Partial Spectral Expansions for Problems in Thermal Convection

The use of spectral expansions for solving nonlinear partial differential equations is explained, and two examples drawn from convective heat transfer are presented. For both problems the results agree well with regular perturbation solutions at parameter values for which the latter remain valid. Evidence is given to indicate that the spectral solutions are valid for considerably larger parameter values than can be reached with the perturbation methods.

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Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling

Advances in Mathematical Physics ◽

10.1155/2014/809367 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 5

Author(s):

O. D. Makinde ◽

S. Khamis ◽

M. S. Tshehla ◽

O. Franks

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Viscous Dissipation ◽

Perturbation Methods ◽

Regular Perturbation ◽

Convective Cooling ◽

Navier Slip ◽

Nusselt Numbers ◽

Similarity Transformations ◽

Friction Pressure Drop

Heat transfer characteristics of a Berman flow of water based nanofluids containing copper (Cu) and alumina (Al2O3) as nanoparticles in a porous channel with Navier slip, viscous dissipation, and convective cooling are investigated. It is assumed that the exchange of heat with the ambient surrounding takes place at the channel walls following Newton’s law of cooling. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. These equations are solved analytically by regular perturbation methods with series improvement technique and numerically using an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop, and Nusselt numbers are presented graphically and discussed quantitatively.

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Transient Convective Heat Transfer for Laminar Boundary Layer Flow With Effects of Wall Capacitance and Resistance

Journal of Heat Transfer ◽

10.1115/1.3450735 ◽

1977 ◽

Vol 99 (4) ◽

pp. 513-519 ◽

Cited By ~ 15

Author(s):

R. C. C. Wang ◽

B. T. F. Chung ◽

L. C. Thomas

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Convective Heat Transfer ◽

Convective Heat ◽

Laminar Boundary Layer ◽

Boundary Layer Flow ◽

Nonlinear Partial Differential Equations ◽

Lower Surface ◽

Interface Temperature ◽

Layer Flow

Transient forced convective heat transfer from a laminar boundary layer flow over a flat plate with appreciable thermal capacity and resistance is studied analytically. In the analysis, the flow is assumed to be steady and incompressible and the solid plate is subjected to a uniform step heat input at the lower surface. The integral method is utilized to reduce systems of nonlinear partial differential equations to a single integro-differential equation in terms of interfacial temperature which is then solved with the aid of finite difference technique. Numerical results for the fluid-solid interface temperature, heat transfer coefficient, and temperature distributions within the fluid and solid are presented. Some limiting solutions are found to agree well with the results of the previous theoretical analyses.

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