G. Nath and P. Upadhyay
This article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and…
Abstract
Purpose
This article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and monochromatic radiation in the presence or absence of gravitational field. This paper also aims to study the effects of physical parameters on the strength of shock wave, and on the flow variables in the flow-field region behind the shock front.
Design/methodology/approach
The Roche model is used to describe the gravitational field effects due to a massive nucleus at the point of symmetry. To derive the similarity solutions, the Lie group symmetry method has been used. Also, the numerical solutions to the present problem are obtained by using Rung–Kutta method of the fourth order with the use of Mathematica software. The effects of variation in the parameter of non-idealness of the gas, the gravitation parameter, the strength of the ambient magnetic field and the adiabatic index of the gas on the shock wave, and on the flow variables is discussed. A comparative study between with and without gravitational field is also, made.
Findings
For different choices of the arbitrary constants that appeared in the solution of infinitesimal generators, we have obtained seven distinct cases of similarity solutions. In the absence of the gravitational field, the similarity solution exists to the power and exponential law shock paths, but in the presence of gravitational field, the similarity solution exists to the power law shock path case only. In the absence of gravitational field, the shock strength is enhanced in the exponential law shock path case in comparison to the power law shock path case. It is found that the shock wave decays with an increase in the value of the adiabatic exponent, the strength of magnetic field, non-idealness of the gas or gravitational parameter.
Research limitations/implications
The consideration of medium under the influence of gravitational field due to a heavy nucleus at the center and presence of magnetic field decrease the shock strength. This result may be helpful in designing space vehicle and jet engine.
Practical implications
The result of the present study may be used in the analysis of data from the measurements by space craft in the solar wind and in neighborhood of the Earth’s magnetosphere.
Social implications
The obtained results may be used for mankind.
Originality/value
The study of spherical shock wave propagation influenced by monochromatic radiation and azimuthal magnetic field in a non-ideal gas with or without gravitational field has yet to be discussed by any authors by using the Lie group symmetry method. In this article, we have discussed all possible cases of similarity solutions using the Lie group symmetry method, which is not studied by anyone as known to us.
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P. Saikrishnan, Satyajit Roy, H.S. Takhar and R. Ravindran
The purpose of this paper is to study the influence of thermally stratified medium on a free convection flow from a sphere, which is rotating about the vertical axis, immersed in…
Abstract
Purpose
The purpose of this paper is to study the influence of thermally stratified medium on a free convection flow from a sphere, which is rotating about the vertical axis, immersed in a stably thermally stratified medium.
Design/methodology/approach
An implicit finite‐difference scheme in combination with the quasi‐linearization technique is applied to obtain the steady state non‐similar solutions of the governing boundary layer equations for flow and temperature fields.
Findings
The numerical results indicate that the heat transfer rate at the wall decreases significantly with an increasing thermal stratification parameter, but its effect on the skin friction coefficients is rather minimum. In fact, the presence of thermal stratification of the medium influences the heat transfer at wall to be in opposite direction, that is, from fluids to the wall above a certain height. The heat transfer rate increases but the skin frictions decrease with the increase of Prandtl number. In particular, the effect of buoyancy force is much more sensitive for low Prandtl number fluids (Pr = 0.7, air) than that of high Prandtl number fluids (Pr = 7, water). Also the skin friction in rotating direction is less sensitive to the buoyancy force as the buoyancy force acts in the streamwise direction for the present study of thermally stratified medium.
Research limitations/implications
The ambient temperature T∞∞ is assumed to increase linearly with height $h$. The viscous dissipation term, which is usually small for natural convection flows, has been neglected in the energy equation. The flow is assumed to be axi‐symmetric. The Boussinesq approximation is invoked for the fluid properties to relate density changes to temperature changes, and to couple in this way the temperature field to the flow field.
Practical implications
Free convection in a thermally stratified medium occurs in many environmental processes with temperature stratification, and in industrial applications within a closed chamber with heated walls. Also, free convections associated with heat rejection systems for long‐duration deep ocean powder modules where ocean environment is stratified are examples of such type.
Originality/value
The research presented in this paper investigates the free convection flow on a sphere, which is rotating with a constant angular velocity along its vertical axis in a stably thermally stratified fluid.
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Ò. À. Bèg, H.S. Takhar and V.M. Soundalgekar
Numerical results generated by a highly efficient finite‐difference method (originated by Keller for aerodynamical flows at the California Institute of Technology in 1970), and a…
Abstract
Numerical results generated by a highly efficient finite‐difference method (originated by Keller for aerodynamical flows at the California Institute of Technology in 1970), and a robust double shooting Runge‐Kutta‐Merson scheme are presented for the boundary layer equations representing the convection flow of a viscous incompressible fluid past a hot vertical flat plate embedded in a non‐Darcy porous medium. Viscous dissipation due to mechanical work is included in the temperature field equation. The computations for both solution techniques are compared at the leading edge (ξ = 0.0) and found to be in excellent agreement. The effects of the viscous heating parameter (Ec), thermal conductivity ratio (λ) and a Darcy porous parameter (Re/GrDa) on the fluid velocities, temperatures, local shear stress and wall heat transfer rate are discussed with applications to geothermal and industrial flows.
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H.S. Takhar, Rama Subba Reddy Gorla and V.M. Soundalgekar
Free convection heat transfer due to the simultaneous action ofbuoyancy, radiation and transverse magnetic field is investigated for asemi‐infinite vertical plate. Solutions are…
Abstract
Free convection heat transfer due to the simultaneous action of buoyancy, radiation and transverse magnetic field is investigated for a semi‐infinite vertical plate. Solutions are derived by expanding the stream function and the temperature into a series in terms of the parameter ζ = x1/2 L–1/2, where L is the length of the plate. Velocity and temperature functions are shown on graphs and the numerical values of functions affecting the shear stress and the rate of heat transfer are entered in a table. The effects of the magnetic field parameter λ and the radiation parameter F on these functions are discussed.
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To achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau…
Abstract
Purpose
To achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau nanofluid past a vertical plate with the periodic variations of surface temperature and the concentration of species. Buongiorno model is considered for nanofluid transport, which includes the relative slip mechanisms, Brownian motion and thermophoresis.
Design/methodology/approach
The governing equations are non-dimensionalized using suitable transformations, further reduced to non-similar form using stream function formulation and solved by local non-similarity method with homotopy analysis method. The numerical computations are validated and verified by comparing with earlier published results and are found to be in good agreement.
Findings
The effects of varying the physical parameters such as Prandtl number, Schmidt number, Weissenberg number, thermophoresis parameter, Brownian motion parameter and buoyancy ratio parameter on velocity, temperature and species concentration are discussed and presented through graphs. The results explored that the velocity of shear thinning fluid is raised by increasing the Weissenberg number, while contrary response is seen for the shear thickening fluid. It is also found that heat transfer in Cattaneo–Christov heat conduction model is less than that in Fourier’s heat conduction model. Furthermore, the temperature and thermal boundary layer thickness expand with the increase in thermophoresis and Brownian motion parameter, whereas nanoparticle volume fraction increases with increase in thermophoresis parameter, but reverse trend is observed with increase in Brownian motion parameter.
Originality/value
The present investigation is relatively original as very little research has been reported on Carreau nanofluids under the effect of Cattaneo–Christov heat flux model.
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Syed Tauseef Mohyud-din, Naveed Ahmed, Umar Khan and Mohammad Mehdi Rashidi
The purpose of this study is to analyze thermo-diffusion and diffusion-thermo effects, combined with first-order chemical reaction, in the flow of a micropolar fluid through an…
Abstract
Purpose
The purpose of this study is to analyze thermo-diffusion and diffusion-thermo effects, combined with first-order chemical reaction, in the flow of a micropolar fluid through an asymmetric channel with porous boundaries. Suction/injection velocities of upper and lower walls are taken to be different from each other. The channel exhibits a parting or embracing motion and the fluid enters, or leaves, the channel because of suction/injection through the permeable walls.
Design/methodology/approach
The solution of the problem is obtained by using the fourth-order Runge-Kutta method combined with the shooting technique.
Findings
The asymmetric nature of the channel that is caused by the different permeabilities of the walls deeply influences the flow. The temperature of the fluid rises significantly by increasing the absolute value of A for both Case I and Case II. While, for the concentration profile, the concentration drops near the lower vicinity of the center in Case I, and, it falls near the lower wall of the channel in Case II. Stronger Dufour effects increase the temperature of the fluid except for Case 1 at the center of the channel and for Case II in lower quarter of the channel.
Originality/value
It is confirmed that the presented work is original and is not under consideration by any other journal.
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Sahin Ahmed, Abdul Batin and Ali J. Chamkha
The purpose of this paper is to examine the effects of Darcian drag force and radiation-conduction on unsteady two-dimensional magnetohydrodynamic flow of viscous, electrically…
Abstract
Purpose
The purpose of this paper is to examine the effects of Darcian drag force and radiation-conduction on unsteady two-dimensional magnetohydrodynamic flow of viscous, electrically conducting and Newtonian fluid over a vertical plate adjacent to a Darcian regime in presence of thermal radiation and transversal magnetic field. A well-tested, numerically stable Crank-Nicolson finite-difference procedure is employed for the conservation equations. Excellent agreement is obtained for numerical solutions with previously published work.
Design/methodology/approach
In this investigation, an efficient, accurate, extensively validated and unconditionally stable finite-difference scheme based on the Crank-Nicolson model is developed to solve the governing coupled, non-linear partial differential equations. The accuracy and effectiveness of the method are demonstrated.
Findings
Different numerical results are obtained and presented graphically to explain the effect of various physical parameters on the velocity and temperature profiles, local, as well as average, skin friction and Nusselt number. It is found that, with a rise in Darcian drag force, flow velocity and temperature are reduced, but increased for all times. Both average and local skin frictions are reduced considerably with an increase in Darcian drag force, but reversed behavior is observed for the local Nusselt number. Increasing the thermal radiation effects accelerated the flow velocity as well as the fluid temperature and wall local skin friction in a saturated porous medium, but effectively reduced the local Nusselt number and average Nusselt number at the wall. Comparison with previously published works in the limits shows excellent agreement.
Research limitations/implications
The analysis is valid for unsteady, two-dimensional laminar flow of an optically thick no-gray gas, electrically conducting, and Newtonian fluid past an isothermal vertical surface adjacent to the Darcian regime with variable surface temperature. An extension to three-dimensional flow case is left for future work.
Practical implications
Practical interest of such study includes applications in electromagnetic lubrication, boundary cooling, bio-physical systems and in many branches of engineering and science. It is well known that the effect of thermal radiation is important in space technology and high temperature processes. Thermal radiation also plays an important role in controlling heat transfer process in polymer processing industry.
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Sumaira Qayyum, Muhammad Ijaz Khan, Tasawar Hayat and Ahmed Alsaedi
The purpose of this study is to analyze the Entropy generation analysis and heat transport in three-dimensional flow between two stretchable disks. Joule heating and heat…
Abstract
Purpose
The purpose of this study is to analyze the Entropy generation analysis and heat transport in three-dimensional flow between two stretchable disks. Joule heating and heat generation/absorption are incorporated in the thermal equation. Thermo-diffusion effect is also considered. Flow is conducting for time-dependent applied magnetic field. Induced magnetic field is not taken into consideration. Velocity and thermal slip conditions at both the disks are implemented. The flow problem is modeled by using Navier–Stokes equations with entropy generation rate and Bejan number.
Design/methodology/approach
Von Karman transformations are used to reduce the nonlinear governing expressions into an ordinary one and then tackled by homotopy analysis method for convergent series solutions. The nonlinear expressions for total entropy generation rate are obtained with appropriate transformations. The impacts of different flow variables on velocity, temperature, entropy generation rate and Bejan number are described graphically. Velocity, temperature and concentration gradients are discussed in the presence of flow variables.
Findings
Axial, radial and tangential velocity profiles show decreasing trend for larger values of velocity slip parameters. For a larger Brinkman number, the entropy generation increases, while a decreasing trend is noticed for Bejan number.
Originality/value
To the best of the authors’ knowledge, no such analyses have been reported in the literature.
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Prabhugouda Mallanagouda Patil, Bharath Goudar and Ebrahim Momoniat
Many industries use non-Newtonian ternary hybrid nanofluids (THNF) because of how well they control rheological and heat transport. This being the case, this paper aims to…
Abstract
Purpose
Many industries use non-Newtonian ternary hybrid nanofluids (THNF) because of how well they control rheological and heat transport. This being the case, this paper aims to numerically study the Casson-Williamson THNF flow over a yawed cylinder, considering the effects of several slips and an inclined magnetic field. The THNF comprises Al2O3-TiO2-SiO2 nanoparticles because they improve heat transmission due to large thermal conductivity.
Design/methodology/approach
Applying suitable nonsimilarity variables transforms the coupled highly dimensional nonlinear partial differential equations (PDEs) into a system of nondimensional PDEs. To accomplish the goal of achieving the solution, an implicit finite difference approach is used in conjunction with Quasilinearization. With the assistance of a script written in MATLAB, the numerical results and the graphical representation of those solutions were ascertained.
Findings
As the Casson parameter
Originality/value
There is no existing research on the effects of Casson-Williamson THNF flow over a yawed cylinder with multiple slips and an angled magnetic field, according to the literature.
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Iskandar Waini, Anuar Ishak and Ioan Pop
The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet.
Abstract
Purpose
The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet.
Design/methodology/approach
In this study, 0.1 solid volume fraction of alumina (Al2O3) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al2O3/water hybrid nanofluid. The hybrid nanofluid equations are converted to the similarity equations by using the similarity transformation. The bvp4c solver, which is available in the Matlab software is used for solving the similarity equations numerically. The numerical results for selected values of the parameters are presented in tabular and graphical forms, and are discussed in detail.
Findings
It is found that dual solutions exist up to a certain value of the stretching/shrinking and suction parameters. The critical value λc < 0 for the existence of the dual solutions decreases as nanoparticle volume fractions for copper increase. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.
Originality/value
The present problem is new, original with many important results for practical problems in the modern industry.