The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet

The influence of temperature-dependent fluid properties on the hydro-magnetic flow and heat transfer over a stretching surface is studied. The stretching velocity and the transverse magnetic field are assumed to vary as a power of the distance from the origin. It is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. Using the similarity transformation, the governing coupled non-linear partial differential equations are transformed into coupled non-linear ordinary differential equations and are solved numerically by the Keller–Box method. The governing equations of the problem show that the flow and heat transfer characteristics depend on five parameters, namely the stretching parameter, viscosity parameter, magnetic parameter, variable thermal conductivity parameter, and the Prandtl number. The numerical values obtained for the velocity, temperature, skin friction, and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of the parameters on the flow and heat transfer characteristics are discussed.     

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.     

Comparative analysis of a Sisko nanofluid over a stretching cylinder through a porous medium

The present article examines the Sisko nanofluid flow and heat transfer through a porous medium due to a stretching cylinder using Buongiorno's model for nanofluids. Suitable similarity transformations are used to transform the governing boundary layer equations of fluid flow into nonlinear ordinary differential equations. The finite difference method is used to solve coupled nonlinear differential equations with MATLAB software. The impact of different parameters viz., the Sisko material parameter, porosity parameter, curvature parameter, thermophoresis parameter, and Brownian diffusion parameter on the velocity and temperature distribution are presented graphically. Moreover, the effect of the involved parameters on the heat transfer rate is also studied and presented through table values. It is noticed from the numerical values that the porosity parameter reduces the velocity while enhancing the temperature. The curvature parameter enhances the velocity throughout the fluid regime and reduces the temperature near the surface while enhancing the temperature far away from the surface. The study reveals that the thermophoresis and Brownian diffusion parameters that characterize the nanofluid flow reduce the wall heat transfer rate, while the curvature parameter enhances it. This investigation of wall heating/cooling has essential applications in solar porous water absorber systems, chemical engineering, metallurgy, material processing, and so forth.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet

The boundary layer flow and heat transfer analysis of electrically conducting viscous fluid over a nonlinearly shrinking sheet is investigated. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The system of equations is solved numerically employing an implicit finite difference scheme known as Keller-box method. It is found that dual solutions exist for this particular problem. The numerical results for the velocity, temperature, wall skin friction coefficient and local rate of heat transfer through the surface for various values of physical parameters both in case of stretching and shrinking sheet are analyzed and discussed for both the solutions. Present results in the hydrodynamic case (M = 0) are compared with existing numerical results in case of stretching flow and found in good agreement.     

Radiation effect on the flow and heat transfer over an unsteady stretching sheet

The effect of radiation on the heat and fluid flow over an unsteady stretching surface is analyzed. Using a similarity transformation the governing time dependent boundary layer equations for momentum and thermal energy are reduced to a set of ordinary differential equations. The resulting three-parameter problem is solved numerically for some representative values of the unsteadiness parameter A, the radiation parameter R and Prandtl number Pr. It is shown that the heat transfer rate is increased with increasing R, A and Pr. Also the effect of radiation parameter on the heat transfer rate is found to be more noticeable at larger values of A and Pr.     

Thermocapillarity in a liquid film on an unsteady stretching surface

The influence of thermocapillarity on the flow and heat transfer in a thin liquid film on a horizontal stretching sheet is analysed. The time-dependent governing boundary layer equations for momentum and thermal energy are reduced to a set of coupled ordinary differential equations by means of an exact similarity transformation. The resulting three-parameter problem is solved numerically for some representative values of an unsteadiness parameter S and a thermocapillarity number M for Prandtl numbers from 0.001 to 100. The thermocapillary surface forces drag the liquid film in the same direction as the stretching sheet and a local velocity minimum occurs inside the film. The surface velocity, the film thickness, and the Nusselt number at the sheet increase with M for Pr?10. For higher Prandtl numbers, the thermal boundary layer is confined to the lower part of the liquid film and the temperature at the free surface remains equal to the slit temperature and the thermocapillary forces vanish.     

Impact of Soret and Dufour on MHD mixed convective flow of non-Newtonian fluid over a coagulated surface

In the present study, we investigated the steady, two-dimensional mixed convective stagnation point flow of an electrically conducting micropolar fluid due to stretching of a variable thicked surface in the attendance of viscous dissipation. The flow is incompressible and laminar. The combined heat and mass transfer features are investigated. Convective and diffusion conditions are considered. The nonlinear thermal radiation, thermo-diffusion, and diffusion thermal effects are considered. The governing partial differential equations are converted to ordinary differential equations by using the appropriate similarity transformations. The obtained nonlinear and coupled ordinary differential equations are elucidated numerically using the fourth-order Runge–Kutta based shooting technique. The influence of various nondimensional parameters on the flow field like velocity, microrotation, temperature, and concentration is examined with the assistance of graphs. Results indicate that the Dufour number has a proclivity to increase the distributions of concentration and temperature correspondingly. Also, fluid temperature and concentration enhance for increasing values of the wall thickness parameter.     

Investigating the magnetohydrodynamic flow of a couple stress dusty fluid along a stretching sheet in the presence of viscous dissipation and suction

A computational study for investigating the flow and heat transfer phenomena in the unsteady magnetohydrodynamic couple stress dusty fluid flow over a linearly stretching porous surface in the presence of viscous dissipation effects is presented. The governing equations, in nondimensional form, are tackled by the exploitation of the standard spectral quasi-linearization methodology. The estimations of flow rate and temperature profiles are pictured diagrammatically. In contrast, the local skin friction and heat transfer rates are placed in tabular form for various values of thermofluidic parameters. The numerical results of a current investigation are compared with previously available results and located to be sensible agreement as shown in Tables 1 and 2. It is analyzed that by elevating the specific heat parameter and couple stress parameter, the temperature profile and the resulting thickness of the boundary layer are depressed. In comparison, an increase in thermal boundary layer thickness and a decrease in thickness of the momentum boundary layer were found with the rising magnetic parameter values.     

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

The convection heat and mass transfer in a hydromagnetic flow of a second grade fluid past a semi-infinite stretching sheet in the presence of thermal radiation and thermal diffusion are considered. The governing coupled non-linear partial differential equations describing the flow problem are transformed into non-linear ordinary differential equations by method of similarity transformation. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration fields for different values of parameters entering into the problem. The skin friction, rate of heat transfer and mass transfer are presented numerically in tabular form. In addition, the results obtained showed that these parameters have significant influence on the flow, heat and mass transfer.     

Magnetohydrodynamic flow of a nanofluid due to a non‐linearly curved stretching surface with high order slip flow

This article numerically scrutinizes magnetohydrodynamic flow of a nanofluid due to a nonlinearly curved stretching surface with third order slip flow conditions. The third order slip flow condition has not yet been discussed in fluid dynamics research. The mathematical modeling of the flow problem is given in partial differential equation form. The governing partial differential equations are transformed to high order ordinary differential equations using the similarity transformation and then solved numerically using a boundary value problem solver, bvp4c from Matlab software. The effect of the governing parameters on the flow of the velocity profile, concentration, and heat transfer characteristics are studied. Also graphs of the skin friction coefficient, local Nusselt number, and Sherwood number are drawn and their numerical values are tabulated. The numerical results of the study are compared with previously published articles in the limiting condition. The velocity of the flow field is reduced as the third order slip parameter and the first order slip parameter rises, but the velocity grows as the values of the second order slip flow parameter are elevated. The findings also indicate that the local Nusselt number is depreciated but local Sherwood numbers are elevated when the Soret and Dufour numbers are larger.     

Buoyancy forces and activation energy on the MHD radiative flow over an exponentially stretching sheet with second‐order slip

The current study explores the effects of second‐order slip and activation energy (AE) on the magnetohydrodynamic and radiative fluid flow caused by a surface with exponential stretching. The binary chemical reaction with mixed convection is considered in this physical model to discover the heat transfer phenomenon. The governing system of equations leads to a set of nonlinear ordinary differential equations by using scaling analysis. The transformed system is calculated computationally by using the most powerful Shooting procedure with the support of MATLAB software. The characteristics of various flow parameters on the governing flow field are exhibited pictorially and deliberated. The results revealed that the coefficient of heat and mass transfer upsurge with growing values of the second‐order slip parameter and skin friction coefficient has a reverse effect on the first‐order slip parameter. The thermal measure of the fluid in the presence of suction and slip conditions is seen to be lesser than that with the nonslip and nonsuction conditions. The heat measure of the fluid augments with the rising buoyancy parameter. The influence of slips coupled with AE is significant in the fluid flow and heat transfer characteristics. The outputs of the current investigation are validated by comparing the Nusselt number with the available results and are found to closely agree as a limiting case.     

Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet

The steady laminar flow and heat transfer of a second grade fluid over a radially stretching sheet is considered. The axisymmetric flow of a second grade fluid is induced due to linear stretching of a 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). Introducing the dimensionless quantities the governing partial differential equations are transformed to ordinary differential equations. The developed non-linear differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence of these solutions is explicitly discussed. The analytical expressions for velocity and temperature are constructed and are shown graphically. The numerical values for the skin friction coefficient and the Nusselt number are entered in tabular form. Attention has been focused to the variations of the emerging parameters such as second grade parameter, Prandtl number and the Eckert number. Finally, comparison between the HAM and numerical solutions are also included and found in excellent agreement.     

Uncertainties in physical property effects on viscous flow and heat transfer over a nonlinearly stretching sheet with nanofluids

The purpose of this paper is to investigate a numerical analysis for the flow and heat transfer in a viscous fluid over a nonlinear stretching sheet utilizing nanofluid. The governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation. Different water-based nanofluids containing Cu, Ag, CuO, Al₂O₃, and TiO₂ are considered in our problem. Furthermore, four different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics are discussed. The variations of dimensionless surface temperature, dimensionless surface temperature gradient as well as the flow and heat transfer characteristics with the governing parameters are graphed and tabulated. Comparison with published results for pure fluid flow is presented and it is found to be in excellent agreement.     

MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with non-uniform source/sink

The analysis includes a steady two-dimensional MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with the effect of non-uniform source/sink. Two types of different heating processes are considered namely (i) prescribed surface temperature (PST) and (ii) prescribed wall heat flux (PHF). The governing system of non-linear partial differential equations are transformed into ordinary differential equations using similarity transformations and which are then solved numerically using Runge Kutta Fehlberg fourth–fifth order method. Comparison of the numerical results is made with the existing literature and the results are found to be in good agreement. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that velocity distribution for clean fluid decreases where as dust fluid increases with the increase of fluid particle interaction parameter when λ > 1 and λ < 1.     

Interaction of Cu and Ag nanoparticles on MHD water‐based nanofluids past a stretching sheet

The study explores the MHD flow of water‐based nanofluids past a stretching sheet that melts at a constant rate. Cu and Ag nanoparticles are considered to merge into the base fluid to discuss the flow, heat and mass transfer characteristics. Suitable transformation is employed to transform the governing partial differential equations to a system of nonlinear coupled ordinary differential equations (ODEs). A semi‐analytical technique, that is, in particular, the Adomian decomposition method is implemented to tackle this system of ODEs. The influences of characterizing parameters for the flow phenomena are determined via graphs and displayed. Furthermore, the computed values of the quantities of engineering interest are exhibited through tables and discussed. The main findings of the results are laid down as follows: the Cu‐water nanofluid momentum is more pronounced than that of Ag‐water due to the heavier density of the Ag nanoparticles and an increasing melting parameter is favorable to decrease the fluid temperature, which is useful for the cooling of the substances at the final stage of production in industries.     

Conjugate heat transfer of magnetic mixed convection with radiative and viscous dissipation effects for second-grade viscoelastic fluid past a stretching sheet

A radiative and viscous dissipation effects conjugate heat transfer problem of a second-grade viscoelastic fluid past a stretching sheet has been studied. Governing equations for heat conduction equation of a stretching sheet, and continuity equation, momentum equation and energy equation of a second-grade fluid have been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite-difference method. These solutions are used to obtain distributions of the local convective heat transfer coefficient and the stretching sheet temperature. The ranges of these dimensionless parameters, the Prandtl number Pr, the elastic number E and the conduction–convection coefficient N_cc are from 0.001 to 10, 0.0001 to 0.01, and 0.5 to 2.0, respectively. A parameter, G, which is used to represent the strength of the buoyancy, is present in the governing equations. A parameter, M_n, which represents the strength of the magnetic filed effect, N_r shows the radiation effect are also present in governing equations. Results indicate that elastic effect in the flow may increase the local heat transfer coefficient and enhance the heat transfer of a stretching sheet. In addition, same as results from Newtonian fluid flow and conduction analysis of a stretching sheet, a better heat transfer has obtained with larger N_cc, G, E, and Pr. It shows that a non-Newtonian flow (E = 0.1, E = 0.01) have a good efficiency to reduce heat for a stretching sheet better than a nearly Newtonian flow (E = 0.001).     

Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source

In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters.     

Boundary Layer Flow of Rotating Two Phase Nanofluid Over a Stretching Surface

An analysis is carried out to discover the influence of a rotating nanofluid over a stretching surface. The two phase nanofluid model is used for this study. Two types of nanoparticles, namely copper and titanium oxide are used in our analysis with water as the base fluid. The governing system of partial differential equations along with the corresponding boundary conditions are presented and then transformed into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically by means of an iterative procedure called the midpoint integration scheme along with Richardson extrapolation. The results for flow and heat transfer characteristics are presented through graphs against nanoparticle volume fraction and rotation parameter for both types of nanoparticles. Quantities of physical interest such as local skin friction coefficients and local heat flux rate at the stretching surface are computed and analyzed. Numerical values for skin frictions and local heat flux rate are computed in the absence of nanoparticle volume fraction and rotation and they are found to be in very good agreement with the existing published literature.     

Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet

The article examines the hydromagnetic laminar boundary layer flow and heat transfer in a power law fluid over a stretching surface. The flow is influenced by linear stretching of the sheet. Also the energy equation with temperature-dependent thermal conductivity, thermal radiation, work done by stress, viscous dissipation and internal heat generation is considered. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by Keller–Box method. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.