is true of electrically conducting as well as electrically non-conducting fluids. The presence of heat generation invigorates the flow and produces larger values of the local Nusselt number compared with the case of zero heat generation.     

Hall and ion slip effects on MHD free convective rotating flow bounded by the semi‐infinite vertical porous surface

Thermodiffusion, thermal radiation, Hall and ion slip effects on heat and mass transport of free convective MHD micropolar fluid flow bounded by a semi‐infinite absorbent plate with rotation and suction have been investigated. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The solutions are found analytically with the perturbation technique. With the help of graphic representations, the impacts of many critical parameters on velocity, temperature, and concentration within the boundary layer are discussed. In addition, local skin‐friction, Nusselt number, and Sherwood numbers are determined and computationally analyzed.     

Effect of chemical reaction and thermal radiation on heat and mass transfer flow of MHD micropolar fluid in a rotating frame of reference

This paper studies the effect of first order chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer flow of a micropolar fluid via a porous medium bounded by a semi-infinite porous plate with constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using small perturbation approximation. The effect of the various dimensionless parameters entering into the problem on the velocity, temperature and concentration profiles across the boundary layer are investigated through graphs. Also the results of the skin friction coefficient, couple stress coefficient, the rate of heat and mass transfer at the wall are prepared with various values of the parameters.     

ENHANCEMENT OF HEAT TRANSFER IN TURBULENT SEPARATED AND REATTACHING FLOW BY LOCAL FORCING

This article presents numerical solutions for solving the problem of a mixed convective micropolar fluid flow and heat transfer along a vertical wavy surface with a discontinuous temperature profile. The overall surface is equally divided into a heated section succeeded by an unheated section alternately. The problems in the present study have been formulated by using a simple transposition theorem and the cubic spline collocation method. Eringen has applied the spline alternating direction implicit (SADI) procedure to solve the governing momentum, angular momentum, and energy equations those formulated. Along the wavy surface, the velocity, temperature, and microrotation profiles are presented. The influences of micropolar parameters R, u , geometry, and Gr/Re 2 number on the skin friction coefficient and Nusselt number have been studied in this work. The results demonstrate that the skin friction coefficient consists of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases, but the skin friction increases. In addition, when the spin gradient viscosity parameter ( u ) increases, the skin friction decreases. Comparisons between a Newtonian fluid and a micropolar fluid are also discussed.     

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.     

Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface

Free convective boundary layer flow and heat transfer of a fluid with variable viscosity over a porous stretching vertical surface in presence of thermal radiation is considered. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. A third-order and a second-order coupled ordinary differential equations corresponding to the momentum and the energy equations are obtained. These equations are then solved numerically. It is found that the skin-friction decreases and heat transfer rate increases due to the suction parameter. Opposite nature is noticed in case of blowing. With the increase of temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity), the fluid velocity increases but the temperature decreases at a particular point of the sheet. Due to suction (injection) fluid velocity decreases (increases) at a particular point of the surface. Effects of increasing Prandtl number as well as radiation parameter on the velocity boundary layer is to suppress the velocity field and the temperature decreases with increasing value of Prandtl number. Due to increase in thermal radiation parameter, temperature at a point of the surface is found to decrease.     

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.     

Transient MHD convective flow of a micropolar fluid past a moving vertical plate in the presence of thermal diffusion

In this article, we investigate a transient magnetohydrodynamic convective micropolar fluid flow over a semi-infinite vertical plate embedded in a porous medium in the presence of chemical reaction and thermal diffusion. The dimensionless governing equations are solved by adopting the regular perturbation technique. The impact of various parameters on the velocity, microrotation, temperature, concentration profiles, skin friction, Sherwood number, and Nusselt number over the boundary layer is analyzed using graphs. The fluid velocity and microrotation reduce under the effect of thermal diffusion and chemical reaction. Furthermore, concentration rises due to thermal diffusion (Soret) effect, but concentration falls under the effect of chemical reaction. It is found that the velocity and skin friction fall with enhancing value of magnetic parameter. But Sherwood number increases as the magnetic parameter increase.     

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Abstract

In this paper, the effects of viscous dissipation, Joule heating, and magnetic field on the Hiemenz flow of a micropolar incompressible, viscous, electrically conducting fluid impinging normal to a plane are investigated. Numerical solutions for the governing momentum, angular momentum, and energy equations are given. A discussion has been provided for the effects of Hartman number, Prandtl number, Eckert number, and the micropolar parameters on two-dimensional flow of a fluid near a stagnation point (Hiemenz flow). Results for the details of the velocity, angular velocity, and temperature distributions as well as the skin friction, wall couples stress, rate of heat transfer, and thermal boundary layer thickness are shown graphically.     

Steady boundary layer flow and heat transfer over a porous moving plate in presence of thermal radiation

An analysis is presented for boundary layer forced convective flow and heat transfer past a moving porous plate parallel to a moving stream. Thermal radiation term is considered in the energy equation. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. It is found that dual solutions exist when the plate and the fluid move in the opposite directions. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter.     

On the oscillating plate-temperature flow of a polar fluid past a vertical porous plate in the presence of couple stresses and radiation

The paper studies the two-dimensional oscillatory flow of a polar electrically conducting viscous incompressible Bossinesq fluid past an infinite vertical plate whose temperature varied periodically about a mean constant non-zero value with time. The governing equations of this class of polar fluids are known to exhibit a boundary layer phenomenon. Employing a standard perturbative series method, expressions are obtained for the flow variables—velocity, temperature and plate surface skin friction, highlighting the effect of viscous dissipation heating. The numerical results obtained agree with and compliment results of earlier studies and are discussed quantitatively with the aid of graphs outlining the effects of radiation on the velocity field.     

Thermal radiation and diffusion effects in MHD Williamson and Casson fluid flows past a slendering stretching surface

The article is presented to analyze the magnetohydrodynamic Casson and Williamson fluids flow over a stretched surface of variable thickness by including the conditions of thermal radiation, velocity slip, temperature, and concentration slip. The equations governing the flow characteristics are transformed to ordinary differential equations by applying similarity transformations. The solution of the simplified equations is obtained by the numerical bvp5c Matlab package. The behavior for Williamson and Casson fluid cases is explored and discussed with the impact of sundry parameters on the flowing fluid, thermal, and diffusion fields. The profiles under the impact of parameters are depicted through graphs. Also, we evaluated the performance of local Nusselt and Sherwood numbers along with the friction of the wall and are displayed through tables. We found that the temperature and mass transfer distribution is low in Williamson fluid when compared to Casson fluid flow. The computed results indicate that the flow, thermal and concentration boundary layer characteristics of Williamson and Casson fluids are not unique.     

Radiation and mass transfer effects on two-dimensional flow past an impulsively started infinite vertical plate

The interaction of free convection with thermal radiation of a viscous incompressible unsteady flow past an impulsively started vertical plate with heat and mass transfer is analyzed. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative flux in the energy equation. The dimensionless governing equations are solved using an implicit finite-difference method of Crank–Nicolson type. Numerical results for the velocity, the temperature, the concentration, the local and average skin-friction, the Nusselt number and Sherwood number are shown graphically. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer. The local and average skin-friction increases with the increase in radiation parameter. For increasing values of radiation parameter the local as well as average Nusselt number increases.     

Unsteady MHD Stagnation‐Point Flow Toward a Shrinking Sheet with Thermal Radiation and Slip Effects

The problem of an unsteady magnetohydrodynamic stagnation point flow of an incompressible viscous fluid over a shrinking sheet is discussed in the presence of thermal radiation and boundary slip, which has not been documented to date in the literature. The governing boundary‐layer equations are transformed to high order nonlinear and ordinary differential equations by similarity transformations and then solved numerically. The effects of magnetic parameter, unsteadiness parameter, radiation parameter, velocity, and thermal slip parameters on velocity and temperature are analyzed and discussed. It is found that dual solutions of both velocity and temperature fields exist for negative values of the velocity ratio parameter. The results indicate that dual solution domains of velocity and temperature expand as the unsteadiness parameter increases.