Effect of nonlinear thermal radiation on silver and copper water nanofluid flow due to a rotating disk with variable thickness in the presence of nonuniform heat source/sink using the homotopy analysis method

An analysis of a steady axisymmetric heat transfer nanofluid flow due to a rotating disk having variable thickness in the presence of nonlinear radiation and nonuniform heat source/sink is presented. Water with Copper (Cu) and Silver (Ag) nanoparticles are utilized in the investigation. The governing equations along with boundary conditions are solved using the homotopy analysis method. A parametric study of the physical parameters is done and results are displayed in the form of graphs. The findings indicate that nonlinear radiation has a significant effect on temperature as well as on wall heat transfer when compared with linear case, which is more useful in few engineering processes.     

Steady flow and heat transfer of the power-law fluid over a rotating disk

This paper deals with the steady flow and heat transfer of a viscous incompressible power-law fluid over a rotating infinite disk. Assumed the thermal conductivity follows the same function as the viscosity, the governing equations in the boundary layer are transformed into a set of ordinary differential equations by generalized Karman similarity transformation. The corresponding nonlinear two-point boundary value problem was solved by multi-shooting method. Numerical results indicated that the parameters of power-law index and Prandtl number have significant effects on velocity and temperature fields. The thickness of the boundary layer decays with power-law index. The peak of the radial velocity changes slightly with power- law index. The values near the boundary are affected dramatically by the thickness of the boundary layer. With the increasing of the Prandtl number the heat conducts more strongly.     

Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition

Non-Newtonian boundary layer flow and heat transfer over an exponentially stretching sheet with partial slip boundary condition has been studied in this paper. The flow is subject to a uniform transverse magnetic field. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. An effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameters on the velocity, skin-friction coefficient and the temperature boundary layer. It is found that the third grade fluid parameter β increases the momentum boundary layer thickness and decreases the thermal boundary layer thickness.     

Heat and mass transfer in MHD Casson nanofluid flow past a stretching sheet with thermophoresis and Brownian motion

The foremost objective of the current article is to explore the impact of Brownian motion on magnetohydrodynamic Casson nanofluid flow toward a stretching sheet in the attendance of nonlinear thermal radiation. The combined heat and mass transfer characteristics are investigated. The influence of chemical reaction, nonuniform heat source/sink, Soret, and Dufour is deemed. The convective boundary condition is taken. The appropriate transformations are utilized to transform the flow regulating partial differential equations into dimensionless ordinary differential equations (coupled). The numerical outcomes of the converted nonlinear system are solved by the Runge-Kutta based Shooting procedure. Results indicate that the temperature is an increasing function of both thermophoresis and Brownian motion parameters. The concentration of the fluid and the corresponding boundary layer thickness reduces with an enhancement in Lewis number.     

Binary chemical reaction with activation energy in radiative rotating disk flow of Bingham plastic fluid

This article presents flow, heat and mass transfer phenomena in Bingham plastic fluid. The flow channel is considered to be a rotating disk with a slip which is different in span and streamwise directions, and heat transfer is investigated using dissipation term of the fluid. Arrhenius activation energy and binary chemical reaction are the imperative features of the study of mass transfer. Bingham plastic fluid and anisotropic slip are the key factors of the study due to their numerous applications in manufacturing industries. On the other hand, the radiative heat transfer phenomenon is considered which is widely used in nuclear and power generating systems. The partial differential equations that govern the flow, and heat and mass transfer are converted into ordinary differential equations by utilizing von Kármán's similarity transformation for rotating disk flows. The velocity, temperature, and concentration profiles and some important physical quantities are examined against important flow parameters. It is observed that the thermal radiation showed an increasing effect on temperature profile and the activation energy enhanced the mass transfer rate. The radial slip increased the volumetric flow rate and reduced the boundary layer thickness. The tangential slip reduced the volumetric flow rate and increased the boundary layer thickness.     

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

Magnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self-similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth-order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.     

Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet

The entrained flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. 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). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip, magnetic field and the third grade fluid parameter on the velocity, skin-friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.     

MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation,slip condition,and viscous dissipation

This study presents the problem of MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation, slip condition, and viscous dissipation. The partial differential equations with the corresponding boundary conditions that govern the fluid flow are reduced to a system of highly nonlinear ordinary differential equations using scaling group transformations. The fourth-order method along shooting technique is applied to solve this system of boundary value problems numerically. The effects of flow parameters on the velocity, temperature, and concentration profiles are presented via graphs. The impact of the physical parameters on the skin friction coefficient reduced Nusselt numbers and reduced Sherwood numbers are investigated through tables. Comparison of the present findings with the previously published results in the literature shows an excellent agreement. It is also noted that a rise in the Eckert number results in a drop in the temperature of the fluid in the thermal boundary layer region of the fluid flow.     

Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink

In the present article an analysis is carried out to study the boundary layer flow and heat transfer characteristics of a second grade, non-Newtonian fluid through a porous medium. The stretching sheet is assumed to be permeable so that suction effects come into play. The effects of viscous dissipation, non-uniform heat source/sink on heat transfer are addressed. The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. Analytical solutions are obtained for the resulting boundary value problems. The effects of viscous dissipation and non-uniform heat source/sink, Prandtl number, Eckert number and suction/injection on heat transfer are shown in several plots for two different heating processes (CST and PST cases). Dimensionless surface temperature gradient is tabulated for various values of the governing the parameters.     

A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

An investigation on the forced convection heat transfer in the gap of two rotating disks with laminar inflow

This study presents forced convection in the gap between two rotating disks with the laminar radial inward flow. The disk surfaces are held at a constant temperature different from the temperature of the fluid flowing. The disks' surfaces may also receive a heat flux. The temperature of the fluid flowing in the gap is predicted by solving the coupled equations of momentum, energy, and continuity in cylindrical coordinate numerically. The finite difference method is used to discretize the energy equation into nonlinear algebraic equations. The tridiagonal matrix algorithm is employed to solve the resulting algebraic equations. Predominantly, throughflow Reynolds number, rotational Reynolds number, gap ratio, speed ratio, and Peclet number are the parameters that affect the temperature distribution for the fixed disk temperature and for the heat flux boundary conditions. The Nusselt number compares reasonably well with the numerical results of other investigators. The heat flow into the fluid is higher for corotating disks than for contrarotating disks for both constant temperatures as well as heat flux boundary conditions. This is the first investigation that predicts temperature distribution due to forced convection in the gap of two rotating disks with laminar inflow.     

Analytical study of heat and mass transfer in unsteady MHD radiant flow of Williamson nanofluid over stretching sheet with heat generation and chemical reaction

This paper presents the analytical study of heat and mass transfer in a two-dimensional time-dependent flow of Williamson nanofluid near a permeable stretching sheet by considering the effects of external magnetic field, viscous dissipation, Joule heating, thermal radiation, heat source, and chemical reaction. Suitable transformations are introduced to reformulate the governing equations and the boundary conditions convenient for computation. The resulting sets of nonlinear differential equations are then solved by the homotopy analysis method. The study on the effects of relevant parameters on fluid velocity, temperature, and concentration profiles is analyzed and presented in graphical and tabular forms. Upon comparison of the present study with respect to some other previous studies, a very good agreement is obtained. The study points out that the transfer of heat can substantially be enhanced by decreasing viscoelasticity of the fluid and the transfer of mass can be facilitated by increasing permeability of the stretching sheet.     

Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature

In this paper we study the flow and heat transfer characteristics of a viscous fluid over a nonlinearly stretching sheet in the presence of non-uniform heat source and variable wall temperature. A similarity transformation is used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge–Kutta scheme is used to obtain the solution of the boundary value problem. The effects of various parameters (such as the power law index n, the Prandtl number Pr, the wall temperature parameter λ, the space dependent heat source parameter A¹ and the temperature dependent heat source parameter B¹) on the heat transfer characteristics are analyzed. The numerical results for the heat transfer coefficient (the Nusselt number) are presented for several sets of values of the parameters and are discussed. The results reveal many interesting behaviors that warrant further study on the effects of non-uniform heat source and the variable wall temperature on the heat transfer phenomena at the nonlinear stretching sheet.     

Approximate Analytical Solution of Stagnation Point Flow and Heat Transfer over an Exponential Stretching Sheet with Convective Boundary Condition

This study is concerned with the stagnation point flow and heat transfer over an exponential stretching sheet via an approximate analytical method known as optimal homotopy asymptotic method (OHAM). The governing partial differential equations are converted into ordinary nonlinear differential equations using similarity transformations available in the literature. The heat transfer problem is modeled using two‐point convective boundary condition. These equations are then solved using the OHAM approach. The effects of controlling parameters on the dimensionless velocity, temperature, friction factor, and heat transfer rate are analyzed and discussed through graphs and tables. It is found that the OHAM results match well with numerical results obtained by Runge–Kutta Fehlberg fourth‐fifth order method for different assigned values of parameters. The rate of heat transfer increases with the stretching parameter. It is also found that the stretching parameter reduces the hydrodynamic boundary layer thickness whereas the Prandtl number reduces the thermal boundary layer thickness.     

Effect of thermal radiation on magnetohydrodynamic three‐dimensional motion of a nanofluid past a shrinking surface under the influence of a heat source

An analytical technique known as the homotopy analysis method is used to acquire solutions for magnetohydrodynamic 3‐D motion of a viscous nanofluid over a saturated porous medium with a heat source and thermal radiation. The governing nonlinear partial differential equations are changed to ordinary differential equations employing appropriate transformations. Validation of the present result is done with the help of error analysis for flow and temperature. The influences of pertinent parameters on momentum, energy, and Nusselt number are studied and discussed. The major findings are: the velocity of the nanofluid is affected by the nanoparticle volume fraction and the thickness of the thermal boundary layer becomes thinner and thinner subject to sink, whereas the effect is revered in case of the source.     

Dissipative heat for the Casson fluid flow past an expanding cylindrical surface

A non-Newtonian model is developed by considering the flow of non-Newtonian Casson fluid past an expanding cylinder embedded in a porous medium. The novelty arises because of the conjunction of dissipative heat, and the additional heat source that enriches the heat transport phenomenon significantly. The application of the study is vital due to the flow of blood through the artery, a physiological study. Therefore, the study of Casson fluid plays an important role. The nonlinear partial differential equations that appeared in the formulation are now renovated to the coupled nonlinear ordinary differential equations. However, a numerical technique associated with shooting-based followed by Runge–Kutta fourth-order is employed for the solution of these transformed equations. The uniqueness of diverse pertinent parameters on the flow phenomena is scrutinized through graphs and numerically simulated results presented in tables. The important observations are as follows; the magnetic parameter and permeability augment the shear rate coefficients, whereas the Casson parameter rendered the opposite impact. Furthermore, the non-Newtonian Casson parameter retards the fluid temperature, and the curvature parameter significantly enhances it.     

Unsteady flow and heat transfer of a ferrofluid between two rotating,vertical moving and stretching disks

Unsteady flow and heat transfer of a magnetic fluid between two rotating disks is investigated. Both the disks are stretchable and the lower disk moves in the vertical direction. A new approach of similarity transformation is adopted to transform the equation of continuity, momentum, and the energy equation into ordinary nonlinear coupled differential equations. The numerical solution of the converted nonlinear differential equations is obtained using the finite element method. The effects of magnetization force, rotational viscosity, Prandtl number, and Eckert number on the velocity and temperature distributions are studied. The impact of stretching, movement, and rotation of the disk is also considered in this computational study. The skin friction coefficients and heat transfer rate on the lower disk for different physical parameters are calculated. Different types of motion of the disks and the magnetization force are crucial aspects in the stress distribution and heat transfer rate near the lower disk.     

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.     

Transient electromagnetohydrodynamic radiative squeezing flow between two parallel Riga plates using a spectral local linearization approach

This article addresses transient electromagnetohydrodynamic radiative squeezing flow due to convectively heated electromagnetic actuator. The transport analysis of heat and mass is explored considering the heat generation/absorption and destructive species homogeneous reaction. Suitable transformations are applied on the mathematical model developed to convert governing partial differential equations to ordinary differential equations (ODEs). Spectral local linearization method (SLLM) is employed on the resultant nonlinear coupled ODEs to compute the numerical results. Influence of sundry physical quantities on heat mass transfer of squeezing flow characteristics are determined using graphs and tabular results. SLLM results exhibit that momentum and temperature improved with rise in squeezing and heat source parameters correspondingly. Momentum enhances at lower plate and detracts with rise in modified Hartmann number. For improved heat source parameter, the rate of heat transfer diminishes and is more significant for higher Prandtl number values. This investigation has relevance in disk style magnetic clutches, rolling elements, food processing, bearings, squeezing film pressure sensors, and flow rheostats.     

Numerical modelling of second‐grade fluid flow past a stretching sheet

The present numerical study reports the chemically reacting boundary layer flow of a magnetohydrodynamic second‐grade fluid past a stretching sheet under the influence of internal heat generation or absorption with work done due to deformation in the presence of a porous medium. To distinguish the non‐Newtonian behaviour of the second‐grade fluid with those of Newtonian fluids, a very popularly known second‐grade fluid flow model is used. The fourth order momentum equation with four appropriate boundary conditions along with temperature and concentration equations governing the second‐grade fluid flow are coupled and highly nonlinear in nature. Well‐established similarity transformations are efficiently used to reduce the dimensional flow equations into a set of nondimensional ordinary differential equations with the necessary conditions. The standard bvp4c MATLAB solver is effectively used to solve the fluid flow equations to get the numerical solutions in terms of velocity, temperature, and concentration fields. Numerical results are obtained for a different set of physical parameters and their behaviour is described through graphs and tables. The viscoelastic parameter enhances the velocity field whereas the magnetic and porous parameters suppress the velocity field in the flow region. The temperature field is magnified for increasing values of the heat source/sink parameter. However, from the present numerical study, it is noticed that the flow of heat occurs from sheet to the surrounding ambient fluid. Before concluding the considered problem, our results are validated with previous results and are found to be in good agreement.