Surface Heat Transfer Rate Research Articles

MHD convective flow of magnetite-Fe3O4 nanoparticles by curved stretching sheet

Present work is devoted to convective flow of ferrofluid due to non linear stretching curved sheet. Electrically conducting fluid is considered in the presence of uniform magnetic field. Nanofluid comprises water and magnetite-Fe3O4 as nanoparticles. Thermal radiation and heat generation/absorption are explained. Homotopy concept is utilized for the development of solutions. Highly nonlinear partial differential systems are reduced into the nonlinear ordinary differential system. Impact of non-dimensional radius of curvature and power law index on the physical quantities like fluid pressure, velocity and temperature field are examined. Computations for surface shear stress and heat transfer rate also analyzed.

Flow due to a convectively heated cylinder with nonlinear thermal radiation

This communication presents non-Newtonian fluid flow over a stretching cylinder. Rheological relations of second-grade fluid are employed in the modeling. Heat transfer is characterized by a convectively heated cylinder. Different from the previous classical studies in the literature, the nonlinear thermal radiation contribution is taken into consideration. Resulting nonlinear mathematical problems are computed for the approximate convergent solutions. Impact of different parameters on the velocity and temperature profiles is examined. Computations for heat transfer rate are presented and examined for the influences of pertinent parameters. It is noted that fluid velocity enhances when curvature parameter is increased. Surface heat transfer rate enhances larger Eckert number, radiation parameter and Prandtl number.

Chemical Reaction Effects on an Unsteady MHD Mixed Convective and Radiative Boundary Layer Flow over a Circular Cylinder

A mathematical model is presented for an optically dense fluid past an isothermal circular cylinder with chemical reaction taking place in it. A constant, static, magnetic field is applied transverse to the cylinder surface. The cylinder surface is maintained at a constant temperature. New variables are introduced to transform the complex geometry into a simple shape and the boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, Crank-Nicolson finite difference scheme. Numerical computations are made and the effects of the various material parameters on the velocity, temperature and concentration as well as the surface skin friction and surface heat and mass transfer rates are illustrated graphs and tables. Increasing magnetohydrodynamic body force parameter (M) is found to decelerate the flow but enhance temperatures. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing radiation parameter.

Computational study of Jeffrey’s non-Newtonian fluid past a semi-infinite vertical plate with thermal radiation and heat generation/absorption

Abstract The nonlinear, steady state boundary layer flow, heat and mass transfer of an incompressible non-Newtonian Jeffrey’s fluid past a semi-infinite vertical plate is examined in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The influence of a number of emerging non-dimensional parameters, namely Deborah number (De), ratio of relaxation to retardation times (λ), Buoyancy ratio parameter (N), suction/injection parameter (fw), Radiation parameter (F), Prandtl number (Pr), Schmidt number (Sc), heat generation/absorption parameter (Δ) and dimensionless tangential coordinate (ξ) on velocity, temperature and concentration evolution in the boundary layer regime is examined in detail. Also, the effects of these parameters on surface heat transfer rate, mass transfer rate and local skin friction are investigated. This model finds applications in metallurgical materials processing, chemical engineering flow control, etc.

MHD Convective Flow of Jeffrey Fluid Due to a Curved Stretching Surface with Homogeneous-Heterogeneous Reactions.

This paper looks at the flow of Jeffrey fluid due to a curved stretching sheet. Effect of homogeneous-heterogeneous reactions is considered. An electrically conducting fluid in the presence of applied magnetic field is considered. Convective boundary conditions model the heat transfer analysis. Transformation method reduces the governing nonlinear partial differential equations into the ordinary differential equations. Convergence of the obtained series solutions is explicitly discussed. Characteristics of sundry parameters on the velocity, temperature and concentration profiles are analyzed by plotting graphs. Computations for pressure, skin friction coefficient and surface heat transfer rate are presented and examined. It is noted that fluid velocity and temperature through curvature parameter are enhanced. Increasing values of Biot number correspond to the enhancement in temperature and Nusselt number.

Magnetohydrodynamic free convection boundary layer flow of non-Newtonian tangent hyperbolic fluid from a vertical permeable cone with variable surface temperature

The nonlinear, non-isothermal steady-state boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian (viscoelastic) fluid from a vertical permeable cone with magnetic field are studied. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using the second-order accurate implicit finite difference Keller-box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely a Weissenberg number (We), rheological power law index (m), surface temperature exponent (n), Prandtl number (Pr), magnetic parameter (M) suction/injection parameter (fw) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime, is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is observed that velocity, surface heat transfer rate and local skin friction are reduced with increasing Weissenberg number, but temperature is increased. Increasing m enhances velocity and surface heat transfer rate but reduces temperature and local skin friction. An increase in non-isothermal power law index (n) is observed to decrease the velocity and temperature. Increasing magnetic parameter (M) is found to decrease the velocity and increase the temperature. Overall, the primary influence on free convection is sustained through the magnetic body force parameter, M, and also the surface mass flux (injection/suction) parameter, fw. The rheological effects, while still prominent, are not as dramatic. Boundary layers (both hydrodynamic and thermal) are, therefore, most strongly modified by the applied magnetic field and wall mass flux effect. The study is pertinent to smart coatings, e.g., durable paints, aerosol deposition processing and water-based solvent thermal treatment in chemical engineering.

Free Convection Flow and Heat Transfer of Tangent Hyperbolic past a Vertical Porous Plate with Partial Slip

This article presents the nonlinear free convection boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from a vertical porous plate with velocity slip and thermal jump effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Velocity slip (Sf), Thermal jump (ST), Prandtl number (Pr) and dimensionless tangential coordinate () on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that velocity, skin friction and heat transfer rate (Nusselt number) is increased with increasing Weissenberg number (We), whereas the temperature is decreased. Increasing power law index (n) enhances velocity and heat transfer rate but decreases temperature and skin friction. An increase in Thermal jump (ST) is observed to decrease velocity, temperature, local skin friction and Nusselt number. Increasing Velocity slip (Sf) is observed to increase velocity and heat transfer rate but decreases temperature and local skin friction. An increasing Prandtl number, (Pr), is found to decrease both velocity and temperature. The study is relevant to chemical materials processing applications.

Natural convection on heat transfer flow of non-newtonian second grade fluid over horizontal circular cylinder with thermal radiation

This article numerically studies for multi-physical transport of an optically-dense, free convective incompressible non-Newtonian second grade fluid past an isothermal, impermeable horizontal circular cylinder. The governing boundary layer equations for momentum and energy transport, which are parabolic in nature, have been reduced to non-similarity non-linear conservation equations using appropriate transformations and then solved numerically by employing with most validated, efficient implicit finite difference method with Keller box scheme. The numerical code is validated with previously existing results and found to be very good agreement. The results are reported graphically and in tabular form for various physical parameters; Deborah number, Prandtl number and thermal radiation on flow velocity and temperature profiles. Furthermore, the effects of these parameters on non dimensional wall shear stress (skin friction) and surface heat transfer rate (Nusselt number) are also investigated. Increasing the Deborah number reduces velocity profile, skin friction and Nusselt number where as it enhances the temperature profile. Increasing Prandtl number decelerates the flow velocity, temperature and skin friction but Nusselt number enhances considerably. Increase in radiation parameter retards the flow velocity, temperature profiles and skin friction. But Nusselt number enhances markedly with increase in radiation parameter. Applications of the model arise in polymer processing in chemical engineering, metallurgical material processing.

Homogeneous-heterogeneous reactions in MHD flow due to an unsteady curved stretching surface

This article addresses the homogeneous-heterogeneous reactions effects in magnetohydrodynamic (MHD) flow of viscous fluid flow by a curved stretching surface. Fluid is electrically conducting in the presence of an applied magnetic field. System of ordinary differential equations is obtained by appropriate transformations. Convergent series solutions are computed for the resulting nonlinear differential system. Impact of different parameters on the velocity, temperature and concentration profiles is examined. Computations for pressure, surface drag force and heat transfer rate are presented and examined for the influences of pertinent parameters. It is noted that fluid velocity enhances when curvature parameter is increased. Surface heat transfer rate enhances for larger Prandtl number. Further, the concentration distribution decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.

Convective heat transfer in a micropolar fluid over an unsteady stretching surface

An unsteady boundary layer free convective flow and heat transfer of a viscous incompressible, microploar fluid over a vertical stretching sheet is investigated. The stretching velocity is assumed to vary linearly with the distance along the sheet. Two equal and opposite forces are impulsively applied along the <i>x</i>-axis so that the sheet is stretched, keeping the origin fixed in the micropolar fluid. The transformed highly non-linear boundary layer equations are solved numerically by an implicit finite difference scheme for the transient, state from the initial to the final steady-state. To validate the numerical method, comparisons are made with the available results in the literature for some special cases and the results are found to be in good agreement. The obtained numerical results are analyzed graphically for the velocity, the microrotation, and the temperature distribution; whereas the skin friction, the couple stress coefficient and the Nusselt number are tabulated for different values of the pertinent parameters. Results exhibit a drag reduction and an increase in the surface heat transfer rate in the micropolar fluid flow compared to the Newtonian fluid flow.

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, radiation parameter Nr, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.

Turbulent energy flux generated by shock/homogeneous-turbulence interaction

High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modelling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the postshock turbulent energy flux is predicted to be strongly dependent on the angle of incidence of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available data from direct numerical simulations. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.

Partial slip effect in flow of magnetite-Fe3O4 nanoparticles between rotating stretchable disks

This paper addresses the flow of magnetic nanofluid (ferrofluid) between two parallel rotating stretchable disks with different rotating and stretching velocities. Water based fluid comprising magnetite-Fe3O4 nanoparticles is addressed. Velocity slip and temperature jump at solid–fluid interface are also taken into account. Appropriate transformations reduce the nonlinear partial differential system to ordinary differential system. Convergent series solutions are obtained. Effects of various pertinent parameters on the velocity and temperature profiles are shown and evaluated. Computations for skin friction coefficient and Nusselt number are presented and examined for the influence of involved parameters. It is noted that tangential velocity of fluid decreases for larger velocity slip parameter. Fluid temperature also reduces for increasing value of thermal slip parameter. Surface drag force and heat transfer rate at lower disk are enhanced when magnetic field strength is increased.

Unsteady hydromagnetic chemically reacting mixed convection flow over a permeable stretching surface with slip and thermal radiation

The present investigation deals with unsteady hydromagnetic chemically reacting mixed convection flow of incompressible viscous fluid past a vertically moving permeable stretching sheet in the presence of suction/injection, heat source/absorption, thermal radiation, viscous dissipation and slip effects. The governing partial differential equations are reduced into a set of non-linear ordinary differential equations by suitable transformations. Keller box method is applied to solve the system of non-linear ordinary differential equations for which the implementation is made with the help of matlab. The important parameters in this study are: Prandtl number Pr, Schmidt number Sc, buoyancy force parameter λ, radiation parameter Nr, magnetic parameter M, buoyancy forces ratio parameter N, the unsteady parameter A, suction/injection parameter s, Eckert number Ec, heat source/sink parameter Q, chemical reaction parameter R, velocity slip parameter sv, temperature slip parameter st and species concentration slip parameter sm. Effects of these parameters on velocity, temperature and species concentration profile of the fluid are presented and analyzed graphically. Furthermore, numerical investigations have been made for the skin friction coefficient and surface heat and mass transfer rates for some of the parameters.

Magnetohydrodynamic Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from Horizontal Circular Cylinder with Biot Number Effects

This article presents the nonlinear, steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from a Horizontal Circular Cylinder in the presence of magnetic field and Biot number effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), power law index (n), Prandtl number (Pr), Biot number $$(\upgamma )$$ , the magnetic parameter (M) and dimensionless tangential coordinate ( $$\xi $$ ) on velocity and temperature evolution on the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that the velocity, skin friction and heat transfer rate reduce with increasing We. Whereas, there is slight increase in temperature. Increasing n is observed to increase the velocity and heat transfer rate but decreases temperature and skin friction. An increasing $$\upgamma $$ is seen to increase velocity, temperature, local skin friction and heat transfer rate. And an increasing M is found to decrease velocity, skin friction and heat transfer rate but increases the temperature. The study is relevant to chemical materials processing applications.

Similarity Solutions for Laminar Boundary Layer Flow of Darcian Fluid over Horizontal Plate with a Convective Boundary Condition

This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x–2/3. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.

Transient Combined Convective Heat Transfer over a Stretching Surface in a Non-Newtonian Nanofluid Using Buongiorno’s Model

The present paper investigates the transient mixed convective boundary layer flow of an incompressible non-Newtonian quiescent nanofluid adjacent to a vertical stretching surface. The effects of the Brownian motion and thermophoresis are included for the nanofluid. Using appropriate non-similarity transformations the non-dimensional, coupled and highly non-linear system of equations is solved numerically using the efficient Keller-box implicit finite difference method for the whole transient from t=0 (initial state) to (final steady-state flow). The box method is unconditionally stable. Numerical results for dimensionless velocity (f’), micro-rotation (g), temperature (θ), nanoparticle volume fraction (Φ) at final steady state flow, skin friction function (), Nusselt number function () and Sherwood number function () have been presented on various parameters inform of tables and graphs. The results indicate that as Nb and Nt increase, the Nusselt number decreases whereas Sherwood number increases at initial and early state time but decreases at the final steady state time. As the K increases, the friction factor decreases whereas surface mass transfer rate and the surface heat transfer rates slightly increase. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work. The study has many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning and drawing plastic films.

Assessment on characteristics of heterogeneous-homogenous processes in three-dimensional flow of Burgers fluid

An analysis is performed to explore the characteristics of heterogeneous-homogeneous processes for the steady three-dimensional flow of Burgers fluid over a bidirectional stretching surface. In this paper, we utilized the advanced model of a homogeneous-heterogeneous reactions with equal diffusivities for reactant and autocatalysis. Additionally, heat transfer analysis is carried out in the presence of nonlinear thermal radiation and convective boundary conditions. The basic governing non-linear problem is presented and reduced into self-similar form with the aid of suitable similarity approach. The advanced non-linear problem is then tackled analytically by employing the homotpy analysis method (HAM). The effectiveness of relevant physical parameters on temperature and concentration profiles are taken into consideration. It is evident from the graphs that the concentration distribution diminishes by uplifting the homogeneous process parameter while it enhances for strength of Schmidt number. Moreover, it is observed that the surface heat transfer rate enhances for larger values of the Prandtl number.

Framing the features of Brownian motion and thermophoresis on radiative nanofluid flow past a rotating stretching sheet with magnetohydrodynamics

This article addresses the combined effects of chemical reaction and viscous dissipation on MHD radiative heat and mass transfer of nanofluid flow over a rotating stretching surface. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of heat source. Similarity transformation variables have been used to model the governing equations of momentum, energy, and nanoparticles concentration. Runge-Kutta-Fehlberg method with shooting technique is applied to solve the resulting coupled ordinary differential equations. Physical features for all pertinent parameters on the dimensionless velocity, temperature, skin friction coefficient, and heat and mass transfer rates are analyzed graphically. The numerical comparison has also presented for skin friction coefficient and local Nusselt number as a special case for our study. It is noted that fluid velocity enhances when rotational parameter is increased. Surface heat transfer rate enhances for larger values of Prandtl number and heat source parameter while mass transfer rate increases for larger values of chemical reaction parameter.

On three-dimensional flow of nanofluids past a convectively heated deformable surface: A numerical study

This paper is concerned with the three-dimensional rotating flow of nanofluid induced by a convectively heated deformable surface. The base fluid is treated as water while three different types of nanoparticles namely copper oxide-CuO, copper-Cu and silver-Ag are analyzed. Two different models for effective thermal conductivity of nanofluids are employed. A self-similar form of the governing differential system is formulated via adequate transformations. Shooting approach combined with fifth order Runge–Kutta method is used to determine the velocity and temperature distributions above the sheet. Our computations reveal that skin friction coefficient has direct relationship with the volume fraction of nanoparticles. Further the surface heat transfer rate is an increasing function of the solid volume fraction of nanoparticles. Sketch for three-dimensional streamlines is also obtained and discussed for a particular case.