Radiation absorption on MHD free conduction flow through porous medium over an unbounded vertical plate with heat source

A numerical solution is presented for unsteady coupled heat and mass transfer by natural convection from a vertical plate embedded in a uniform porous medium in the presence of thermal radiation and chemical reaction effects. The governing equations for this problem were developed and non-dimensionalized and the resulting equations were then solved numerically by an explicit finite-difference scheme. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The solutions at each time step have been found to reach the steady state solution properly. The numerical results are presented in the graphical form to show the effects of material parameters including the thermal buoyancy, the solutal buoyancy, Reynolds number, the inverse thermal radiation parameter, the permeability parameter, Prandtl number, Schmidt number and the chemical reaction parameter on the skin-friction coefficient, the Nusselt number, the Sherwood number, the velocity profiles, the temperature profiles and the concentration profiles in the boundary layer.

Network numerical analysis of radiation absorption and chemical effects on unsteady MHD free convection through a porous medium

Hall, Soret, and rotational effects on unsteady MHD rotating flow of a second-grade fluid through a porous medium in the presence of chemical reaction and aligned magnetic field

Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion

The mixed Marangoni assisting/resisting flow of a nanofluid with thermal radiative heat flux is analyzed when thermal and solutal buoyant forces are significant. The heat and mass transfer rates are simultaneously optimized by utilizing the Response Surface Methodology (RSM). The face‐centered Central Composite Design (fc‐CCD) is used for the numerical experimental design involved in RSM. The sensitivities of the heat and mass transfer rates are evaluated to compare the impact of the thermal and solutal buoyant forces. Appropriate scaling and similarity transformations are utilized to simplify the problem and then numerical solutions are obtained. The nanoliquid flow, temperature, and concentration profiles are plotted for the buoyancy assisting and opposing Marangoni cases. The Marangoni flow with opposite buoyancy is found to have a greater magnitude of velocity while the flows assisted by the buoyancy have a greater magnitude of temperature and concentration profiles. Thermal buoyancy force has a predominant (0.6%) impact on both heat and mass transfer rates compared to solutal buoyancy force. Buoyancy forces are positively sensitive to heat and mass transfer rates. The thermal radiation aspect augments the temperature profile throughout the domain. The optimized mass and heat transfer rates ( and ) is achieved at the highest level of the buoyancy forces and ratio of Marangoni numbers.

Natural convection and thermal radiation influence on nanofluid flow over a stretching cylinder in a porous medium with viscous dissipation

PurposeThe purpose of this paper is to solve the problem of steady, laminar, coupled heat and mass transfer by MHD natural convective boundary‐layer flow over a permeable truncated cone with variable surface temperature and concentration in the presence of thermal radiation and chemical reaction effects.Design/methodology/approachThe governing equations are derived and transformed into a set of non‐similar equations which are then solved by an adequate implicit finite difference method.FindingsIt is found that the presence of thermal radiation, magnetic field and chemical reaction have significant effects on the rates of heat and mass transfer. The variation of the wall temperature and concentration exponent contribute to significant changes in the Nusselt and Sherwood numbers as well.Originality/valueThe titled problem with the various considered effects has not been solved before and it is of special importance in various industries. The problem is original.

The unsteady flow of a viscous incompressible flow past an infinite isothermal vertical oscillating plate, in the presence of thermal radiation and homogeneous chemical reaction of first order has been studied. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised to Tw and the concentration level near the plate is raised linearly with respect to time. An exact solution to the dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity, temperature, and concentration are studied for different physical parameters like phase angle, radiation parameter, chemical reaction parameter, Schmidt number, thermal Grashof number, mass Grashof number, and time are studied graphically. It is observed that the velocity increases with decreasing phase angle wt.

The flow characteristics of Williamson nanofluids flow caused by a permeable vertical plate are investigated in this research. Influence of magnetic field on mixed convection flow in the presence of thermal radiation and heat source/sink is further studied. To develop the mathematical model of Williamson nanofluids, we employ the Brownian motion and thermophoresis impacts. By using Sparrow–Quack–Boerner local nonsimilarity method, the governing equations are transformed into a set of ordinary differential equations. Additionally, the obtained equations are numerically tackled by employing an efficient Runge–Kutta–Fehlberg method with MATLAB. The effect of emerging parameters on dimensionless velocity, temperature and concentration as well as the skin friction coefficient, the local Nusselt number and a local Sherwood number are explored with the help of graphs. The results indicate that as the value of buoyancy parameter increases, the nanofluid temperature and concentration decrease, whereas the velocity distribution increases. Further, the skin friction coefficient is increased with the higher buoyancy parameter. On the other hand, the rate of heat transfer is decreased by Brownian motion parameter. A comparison with the previous data in the literature shows good agreement with the obtained results.

The natural convection flow from a magnetized sphere in the presence of thermal radiation is considered. The characteristics of boundary-layer flow in the form of skin friction, rate of heat transfer, and current density at different positions of the sphere are evaluated. The numerical solutions of velocity profile, temperature distribution, and transverse component of the magnetic field are also presented. In the present study, the finite-difference method is used to find the numerical solutions of the flow model.

Simultaneous mass and heat transfer with reactions in a multicomponent, laminar, falling liquid film

In the context of advancements in both heat and mass transfer, the current study intends to analyze the impacts of thermal radiation, Soret, and Dufour on the magnetohydrodynamic boundary layer flow through a vertical spinning cone in porous media. The Dufour effect is the energy flux due to the mass concentration gradient with a reciprocal phenomenon, the Soret effect. Energy expression considers the physical aspects of heat generation and absorption. It is expected that the tangential, circumferential, and normal directions will all have velocity components in flow through a porous media. The governing equations are nonlinear partial differential equations that are rearranged into ordinary differential equations via similarity transformation, and then they are numerically solved using the Runge–Kutta method along with a proper shooting strategy. Graphs are used to examine the impacts of many parameters on flow characteristic velocity, temperature, and concentration, including magnetic parameters, porous parameters, Dufour and Soret parameters, chemical reaction parameters, and more. The numerical findings of the gradient of velocity, the Nusselt and Sherwood numbers, and the surface drag force are tabulated and compared with the current result and the one from the literature. The findings are found to be in good agreement. Circumferential and normal velocities are improved visually for greater values of the porosity parameter, but the tangential velocity behavior of the magnetic parameter exhibits the reverse behavior. In addition, the Dufour parameter and chemical reaction both exhibit diminishing behavior when the Soret parameter increases.

Effects of heat and mass transfer in the flow of Burgers fluid over an inclined sheet are discussed. Problems formulation and relevant analysis are given in the presence of thermal radiation and non-uniform heat source/sink. Thermal conductivity is taken temperature dependent. The nonlinear partial differential equations are simplified using boundary layer approximations. The resultant nonlinear ordinary differential equations are solved for the series solutions. The convergence of series solutions is obtained by plotting the ħ -curves for the velocity, temperature and concentration fields. Results of this work describe the role of different physical parameters involved in the problem. The Deborah numbers corresponding to relaxation time (β1 and β2) and angle of inclination (α) decrease the fluid velocity and concentration field. Concentration field decays as Deborah numbers corresponding to retardation time (β3) and mixed convection parameter (G) increase. Large values of heat generation/absorption parameters A/B, and the temperature distribution across the boundary layer increase. Numerical values of local Nusselt number, −θ′(0), and local Sherwood number, −ϕ′(0), are computed and analyzed. It is found that θ′(0) increases with an increase in β3.

Heat and Mass transfer of a Casson nanofluid flow over an accelerating porous surface with dissipation, radiation and chemical reaction in the presence of a temperature gradient dependent heat sink subject to suction is analyzed. The governing non-linear partial differential equations are converted into the non-linear ordinary equations by using suitable similarity transformations. The exact solution to the momentum equation is obtained. Analytical solutions to energy and species concentration are obtained and the results are expressed in terms of confluent hyper geometric function. The influences of physical parameters such as the Nanoparticle volume fraction, Casson fluid parameter, Suction parameter, permeability parameter, Heat sink parameter, Prandtl number, Eckert number, Radiation parameter, Schmidt number and Chemical reaction parameter over the velocity, temperature and species concentration distribution are analyzed with the help of graphs. Skin Friction Coefficient, Nusselt and Sherwood number of various nano fluids with nanoparticles (Cu, Ag, Au, Al, Al2O3 and TiO2) are also found and analyzed.

The present work deals with the numerical study of two-dimensional incompressible, magnetohydrodynamic Falkner-Skan flow of Carreau nanofluid over wedge, plate and stagnation of the flat plate with convective boundary condition and chemical reaction. The influence of thermophoresis and Brownian motion are taken into account. Similarity transformations are utilized to transform the governing equations into a system of non-linear ordinary differential equations and solved numerically using Runge–Kutta Fehlberg scheme. A comparison has been made with the published results which reveals a good agreement. The influence of different physical parameters on flow, temperature and nanoparticle concentration distributions have been discussed in detail. A constitutional analysis has been made for skin friction coefficient, heat and mass transfer rates. Results elucidate that the influence of magnetic parameter on velocity is high over flat plate compared with wedge and stagnation point of the flat plate. Heat transfer performance is higher on shear thinning fluid compared with shear thickening fluid. Further, an increase in Brownian motion decreases the heat transfer rate but enhances the mass transfer rate.