scholarly journals The thermal boundary layer due to viscous dissipation in impulsively started Poiseuille flow

2019 ◽  
Vol 84 (3) ◽  
pp. 517-532
Author(s):  
Anthony Kay
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Viscous Dissipation ◽  
Temperature Rise ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Dissipative Heating ◽  
Viscous Layer ◽  
Adiabatic Wall ◽  
Wall Condition

Abstract Viscous dissipation occurs in the boundary layers on the walls of a channel in which a flow is accelerated from rest by the sudden imposition of a pressure gradient. We analyse the thermal boundary layer due to this dissipative heating, obtaining numerical solutions and also asymptotic solutions for the cases of both large and small Prandtl number, with both isothermal and adiabatic wall conditions. With large $\mathrm{Pr}$ the temperature rise is controlled by the viscous layer, so is independent of $\mathrm{Pr}$ and of the wall condition. With small $\mathrm{Pr}$ heat is conducted away from the viscous layer more rapidly, so the temperature rise is reduced as $\mathrm{Pr}$ decreases.

Periodic momentum and thermal boundary layer mixed convection flow around the surface of a sphere in the presence of viscous dissipation

2017 ◽  
Vol 95 (10) ◽  
pp. 976-986 ◽  
Author(s):  
Muhammad Ashraf ◽  
Almas Fatima ◽  
R.S.R. Gorla
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Viscous Dissipation ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Implicit Finite Difference ◽  
Convection Parameter

Numerical solutions for the periodic laminar boundary layer mixed convection flow around the surface of a heated sphere in the presence of viscous dissipation have been obtained by solving the governing equations using an implicit finite difference numerical technique. The fluid under consideration is assumed to be viscous and incompressible. Periodic momentum and thermal boundary layer profiles for different positions of x around the surface of the sphere are evaluated. The features of the obtained results for different values of mixed convection parameter λ, Prandtl number Pr, viscous dissipation parameter N, and frequency parameter ω are shown graphically. The obtained results confirm significant effect of all these mentioned parameters on periodic momentum and thermal boundary layer mixed convection flow around different positions of the sphere.

Compressibility Effects on the Extended Crocco Relation and the Thermal Recovery Factor in Laminar Boundary Layer Flow

2004 ◽  
Vol 126 (1) ◽  
pp. 32-41 ◽  
Author(s):  
B. W. van Oudheusden
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Thermal Recovery ◽  
Recovery Factor ◽  
Perturbation Approach ◽  
Layer Flow ◽  
Compressibility Effects

The relation between velocity and enthalpy in steady boundary layer flow is known as the Crocco relation. It describes that for an adiabatic wall the total enthalpy remains constant throughout the boundary layer, when the Prandtl number (Pr) is one, irrespective of pressure gradient and compressibility. A generalization of the Crocco relation for Pr near one is obtained from a perturbation approach. In the case of constant-property flow an analytic expression is found, representing a first-order extension of the standard Crocco relation and confirming the asymptotic validity of the square-root dependence of the recovery factor on Prandtl number. The particular subject of the present study is the effect of compressibility on the extended Crocco relation and, hence, on the thermal recovery in laminar flows. A perturbation analysis for constant Pr reveals two additional mechanisms of compressibility effects in the extended Crocco relation, which are related to the viscosity law and to the pressure gradient. Numerical solutions for (quasi-)self-similar as well as non-similar boundary layers are presented to evaluate these effects quantitatively.

Heat Transfer in the Laminar Boundary Layer Over an Impulsively Started Flat Plate

1975 ◽  
Vol 97 (3) ◽  
pp. 482-484 ◽  
Author(s):  
C. B. Watkins
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Constant Temperature ◽  
Laminar Boundary Layer ◽  
Temperature Difference ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Prandtl Numbers

Numerical solutions are described for the unsteady thermal boundary layer in incompressible laminar flow over a semi-infinite flat plate set impulsively into motion, with the simultaneous imposition of a constant temperature difference between the plate and the fluid. Results are presented for several Prandtl numbers.

Momentum and Thermal Boundary-layer Thickness in a Stagnation Flow Chemical Vapor Deposition Reactor

1997 ◽  
Vol 12 (4) ◽  
pp. 1112-1121 ◽  
Author(s):  
David S. Dandy ◽  
Jungheum Yun
Keyword(s):  
Boundary Layer ◽  
Chemical Vapor Deposition ◽  
Layer Thickness ◽  
Vapor Deposition ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Chemical Vapor ◽  
Square Root ◽  
Thermal Boundary Layer Thickness

Explicit expressions have been derived for momentum and thermal boundary-layer thickness of the laminar, uniform stagnation flows characteristic of highly convective chemical vapor deposition pedestal reactors. Expressions for the velocity and temperature profiles within the boundary layers have also been obtained. The results indicate that, to leading order, the momentum boundary-layer thickness is inversely proportional to the square root of the Reynolds number, while the thermal boundary-layer thickness is inversely proportional to the square root of the Peclet number. Values computed using the approximate expressions are compared directly with numerical solutions of the equations of motion and thermal energy equation, for a specific set of conditions typical of diamond chemical vapor deposition. Because values of the Lewis number do not vary significantly from unity for many different chemical vapor deposition systems, the expression derived here for thermal boundary-layer thickness may be used directly as an approximate concentration boundary-layer thickness.

On the sensitivity of heat transfer in the stagnation-point boundary layer to free-stream vorticity

1963 ◽  
Vol 16 (4) ◽  
pp. 497-520 ◽  
Author(s):  
S. P. Sutera ◽  
P. F. Maeder ◽  
J. Kestin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Stokes Equations ◽  
Point Boundary ◽  
Oncoming Flow ◽  
Flat Plates

Experiments have given evidence of strong sensitivity of the stagnation-point heat transfer on cylinders to small changes in the intensity of free-stream turbulence. A similar effect on local heat-transfer rates to flat plates has been measured, but only when a favourable pressure gradient is present. In this work it is theorized that vorticity amplification by stretching is a possible, and perhaps the dominant, underlying mechanism responsible for this sensitivity. A mathematical model is presented for a steady, basically plane stagnation flow into which is steadily transported disturbed unidirectional vorticity having the only orientation susceptible to stretching. The resulting velocity and temperature fields in the stagnation-point boundary layer are analysed assuming the fluid to be incompressible and to have constant properties. By means of iterative procedures and electronic analogue computation an approximate solution to the full Navier-Stokes equations is achieved which indicates that amplification by stretching of vorticity of sufficiently large scale can occur. Such vorticity, present in the oncoming flow with a small intensity, can appear near the boundary layer with an amplified intensity and induce substantial three-dimensional effects therein. It is found that the thermal boundary layer is much more sensitive to the induced effects than the velocity boundary layer. Computations indicate that a certain amount of distributed vorticity in the oncoming flow causes the shear stress at the wall to increase by 5%, while the heat transfer there is augmented by 26% in a fluid with a Prandtl number of 0.74. Preliminary computations reveal that the sensitivity of the thermal boundary layer increases with Prandtl number.

An integral approach to the calculation of skin friction and heat transfer in the laminar flow of a high-Prandtl-number power-law non-Newtonian fluid past a wedge

1991 ◽  
Vol 69 (2) ◽  
pp. 83-89 ◽  
Author(s):  
G. Ramamurty ◽  
K. Narasimha Rao ◽  
K. N. Seetharamu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Layer Thickness ◽  
Power Law ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Integral Approach ◽  
High Prandtl Number

An integral approach to the theoretical analysis for the skin friction of a non-Newtonian, power-law-fluid flow over a wedge is presented, when the inertia terms in the boundary-layer equations are small but need consideration. The method adopted for the solution of the equations considers an integrated average value of the inertia terms in the momentum equation. The values of the velocities and the boundary-layer thickness obtained from the hydrodynamic analysis are used for the calculation of the thermal-boundary-layer thickness. A linear velocity profile is assumed for the flow field within the thermal boundary layer as the fluids chosen for the analysis are high-Prandtl-number fluids. The results of the skin friction and the rates of the heat transfer are tabulated for a number of values of the flow behaviour index, n, varying from 0.05 to 5.0. This analysis is applicable to viscous polymer solutions having high Prandtl numbers.

scholarly journals A note on the free convection boundary layer on a vertical surface with prescribed heat flux at small Prandtl number

1992 ◽  
Vol 15 (3) ◽  
pp. 605-608
Author(s):  
J. H. Merkin ◽  
V. Kumaran
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Surface Heat Flux ◽  
Numerical Solutions ◽  
Vertical Surface ◽  
Surface Heat ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Free Convection Boundary Layer

It is shown that for a particular case of the surface heat flux the equations for small Prandtl number have simple analytical solutions. These are presented and compared with numerical solutions of the general equations.

Exponentially Stretching Sheet in a Powell–Eyring Fluid: Numerical and Series Solutions

2013 ◽  
Vol 68 (12) ◽  
pp. 791-798 ◽  
Author(s):  
Ammar Mushtaq ◽  
Meraj Mustafa ◽  
Tasawar Hayat ◽  
Mahmood Rahi ◽  
Ahmed Alsaedi
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Velocity Ratio ◽  
Exponentially Stretching Sheet ◽  
Viscoelastic Effects ◽  
Homotopy Analysis ◽  
Analytic Expressions ◽  
Exponentially Stretching

This work theoretically examines the flow and heat transfer characteristics due to an exponentially stretching sheet in a Powell-Eyring fluid. Governing partial differential equations are nondimensionalized and transformed into non-similar forms. Explicit analytic expressions of velocity and temperature functions are developed by homotopy analysis method (HAM). The Numerical solutions are obtained by using shooting method with fourth-order Runge-Kutta integration technique. The fields are influence appreciably with the variation of embedding parameters. We noticed that the velocity ratio has a dual behaviour on the momentum boundary layer. On the other hand the thermal boundary layer thins when the velocity ratio is increased. The results indicate a significant increase in the velocity and a decrease in thermal boundary layer thickness with an intensification in the viscoelastic effects.

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