Cattaneo–Christov heat flux model and multiple slip effect on carbon nanofluid over a stretching sheet in a Darcy–Forchheimer porous medium

In several biotechnological processes, multiple slips are the most paramount, such as blood pumping from the heart to different body components, endoscopy treatment, pabulum distribution, and the heat transport phenomenon regulation. In the current research, we have studied the multiple slips, Darcy–Forchheimer, and Cattaneo–Christov heat flux model on a stretching surface exposed to magnetic carbon nanotube nanofluid. We have additionally included a heat source or sink, a chemical reaction for manipulating the heat and mass transport phenomena. The resulting governing partial differential equations have been transformed into ordinary differential equations. With the Runge–Kutta–Fehlberg fourth–fifth-order procedure, the transformed governing equations are numerically solved. Numerical solutions for different parameters for velocity, temperature, and concentration profiles (Eckert number, velocity slip, thermal slip, mass slip, etc.) are highlighted. Graphical and numerical results for the various parameters in the modeled problem have been outlined. The present numerical results are compared with the published ones for some limiting cases. The slip has been found to control the flow of the boundary layer.     

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.     

Effect of nonlinear partial slip and thermal radiation on Oldroyd 8‐constant fluid in a channel with convective boundary condition

This investigation deals with the effects of nonlinear slip, nonlinear thermal radiation, and non‐Newtonian flow parameters on heat transfer of an incompressible magnetohydrodynamic steady flow of an Oldroyd 8‐constant fluid through two parallel infinite plates with convective cooling. The Rosseland approximation is adopted to simulate the radiation effects. Heat exchange with the surrounding at the surfaces is assumed to obey Newton's law of cooling. The system of coupled and highly nonlinear ordinary differential equations governing the model is solved numerically using the method of weighted residual. The combined effects of non‐Newtonian flow parameters, velocity slip parameter, magnetic field parameter, Biot numbers, thermal radiation on the fluid velocity, temperature distributions, skin friction, and the Nusselt number are presented graphically and discussed. It is found that the velocity slip has an increasing effect on the fluid velocity and temperature profiles. For larger values of the thermal radiation parameter, the temperature profile and the Nusselt number are noticed to be increased.     

Lie group analysis of hyperbolic tangent fluid flow in the presence of thermal radiation

The present study is devoted to the flow and heat transfer analysis of the hyperbolic tangent fluid through a stretching sheet by considering the effect of thermal radiation in addition to an applied transverse magnetic field, as well as thermal and velocity slip conditions. The Lie group analysis technique has been utilized for establishing similarity transformations, which effectively transform the governing equations to a system of nonlinear ordinary differential equations (ODEs). These ODEs are numerically solved by utilizing the shooting method. The heat transfer properties and flow features under the influence of various physical parameters are also studied. We noted that by increasing the thermal radiation parameter, the temperature profile increases and also the thermal boundary layer thickens. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number. Moreover, the numerical results obtained are in agreement with the existing results in the literature.     

The thermal response of a cold LHTS unit with heat leak through side walls

A LHTS unit employed for cold thermal storage in an air conditioning plant has been numerically studied considering heat leak through sidewalls by convection. A temperature based system of governing equations has been arrived and solved numerically to investigate the influence of various parameters such as porosity, Stanton number, Stefan number and convective heat leak ratio on temperature, solidified fraction, energy storage and total charge fraction. The results indicate a significant delay in the solidification process with a relatively lower charging rate for the LHTS unit with convective heat leak. Limiting values of heat leak ratio has been presented to enable designing cold LHTS units with convective heat leak and operation of such units beyond the limiting values could result in partial charging with incomplete solidification.     

Heat and mass transfer effect on an unsteady MHD radiative chemically reactive Casson fluid over a stretching sheet in porous medium

The objective of the present study is to investigate the effects of the variable magnetic field, chemical reaction, thermal radiation, Soret effect, and variable heat absorption on the fluid flow and heat and mass transfer of an unsteady Casson fluid past a stretching surface in a saturated porous medium. Velocity slip near the plate and conjugate heating boundary conditions in heat and mass transfer have been considered in this study. Due to the complexities in boundary conditions, the analytic solution of the governing equations of the present model is not possible. Thus, to overcome these issues, the coupled partial differential equations of the model are converted into a set of ordinary differential equations using similarity transformation. These equations have then been solved numerically using the fourth-order Runge-Kutta technique via the shooting method. The effects of various pertinent flow parameters on the velocity, concentration, and temperature field have been studied graphically. For the field of engineering, to get an insight into the physical quantities, especially Nusselt number, Sherwood number, and skin friction, their numerical values have been estimated against various parameters and presented in tables. From the tabulated values, it has been perceived that the shear stress increases with an increase in magnetic parameter, unsteadiness parameter, Casson parameter, and heat source parameter, whereas the Biot number shows the reverse trend. The mixture of porous media has justified that the heat transport process over a stretching sheet results in averting heat loss and accelerating the process of cooling, which is a significant outcome of the study. Furthermore, it has also been revealed that with the increase in the Soret effect and magnetic field, there is a reduction in the fluid velocity and temperature near the plate, whereas there is an increase in the species concentration. It has also been mentioned that the effects of the variable magnetic field have been widely applied in various engineering applications like magnetohydrodynamic (MHD) propulsion forces, rate of cooling, MHD power generation, and so on.     

Influence of variable viscosity and thermal conductivity,hydrodynamic, and thermal slips on magnetohydrodynamic micropolar flow: A numerical study

Thermophysical and wall‐slip effects arise in many areas of nuclear technology. Motivated by such applications, in this article, the collective influence of variable‐viscosity, thermal conductivity, velocity and thermal slip effects on a steady two‐dimensional magnetohydrodynamic micropolar fluid over a stretching sheet is analyzed numerically. The governing nonlinear partial differential equations have been converted into a system of nonlinear ordinary differential equations using suitable coordinate transformations. The numerical solutions of the problem are expressed in the form of nondimensional velocity and temperature profiles and discussed from their graphical representations. The Nachtsheim‐Swigert shooting iteration technique together with the sixth‐order Runge‐Kutta integration scheme has been applied for the numerical solution. A comparison with the existing results has been done, and an excellent agreement is found. Further validation with the Adomian decomposition method is included for the general model. Interesting features in the heat and momentum characteristics are explored. It is found that a greater thermal slip and thermal conductivity elevate thermal boundary layer thickness. Increasing Prandtl number enhances the Nusselt number at the wall but reduces wall couple stress (microrotation gradient). Temperatures are enhanced with both the magnetic field and viscosity parameter. Increasing momentum (hydrodynamic) slip is found to accelerate the flow and elevate temperatures.     

Second law analysis of pseudo-plastic nanofluid stream past a stretching sheet with a sliding consequence

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power-law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power-law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power-law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.     

Slip Flow of Casson Rheological Fluid Under Variable Thermal Conductivity with Radiation Effects

This paper investigates the radiation and chemical reaction effects on Casson non‐Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions. The governing boundary layer conservation equations are normalized into nonsimilar form using similarity transformations. A numerical approach is applied to the resultant equations. The behavior of the velocity, temperature, concentration, as well as the skin friction coefficient, Nusselt number, and Sherwood number for various governing physical are discussed. Increasing the radiation parameter decreases the temperature. An increase in the rheological parameter (Casson parameter) induces an elevation in the skin friction coefficient, the heat and mass transfer rates. The larger the β values the closer the fluid is in behavior to a Newtonian fluid and further departs from plastic flow. Temperature of the fluid was found to decrease with increasing values of the Casson rheological parameter. The most important non‐Newtonian fluid possessing a yield value is the rheological Casson fluid, which finds significant applications in polymer processing industries, biomechanics, and chocolate food processing.     

Spectral relaxation method analysis of Casson nanofluid flow over stretching cylinder with variable thermal conductivity and Cattaneo–Christov heat flux model

This article deals with non‐Newtonian Casson nanofluid flow and heat transfer over stretching cylinder in a porous medium. The mode of heat transfer is presented considering temperature‐dependent thermal conductivity by integrating the Cattaneo–Christov heat flux and mass flux models. Boundary layer theory is applied to develop the governing partial differential equations from the physical problem. Employing proper similarity transformation, the governing boundary layer equations are transformed into dimensionless system of nonlinear ordinary differential equations. Then, the resulting problem is numerically solved by means of spectral relaxation method. The convergence analysis of the proposed numerical scheme is presented via a table, which confirms almost the 10th order of approximation is enough for the convergence of the skin friction coefficient, local heat transfer, and mass transfer rates. The effects of various embedded parameters on velocity, temperature, and concentration profiles as well as skin friction coefficient, surface heat and mass transfer rates are examined through graphs and tables. The findings reveal that the growth of permeability and velocity slip parameters appears to decelerate the velocity distributions of fluid. Thermal boundary layer thickness tends to develop with greater values of permeability and Brownian motion parameters. Also, the local heat transfer rate is less with Fourier's law of heat conduction than Cattaneo–Christov heat flux model. Furthermore, the validity and accuracy of the present result is checked with the available literature, and very sound agreement has been obtained.     

Unsteady MHD Stagnation‐Point Flow Toward a Shrinking Sheet with Thermal Radiation and Slip Effects

The problem of an unsteady magnetohydrodynamic stagnation point flow of an incompressible viscous fluid over a shrinking sheet is discussed in the presence of thermal radiation and boundary slip, which has not been documented to date in the literature. The governing boundary‐layer equations are transformed to high order nonlinear and ordinary differential equations by similarity transformations and then solved numerically. The effects of magnetic parameter, unsteadiness parameter, radiation parameter, velocity, and thermal slip parameters on velocity and temperature are analyzed and discussed. It is found that dual solutions of both velocity and temperature fields exist for negative values of the velocity ratio parameter. The results indicate that dual solution domains of velocity and temperature expand as the unsteadiness parameter increases.     

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.     

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Mixed convection flow in an inclined enclosure under magnetic field with thermal radiation and heat generation

The influence of thermal radiation and heat generation on an unsteady two-dimensional natural convection flow in an inclined enclosure heated from one side and cooled from the adjacent side under the influence of a magnetic field using staggered grid finite-difference technique has been studied. The governing equations have been solved numerically for streamlines, isotherms, local Nusselt numbers and the average Nusselt number for various values of thermal radiation and heat generation parameters by considering three different inclination angles and magnetic field directions, keeping the aspect ratio fixed. The results indicate that the flow pattern and temperature fields are significantly dependent on the above mentioned parameters. It is found that magnetic field suppresses the convection flow and its direction influences the flow pattern which results in the appearance of inner loop and multiple eddies.     

Heat transfer in the flow of blood‐gold Carreau nanofluid induced by partial slip and buoyancy

Dynamics of blood containing gold nanoparticles on a syringe and other objects with a nonuniform thickness is of importance to experts in the industry. This study presents the significance of partial slip (i.e. combination of linear stretching and velocity gradient) and buoyancy on the boundary layer flow of blood‐gold Carreau nanofluid over an upper horizontal surface of a paraboloid of revolution (uhspr). In this report, the viscosity of the Carreau fluid corresponding to an infinite shear‐rate is assumed as zero, meanwhile, the viscosity corresponding to zero shear‐rate, density, thermal conductivity, and heat capacity were assumed to vary with the volume fraction of nanoparticles. The governing equation that models the transport phenomenon were non‐dimensionalized and parameterized using suitable similarity variables and solved numerically using classical Runge–Kutta method with shooting techniques and MATLAB bvp4c package for validation. The results show that temperature distribution across the flow decreases more significantly with buoyancy‐related parameter when the influence of partial slip was maximized. Maximum velocity of the flow is ascertained at larger values of partial slip and buoyancy parameters. At smaller values of Deborah number and large values of volume fraction, maximum local skin friction coefficient, and local heat transfer rate are ascertained.     

Influence of Hall current on hydromagnetic natural convective flow between two vertical concentric cylinders in presence of heat source/sink

The fully developed laminar magnetohydrodynamic free convection between two concentric vertical cylinders with Hall currents and heat source/sink, in the presence of the radial magnetic field, are studied. The governing thermal energy and momentum equations are changed into ordinary differential equations whose solutions are determined in closed‐form expressions of the Bessel and modified Bessel functions of order zero. A parametric investigation illustrating the impacts of the Hall current, magnetic field, heat source, and radii ratio has been accomplished graphically to examine the changes in temperature as well as velocity while the Nusselt number, mass flux, and skin friction values have been presented in tabular forms. The results ensure that the Hall current has a strong and direct impact on the flow character, such that the influence of the Hall parameter enhances the velocity fields in the appearance of heat source and sink. The velocity remains almost constant as the Hall parameter value is greater than four. Moreover, the velocity and temperature fields have an increasing tendency due to the heat source and inversely for the heat sink.     

Analytical solution for slip flow and heat transfer due to a stretching sheet

An analysis has been carried out to investigate the analytical solution to the flow and heat transfer characteristics of a viscous flow over a stretching sheet in the presence of second‐order slip in flow. The governing partial differential equations of flow and heat transfer are converted into non‐linear ordinary differential equations by using suitable similarity transformations. The exact solution of momentum equation is assumed in exponential form and analytical solutions of heat transfer for both PST and PHF cases are obtained by the power series method in terms of Kummer's hypergeometric function. The temperature profiles are drawn for different governing parameters. The numerical values of wall temperature gradient and wall temperature are compared with earlier numerical results which have a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21044     

Effects of slip and heat transfer on the peristaltic flow of a third order fluid in an inclined asymmetric channel

The present investigation is concerned with the peristaltic flow of an incompressible and magnetohydrodynamic MHD third order fluid in an inclined asymmetric channel. Both thermal and velocity slip conditions have been taken into account. The channel walls are maintained at different temperatures. The governing differential systems subjected to their boundary conditions have been solved for small Deborah number. In the derived solution expressions, the long wavelength and low Reynolds number assumptions are utilized. Graphical results are presented for the pressure rise, longitudinal velocity and temperature. Comparison with the previous published work regarding viscous fluid and no-slip case is performed. Pumping and trapping phenomena are displayed graphically just to examine the various interesting aspects of the present work.     

The effect of creep flow on two-dimensional isoflux microchannels

Microchannel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second-order slip boundary conditions, creep flow, and hydrodynamically/thermally developing flow are considered. These effects are compared through the Poiseuille number and the Nusselt number. Numerical values for the Poiseuille and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions of the hydrodynamically and thermally fully developed momentum and energy equations have been derived subject to both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature profiles are then utilized to obtain the microchannel Poiseuille and Nusselt numbers as a function of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second-order slip terms and creep velocity are shown to have significant effects on microchannel Poiseuille and Nusselt numbers within the slip flow regime.     

Effects of slip conditions on stretching flow with ohmic dissipation and thermal radiation

The present work addresses the magnetohydrodynamic (MHD) flow and heat transfer over a permeable stretching sheet. Analysis has been carried out in the presence of thermal radiation and ohmic dissipation. The velocity and thermal slip effects are given main attention. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non‐linear partial differential equations are reduced to a set of non‐linear ordinary differential equations which are solved analytically by the homotopy analysis method (HAM). The effects of emerging physical parameters on the velocity and temperature profiles are interpreted. Numerical data for skin friction coefficient and Nusselt number have been tabulated for various values of the parameters. The results have been compared with the known exact solution from the literature in a limiting sense. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20367