This paper deals with a new self-similar solution of unsteady mixed convection flow on a rotating cone in a rotating fluid due to the combined effects of thermal and mass diffusion. It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear functions of time. The system of ordinary differential equations governing the flow has been solved numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. Both prescribe wall temperature and prescribed heat flux conditions are considered. Numerical results are reported for the skin friction coefficients, Nusselt number and Sherwood number. The effect of various parameters on the velocity, temperature and concentration profiles are also presented here. © 2003 Elsevier Inc. All rights reserved.

Satyajit Roy

Department of Mathematics

Boundary layers

Computational complexity

Differential equations

linearization

Mixed convection

Nusselt number

Problem solving

ROTATING CONES

self-similar solutions

Flow of fluids

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

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IIT Madras

Unsteady mixed convection flow on a rotating cone in a rotating fluid

Applied Mathematics and Computation

An unsteady mixed convection flow over a permeable nonlinearly stretching vertical slender cylinder is considered to investigate the combined effects of thermal and mass diffusion in the presence of surface mass transfer and linear chemical reaction, where the slender cylinder is in line with the flow. The unsteadiness in the flow, temperature, and concentration fields is caused by the continuously nonlinearly stretching vertical slender cylinder. The effect of surface curvature is also taken into account, particularly for the applications of wire and fiber drawing where exact predictions are expected. The governing boundary layer equations are transformed into a nondimensional form by a group of nonsimilar transformations. The resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are performed to understand the physical situations of linearly and nonlinearly stretching surface for various values of the governing parameters to display the effects of velocity, temperature, and concentration profiles graphically. Our main objective in this work is to focus on opposing flow situations. Numerical results for the local skin-friction coefficient, local Nusselt number, and local Sherwood number are also presented. The present results are compared with previously published work, and these comparisons are found to be in excellent agreement. © 2013 Copyright Taylor and Francis Group, LLC.

Chemical Engineering Communications

Chemical reaction effects on unsteady mixed convection boundary layer flow past a permeable slender vertical cylinder due to a nonlinearly stretching velocity

The objective of the paper is to investigate the numerical study of an unsteady two-dimensional mixed convection flow along a vertical semi-infinite power-law stretching sheet in a parallel free stream with a power-law wall temperature distribution of the form TW(x)=T∞+Ax2m-1. The unsteadiness is caused by the free stream velocity as well as by the stretching sheet velocity. The governing non-linear partial differential equations in the velocity and temperature fields are written in non-dimensional form using suitable transformations. The resulting final set of coupled non-linear partial differential equations is solved using an implicit finite difference scheme in combination with a quasi-linearization technique. The effects of various governing parameters on the velocity and temperature profiles are discussed in the present numerical study. In addition, the numerical results for the local skin friction coefficient and local Nusselt number are also presented. The numerically computed results are compared with previously reported work and are found to be in excellent agreement. © 2010 Elsevier Ltd.

International Journal of Heat and Mass Transfer

Unsteady mixed convection flow over a vertical stretching sheet in a parallel free stream with variable wall temperature

An unsteady mixed convection flow over a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of heat generation or absorption. The unsteadiness is introduced by the time dependent free stream velocity as well as by the moving plate velocity. The governing boundary layer equations are transformed into a non-dimensional form by a special group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Computations are performed and numerical results are displayed graphically to illustrate the influence of the buoyancy (mixed convection) parameter, Prandtl number, the ratio of free stream velocity to the composite reference velocity and heat generation or absorption parameter on the velocity and temperature profiles. The numerical results for the local skin-friction coefficient and local Nusselt number are also presented. Present results are compared with previously published work and are found to be in excellent agreement. It is found that in presence of buoyancy force (λ>0), the velocity profile exhibits velocity overshoot 80% more for lower Prandtl number (Pr=0.7) as compared to the magnitude of the velocity overshoot for higher Prandtl number (Pr=7.0). © 2010 Elsevier Ltd.

Unsteady mixed convection flow from a moving vertical plate in a parallel free stream: Influence of heat generation or absorption

Non-similar solution of an unsteady mixed convection flow over a vertical cone in the presence of surface mass transfer has been obtained when the axis of the cone is inline with the flow. The time dependent free stream velocity varying arbitrarily with time introduces unsteadiness in the flow field. The results have been obtained for accelerating and decelerating free stream velocities. The numerical difficulties arising at the starting point of the stream wise coordinate and for time dependent flow field are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results are reported here to account the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different streamwise locations for various times on velocity and temperature profiles, and skin friction and heat transfer coefficients. © 2006 Elsevier Ltd. All rights reserved.

Non-similar solution of an unsteady mixed convection flow over a vertical cone with suction or injection

AbstractIn the study, we inspect the impact of cross diffusion and aligned magnetic field on Casson fluid flow along a stretched surface of variable thickness. The differential equations explaining the flow situation have been transitioned with the succor of suited transfigurations. The solution of the problem is achieved by using bvp5c Matlab package. From the solution, it is perceived that the flow, temperature and concentration fields are affected by the sundry physical quantities. Results explored for the flow over a uniform and a non-uniform thickness surfaces. The influence of emerging parameters on the flow, energy and mass transport are discussed with graphical and tabular results. Results show that the thermal, flow and species boundary layers are uneven for the flow over a uniform and non-uniform thickness stretched surfaces.

Fulltext

Nonlinear Engineering

Effect of aligned magnetic field on Casson fluid flow over a stretched surface of non-uniform thickness

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x-component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature. © Springer-Verlag 2003.

Heat and Mass Transfer/Waerme- und Stoffuebertragung

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

International Journal of Thermal Sciences

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

Springer Series in Computational Mathematics

Matrix Iterative Analysis

Journal of Heat Transfer

Similarity Solution of Combined Convection Heat Transfer From a Rotating Cone or Disk to Non-Newtonian Fluids

Journal of Electronic Packaging

Buoyancy-Induced Flows and Transport

Journal	Applied Mathematics and Computation
ISSN	00963003
Open Access	No