C. V. Raghavarao

Approximation theory

Axial flow

Flow patterns

Gravitational effects

Heat flux

Pipe flow

Rotational flow

Spheres

Temperature distribution

Torque

Boundary conditions

Buoyancy

Galerkin methods

Navier Stokes equations

Nusselt number

Perturbation techniques

Polynomial approximation

Reynolds number

Steady flow

Thermal stratification

Vortex flow

BOUSSINESQ FLUID

PARAMETRIC SPLINE FUNCTION APPROXIMATION

Angular velocity

Energy equations

spline functions

TEMPERATURE GRADIENTS

Heat convection

convection

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.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

A numerical study of thermal convection in a rotating spherical annulus with axial gravitational field by using parametric spline function approximation

International Journal of Numerical Methods for Heat and Fluid Flow

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 longduration 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. © Emerald Group Publishing Limited.

Role of thermally stratified medium on a free convection flow from a rotating sphere

The application of a parametric spline function which depends on a parameter p > 0 to two linear partial differential equations is discussed. For p = 0, the parametric spline reduces to the ordinary cubic spline. © 1995.

Computers and Mathematics with Applications

A note on parametric spline function approximation

International Journal of Heat and Mass Transfer

Heat transfer: a review of 1998 literature

Numerical Heat Transfer, Part A: Applications

NUMERICAL COMPUTATION OF THE NATURAL CONVECTION FLOW ABOUT A HORIZONTAL CYLINDER USING SPLINES

Journal	International Journal of Numerical Methods for Heat and Fluid Flow
Publisher	Emerald Group Publishing Ltd.
ISSN	09615539
Open Access	No