Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

Chemical reaction effects on unsteady MHD flow past semi-infinite vertical porous plate with viscous dissipation

The chemical reaction effect on an unsteady magnetohydrodynamic （MHD） flow past a semi-infinite vertical porous plate with viscous dissipation is analyzed. The governing equations of motion, energy, and species are transformed into ordinary differential equations （ODEs） using the time dependent similarity parameter. The resultant ODEs are then solved numerically by a finite element method. The effects of various parameters on the velocity, temperature, and concentration profiles are presented graphically, and the values of the skin-friction, Nusselt number, and Sherwood number for various values of physical parameters are presented through tables.

EFFECTS OF VISCOUS DISSIPATION ON THERMALLY DEVELOPING FORCED CONVECTION IN A POROUS SATURATED CIRCULAR TUBE WITH AN ISOFLUX WALL

The viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model. For the thermally developing region, a numerical study is reported while a perturbation analysis is presented to find expressions for the temperature profile and the Nusselt number for the fully developed region. The fully developed Nusselt number found by numerical solution for the developing region is compared with that of asymptotic analysis and a good degree of agreement is observed.

Effect of slip velocity on Casson thin film flow and heat transfer due to unsteady stretching sheet in presence of variable heat flux and viscous dissipation

The aim of the present paper is to study flow and heat transfer charac- teristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation. The governing equations are partial differential equations. They are reduced to a set of highly nonlinear ordinary differential equations by suitable similarity transformations. The re- sulting similarity equations are solved numerically with a shooting method. Comparisons with previous works are macle, and the results are found to be in excellent agreement. In the present work, the effects of the unsteadiness parameter, the Casson parameter, the Eckert number, the slip velocity parameter, and the Prandtl number on flow and heat transfer characteristics are discussed. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed.

Hydromagnetic flow of a Cu water nanofluid past a moving wedge with viscous dissipation

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper （Cu）-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das （Tiwari I K and Das M K 2007 Int. J. HeatMass Transfer 50 2002）. A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter ~, solid volume fraction tp, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

Entropy analysis in electrical magnetohydrodynamic(MHD) flow of nanofluid with effects of thermal radiation,viscous dissipation,and chemical reaction

The unsteady mixed convection flow of electrical conducting nanofluid and heat transfer due to a permeable linear stretching sheet with the combined effects of an electric field, magnetic field, thermal radiation, viscous dissipation, and chemical reaction have been investigated. A similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations.The resultant system of equations is then solved numerically using implicit finite difference method.The velocity, temperature, concentration, entropy generation, and Bejan number are obtained with the dependence of different emerging parameters examined. It is noticed that the velocity is more sensible with high values of electric field and diminished with a magnetic field. The radiative heat transfer and viscous dissipation enhance the heat conduction in the system. Moreover, the impact of mixed convection parameter and Buoyancy ratio parameter on Bejan number profile has reverse effects. A chemical reaction reduced the nanoparticle concentration for higher values.

Hydromagnetic Nanofluid Film Flow over a Stretching Sheet with Prescribed Heat Flux and Viscous Dissipation

Thermal radiative heat transfer through a thin horizontal liquid film of a Newtonian nanofluid subjected to a magnetic field is considered.The physical boundary conditions are a variable surface heat flux and a uniform concentration along the sheet.Moreover,viscous dissipation is present and concentration is assumed to be influenced by both thermophoresis and Brownian motion effects.Using a similarity method to turn the underlying Partial differential equations into a set of ordinary differential equations(ODEs)and a shooting technique to solve these equations,the skin-friction coefficient,the Nusselt number,and the Sherwood number are determined.Among other things,it is shown that large values of the thermal radiation heat transfer rate,thermal conductivity parameter,and the Brownian motion parameter can enhance the cooling of the sheet.

Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating

The combined effects of viscous dissipation and Newtonian heating on bound- ary layer flow over a moving flat plate are investigated for two types of water-based New- tonian nanofluids containing metallic or nonmetallic nanoparticles such as copper （Cu） and titania （Ti02）. The governing partial differential equations are transformed into ordinary differential equations through a similarity transformation and are solved numer- ically by a Runge-Kutta-Fehlberg method with a shooting technique. The conclusions are that the heat transfer rate at the moving plate surface increases with the increases in the nanoparticle volume fraction and the Newtonian heating, while it decreases with the increase in the Brinkmann number. Moreover, the heat transfer rate at the moving plate surface with Cu-water as the working nanofiuid is higher than that with TiO2-water.

Finite element solution of heat and mass transfer flow with Hall current,heat source,and viscous dissipation

The aim of the paper is to investigate the effect of heat and mass transfer on the unsteady magnetohydrodynamic free convective flow with Hall current, heat source, and viscous dissipation. The problem is governed by the system of coupled non-linear partial differential equations whose exact solution is difficult to obtain. Therefore, the problem is solved by using the Galerkin finite element method. The effects of the various parameters like Hall current, Eckert number, heat source parameter, Prandtl number, and Schmidt number on the velocity components, the temperature, and the concentration are also examined through graphs.

Numerical Treatment of MHD Flow of Casson Nanofluid via Convectively Heated Non-Linear Extending Surface with Viscous Dissipation and Suction/Injection Effects

This paper introduces the effect of heat absorption(generation)and suction(injection)on magnetohydrodynamic(MHD)boundary-layer flow of Casson nanofluid(CNF)via a non-linear stretching surface with the viscous dissipation in two dimensions.By utilizing the similarity transformations,the leading PDEs are transformed into a set of ODEs with adequate boundary conditions and then resolved numerically by(4–5)^(th)-order Runge-Kutta Fehlberg procedure based on the shooting technique.Numerical computations are carried out by Maple 15 software.With the support of graphs,the impact of dimensionless control parameters on the nanoparticle concentration profiles,the temperature,and the flow velocity are studied.Other parameters of interest,such as the skin friction coefficient,heat,and mass transport at the diverse situation and dependency of various parameters are inspected through tables and graphs.Additionally,it is verified that the numerical computations with the reported earlier studies are in an excellent approval.It is found that the heat and mass transmit rates are enhanced with the increasing values of the power-index and the suction(blowing)parameter,whilst are reduced with the boosting Casson and the heat absorption(generation)parameters.Also,the drag force coefficient is an increasing function of the powerindex and a reduction function of Casson parameter.

MHD and Viscous Dissipation Effects in Marangoni Mixed Flow of a Nanofluid over an Inclined Plate in the Presence of Ohmic Heating

The problem of Marangoni mixed convection in the presence of an inclined magnetic field with uniform strength in a nanofluid(formed by the dispersion of two metallic nanoparticles,i.e.,Copper(Cu),and alumina(Al_(2)O_(3))in water)is addressed numerically.The effects of viscous dissipation and Ohmic heating are also considered.The original set of governing partial differential equations is reduced to a set of non-linear coupled ordinary differential equations employing the similarity transformation technique.The simplified equations are numerically solved through MATLAB‘bvp4c’algorithm.The results are presented in terms of graphs for several parameters.It is found that enhancing the stratification parameter leads to a decrease in the fluid temperature,and an increase in the aligned magnetic field angle reduces the flow velocity.Moreover,mixed convection tends to enhance both the Nusselt and Sherwood numbers.If the angle of inclination is made higher,the fluid velocity is reduced and the thickness of the thermal and concentration boundary layer grows.

Mixed Convection MHD Stagnation Point Flow over a Stretching Surface with the Effects of Heat Source or Sink and Viscous Dissipation

The present study deals with MHD mixed convection stagnation point flow over a stretching sheet with the effects of heat source/sink and viscous dissipation including convective boundary conditions. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. These equations are then solved numerically by using finite difference scheme known as the Keller Box method. The effects of various parameters on velocity and temperature profiles are presented graphically interpreted and the results are discussed.

Effects of Viscous Dissipation on Unsteady MHD Thermo Bioconvection Boundary Layer Flow of a Nanofluid Containing Gyrotactic Microorganisms along a Stretching Sheet

This paper presents a numerical study of the problem of unsteady thermo bioconvection boundary layer flow of a nanofluid containing gyrotactic microorganisms along a stretching sheet under the influence of magnetic field and viscous dissipation. With the help of usual transformation, the governing equations are transformed into unsteady nonlinear coupled partial differential equations. The numerical solution is obtained by using an explicit finite difference scheme. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. From the results it is found that both magnetic parameter and bioconvection Rayleigh number have positive effect on the dimensionless Nusselt number and density number of the motile microorgan-isms while the opposite behavior became clear in the case of Grashof number and Eckert number. The rescaled velocity, temperature, concentration and the density of motile microorganisms depend strongly on the governing parameters.

MHD Stagnation Point Flow of a Casson Fluid over a Nonlinearly Stretching Sheet with Viscous Dissipation

Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transformed into coupled nonlinear ordinary differential equations with suitable similarity transformations. These equations were then solved by finite difference technique known as Keller Box method. The various parameters such as Prandtl number (Pr), Eckert number (Ec), Magnetic parameter (M), Casson parameter (β) and non linear stretching parameter (n) determining the velocity and temperature distributions, the local Skin friction coefficient and the local Nusselt number governing such a flow were also analyzed. On analysis it was found that the Casson fluid parameter (β) decreased both the fluid velocity and temperature whereas an increase in (β) increased both the heat transfer rate and wall skin-friction coefficient.

Joule Heating and Viscous Dissipation on Effects on MHD Flow over a Stretching Porous Sheet Subjected to Power Law Heat Flux in Presence of Heat Source

In the present work we investigate the effects of Joule heating and viscous dissipation on MHD fluid flow. The viscous incompressible fluid flows over a stretching porous horizontal sheet subjected to power law heat flux in presence of heat source. The equations of momentum and heat transfer governing the problem are transformed into a system of dimensionless differential equations, which in turn solved numerically using shooting technique. The effects of the Joule heating parameter, permeability parameter, heat source parameter, Eckert number and Prandtl number are discussed and tabulated.

Analysis of Combined Convective and Viscous Dissipation Effects for Peristaltic Flow of Rabinowitsch Fluid Model

In this article, mathematical modeling for peristaltic flow of Rabinowitsch fluid model is considered in a non-uniform tube with combined effects of viscous dissipation and convective boundary conditions. Wall properties analysis is also taken into account. Non-dimensional differential equations are simplified by using the well-known assumptions of low Reynolds number and long wavelength. The influence of various parameters connected with this flow problem such as rigidity parameter E1, stiffness parameter E2, viscous damping force parameter E3, Brickman number and Biot number are plotted for velocity distribution, temperature profile and for stream function. Results are plotted and discussed in detail for shear thinning, shear thickening and for viscous fluid. It is found that velocity profile is an increasing function of rigidity parameter, stiffness parameter, and viscous damping force parameter for shear thinning and for viscous fluid, due to the less resistance offered by the walls but, quite opposite behavior is depicted for shear thickening fluids. It is seen that Brickman number relates to the viscous dissipation effects, so it contributes in enhancing fluid temperature for all cases.

Effects of viscous dissipation and Joule heating on the Couette and Poiseuille flows of a Jeffrey fluid with slip boundary conditions

In this article,we have presented the exact solutions of the Couette,Poiseuille and generalized Couette flows of an incompressible magnetohydrodynamic Jeffrey fluid between parallel plates through homogeneous porous medium.The effects of slip boundary conditions and heat transfer are considered.Viscous dissipation,radiation and Joule heating are also considered in the energy equation.The governing equations of the Jeffrey fluid flow are modeled in Cartesian coordinate system.Analytical solutions for the velocity and temperature the velocity and temperature profiles are studied and the results are presented through graphs.It Temperature behaves as a decreasing function due to the impact of Hartmann number,non-Newtonian parameter and slip parameter in all noted problems.

Joule heating and viscous dissipation effect on electroosmotic mixed convection flow in a vertical microchannel subjected to asymmetric heat fluxes

The impact of Joule heating due to electric double layer(EDL)and viscous dissipation on electroosmotic mixed convection flow in a vertical microchannel with asymmetric heat fluxes is established in this article.The Poisson-Boltzmann,momentum and energy equations representing the electric potential,velocity profile and temperature distribution in the microchannel are obtained in dimensionless forms.Using the Debye-Hückel linearization,exact solutions are obtained for electric potential,velocity profile and temperature distributions by method of undetermined coefficients in the absence of viscous dissipation and Joule heating while an inbuilt Matlab function called pdepe is employed to solve the coupled nonlinear momentum and energy equations in the presence of Joule heating and viscous dissipation.Results show that the presence of Joule heating and viscous dissipation lead to decrease in velocity profile and temperature distributions throughout the microchannel.

Entropy generation under the influence of radial magnetic field and viscous dissipation of generalized Couette flow in an annulus

This paper investigates the combined effect of radial magnetic field and viscous dissipation on entropy generation in horizontal co-axial cylinders of generalized Couette flow.The analytical solutions for velocity and temperature profiles are obtained and utilized to compute the entropy generation,Bejan number as well as the average entropy generation number.The effect of relevant parameters on temperature field,velocity field,entropy generation,average entropy and Bejan number are portrayed graphically and discussed.We isoflux heating near the inner surface of the fixed outer cylinder with higher dominance in the case of isoflux heating.The reverse is seen on the moving inner cylinder.