# Convective Heat Transfer

**Mathematical and Computational Modelling of Viscous Fluids and Porous Media**

**By**

- I. Pop, University of Cluj, Faculty of Mathematics, R-3400 Cluj, CP 253, Romania
- Derek Ingham, Department of Applied Mathematics Ingham Centre for Computational Fluid Dynamics University of Leeds Leeds LS2 9JT UNITED KINGDOM

Interest in studying the phenomena of convective heat and mass transfer between an ambient fluid and a body which is immersed in it stems both from fundamental considerations, such as the development of better insights into the nature of the underlying physical processes which take place, and from practical considerations, such as the fact that these idealised configurations serve as a launching pad formodelling the analogous transfer processes in more realistic physical systems. Such idealised geometries also provide a test ground for checking the validity of theoreticalanalyses. Consequently, an immense research effort has been expended in exploring and understanding the convective heat and mass transfer processes between a fluid and submerged objects of various shapes. Among several geometries which have received considerable attention are plates, circular and elliptical cylinders, and spheres, although much information is also available for some other bodies, such ascorrugated surfaces or bodies of relatively complicated shapes.

The book is a unified progress report which captures the spirit of the work in progress in boundary-layer heat transfer research and also identifies potential difficulties and areas for further study. In addition, this work provides new material on convective heat and mass transfer, as well as a fresh look at basic methods in heat transfer. Extensive references are included in order to stimulate further studies of the problems considered. A state-of-the-art picture of boundary-layer heat transfer today is presented by listing and commenting also upon the most recent successful efforts and identifying the needs for further research.

View full descriptionThe book is a unified progress report which captures the spirit of the work in progress in boundary-layer heat transfer research and also identifies potential difficulties and areas for further study. In addition, this work provides new material on convective heat and mass transfer, as well as a fresh look at basic methods in heat transfer. Extensive references are included in order to stimulate further studies of the problems considered. A state-of-the-art picture of boundary-layer heat transfer today is presented by listing and commenting also upon the most recent successful efforts and identifying the needs for further research.

### Audience

For postgraduates and researchers in the fields of applied mathematics, fluid mechanics, heat transfer, physics, geophysics, and chemical and mechanical engineering.

### Book information

- Published: February 2001
- Imprint: PERGAMON
- ISBN: 978-0-08-043878-8

### Table of Contents

**Preface.**

**Acknowledgements.**

**Nomenclature.**

**I Convective Flows: Viscous Fluids.**

**Free convection boundary-layer flow over a vertical flat plate.**Introduction. Basic equations. Similarity solutions for an impermeable flat plate with a variable wall temperature. Similarity solutions for an impermeable flat plate with a variable surface heat flux. Flat plate with a variable wall temperature in a stratified environment. Flat plate with a sinusoidal wall temperature. Free convection boundary-layer flow over a vertical permeable flat plate.

**Mixed convection boundary-layer flow along a vertical flat plate.**Introduction. Basic equations. Behaviour near separation in mixed convection. Mixed convection along a flat plate with a constant wall temperature in paraboliccoordinates. Effect of Prandtl number on the mixed convection boundary-layer flow along a vertical plate with a constant wall temperature. Mixed convection boundary-layer flow along a vertical flat plate with a variable heatflux for a large range of values of the Prandtl number. Three-dimensional mixed convection boundary-layer flow near a plane of symmetry.

**Free and mixed convection boundary-layer flow past inclined and horizontalplates.**Introduction. Basic equations. Free convection over an isothermal flat plate at small inclinations. Free convection boundary-layer flow above an isothermal flat plate of arbitrary inclination. Mixed convection boundary-layer flow from a horizontal flat plate. Mixed convection boundary-layer flow along an inclined permeable plate with variable wall temperature.

**Double-diffusive convection.**Introduction. Double diffusive free convection boundary-layer flow over a vertical flat plate in the case of opposing buoyancy forces. Free convection boundary-layer flow driven by catalytic surface reactions.

**Convective flow in buoyant plumes and jets.**Introduction. Free convection in a wall plume. Inclined wall plumes. Free convection far downstream of a heated source on a solid wall. Laminar plane buoyant jets.

**Conjugate heat transfer over vertical and horizontal flat plates.**Introduction. Conjugate free convection over a finite vertical flat plate. Conjugate free convection boundary-layer flow past a horizontal at plate.

**Free and mixed convection from cylinders.**Introduction. Free convection from horizontal cylinders. Conjugate free convection from a horizontal circular cylinder. Mixed convection boundary-layer flow from a horizontal cylinder. Mixed convection boundary-layer flow along a heated longitudinal horizontal cylinder. Mixed convection boundary-layer flow along a vertical circular cylinder.

**Free and mixed convection boundary-layer flow over moving surfaces.**Introduction. Free convection boundary-layer flow from a moving vertical sheet. Free convection boundary-layer flow from a horizontal moving sheet. Free convection boundary-layer flow from a moving vertical cylinder. Free convection boundary-layer flow due to a continuously moving vertical at plate. Mixed convection boundary-layer ow from a moving horizontal at plate.

**Unsteady free and mixed convection.**Introduction. Basic equations. Transient free convection boundary-layer flow over a suddenly heated vertical plate. Transient free convection boundary-layer flow over a suddenly cooled vertical plate. Transient free convection boundary-layer flow over a vertical flat plate at small and large Prandtl numbers. Transient free convection boundary-layer flow over a vertical plate subjected to a sudden change in surface temperature. Transient free convection from a horizontal circular cylinder. Transient mixed convection boundary-layer flow from a horizontal circular cylinder. Unsteady free convection boundary-layer flow past a sphere.

**Free and mixed convection boundary-layer flow of non-Newtonian fluids.**Introduction. Free convection boundary-layer flow of power-law fluids over a vertical flat plate. Free convection boundary-layer flow of non-Newtonian power-law fluids over a vertical wavy surface. Free convection boundary-layer wall plume in non-Newtonian power-law fluids. Mixed convection boundary-layer flow from a horizontal circular cylinder and asphere in non-Newtonian power-law fluids. Free convection boundary-layer flow of a micropolar fluid over a vertical flat plate. Gravity-driven laminar film flow for non-Newtonian power-law fluids along a vertical wall.

**Convective Flows: Porous Media.**

**Free and mixed convection boundary-layer flow over vertical surfaces in porous media.**Introduction. Basic equations. Similarity solutions of the boundary-layer equations for surfaces with a variable wall temperature. Similarity solutions of the boundary-layer equations for surfaces with variable wallheat flux. Combined heat and mass transfer by free convection over a vertical surface. Free convection boundary-layer flow over reacting surfaces. Free convection boundary-layer flow over a vertical surface in a layered porous medium. Free convection boundary-layer flow over a vertical surface in a porous medium using a thermal non-equilibrium model. Mixed convection boundary-layer flow along a vertical surface.

**Free and mixed convection past horizontal and inclined surfaces in porous media.**Introduction. Basic equations. Free convection boundary-layer flow above a horizontal surface. Mixed convection past a horizontal flat plate. Free convection boundary-layer flow past an inclined surface. Mixed convection boundary-layer flow along an inclined permeable surface.

**Conjugate free and mixed convection over vertical surfaces in porous media.**Introduction. Conjugate free convection boundary-layer flow over a vertical surface. Free convection boundary-layer flow over a vertical surface with Newtonian heating. Conjugate free convection boundary-layer flow due to two porous media separatedby a vertical wall. Conjugate mixed convection boundary-layer flow along a vertical surface.

**Free and mixed convection from cylinders and spheres in porous media.**Introduction. Free convection from a horizontal circular cylinder. Free convection boundary-layer flow over a vertical cylinder. Mixed convection boundary-layer flow along a vertical cylinder. Horizontal boundary-layer flow past a partially heated vertical cylinder. Free convection past a heated sphere.

**Unsteady free and mixed convection in porous media.**Introduction. Transient free convection boundary-layer flow from a vertical at plate suddenly heated. Transient free convection boundary-layer flow over a vertical plate subjected to a sudden change in the heat flux. Transient mixed convection boundary-layer flow from a vertical flat plate suddenly heated or suddenly cooled. Transient free convection boundary-layer flow from a horizontal circular cylinder. Transient mixed convection from a horizontal circular cylinder. Transient free convection from a sphere.

**Non-Darcy free and mixed convection boundary-layer flow in porous media.**Introduction. Similarity solutions for free convection boundary-layer flow over a non-isothermal body of arbitrary shape in a porous medium using the Darcy-Forchheimer model. Non-Darcy mixed convection boundary-layer flow along a vertical at plate in a porous medium. Transient non-Darcy free, forced and mixed convection boundary-layer flow over avertical surface in a porous medium. Non-Darcy free convection boundary-layer flow past a horizontal surface in a porous medium. Effects of heat dispersion on mixed convection boundary-layer flow past a horizontal surface. Free convection boundary-layer flow from a point heat source embedded in a porous medium filled with a non-Newtonian power-law fluid.

**Bibliography. Author Index.**