Correlating equations for laminar and turbulent free convection from a horizontal cylinder

In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation $u_t = \Delta u + u^p $ in $R^N $ with $p > 1$ and nonnegative initial values. Fujita showed that if $1 1 + {2 / N}$, there were nontrivial global solutions. This paper discusses similar results for other geometries and other equations including a nonlinear wave equation and a nonlinear Schrodinger equation.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1048&context=math_pubs

The role of critical exponents in blowup theorems

This paper investigates the effect of radiation on the forced and free convection flow of an optically dense viscous incompressible fluid along a heated vertical flat plate with uniform free stream and uniform surface temperature with Rosseland diffusion approximation. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations valid in the forced convection regime as well as in the free convection regime. A group of transformation is, also, introduced to reduce the boundary layer equations to a set of local nonsimilarity equations valid in both the forced and free convection regimes. Solutions of the governing equations are obtained by employing the implicit finite difference methods together with Keller box scheme and are expressed in terms of local shear stress and local rate of heat transfer for a range of values of the pertinent parameters.

Radiation effect on mixed convection along a vertical plate with uniform surface temperature

Confluent Hypergeometric Functions.

Natural-convection boundary-layer flow on a vertical surface with Newtonian heating

Combined forced and free convection flow on vertical surfaces

The magnetohydrodynamic free convection flow of an electrically conducting fluid past a semi-infinite plate in a strong cross-field has been examined. Formulation in terms of a characteristic length has enabled a full numerical solution to be obtained providing details of skin friction and heat transfer at all stations along the plate. An estimate of an indeterminacy in asymptotic solutions allows favourable comparison to be made between series solutions estimates of these quantities and their exact numerical values.

Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross field

Continuous transformation computation of boundary layer equations between similarity regimes

The flow of a uniform stream over a semi-infinite vertical flat plate with uniform surface heat flux

The magnetohydrodynamic free convection flow of an electrically conducting fluid past a vertical, semi-infinite plate in a strong cross field has been examined when a uniform heat flux is present at the plate. Formulation in terms of a characteristic length has enabled a full numerical solution to be obtained providing details of skin friction and heat transfer at all stations along the plate for a range of Prandtl numbers appropriate to liquid metal coolants. Series solutions are also presented which give good estimates of the skin friction and heat transfer coefficients.

Graham Wilks

Papers

Combined forced and free convection flow on vertical surfaces

Magnetohydrodynamic free convection about a semi-infinite vertical plate in a strong cross field

Continuous transformation computation of boundary layer equations between similarity regimes

The flow of a uniform stream over a semi-infinite vertical flat plate with uniform surface heat flux

Magnetohydrodynamic free convection flow about a semi-infinite plate at whose surface the heat flux is uniform