Unsteady Stagnation Point Heat Transfer

1965 ◽  
Vol 87 (2) ◽  
pp. 221-230 ◽  
Author(s):  
B. T. Chao ◽  
D. R. Jeng
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Surface Temperature ◽  
Thermal Boundary Layer ◽  
Essential Feature ◽  
Step Change ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Time Solution

An analysis is presented for the unsteady laminar, forced-convection heat transfer at a two-dimensional and axisymmetrical front stagnation due to an arbitrarily prescribed wall temperature or heat flux variation. The flow is incompressible and steady. The procedure begins with a consideration of the thermal boundary-layer response caused by either a step change in surface temperature or heat flux. Two appropriate asymptotic solutions, valid for small and large times, respectively, are found and satisfactorily joined for Prandtl numbers ranging from 0.01 to 100. The key to the small time solution is the transformation of the energy equation in the Laplace transform plane to an ordinary differential equation with a large parameter. An essential feature of the large time solution is the use of Meksyn’s transformation variable and the method of steepest descent in the evaluation of integrals. It is found that, for both two-dimensional and axisymmetrical stagnation, the time required for the thermal boundary layer to attain steady condition, for either a step change in surface temperature or heat flux, varies inversely with the free stream velocity and directly with 1/4 power of the Prandtl number of the fluid.

Calculation of a Turbulent Boundary Layer Downstream of a Step Change in Surface Temperature

1979 ◽  
Vol 101 (1) ◽  
pp. 144-150 ◽  
Author(s):  
L. W. B. Browne ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Surface Temperature ◽  
Reynolds Shear Stress ◽  
Turbulent Viscosity ◽  
Step Change ◽  
Mean Temperature ◽  
Thermal Layer ◽  
Good Agreement

Mean temperature and heat flux distributions in a thermal layer that develops within a momentum boundary layer subjected to a step change in surface temperature are calculated using two different methods. The method of Bradshaw and Unsworth, which uses the method of Bradshaw, Ferriss and Atwell to determine the mean velocity and Reynolds shear stress distributions and then assumes a constant turbulent Prandtl number for the heat flux calculation, yields heat flux distributions that are significantly different than the available experimental results at small distances from the step. Good agreement between calculations and experimental values is achieved when the distance x from the step is about 20 δ0, where δ0 is the boundary layer thickness at the step. To obtain good agreement with measurements of heat flux and mean temperature near the step, estimated distributions of turbulent viscosity and effective Prandtl number have been derived using an iterative updating procedure and the calculation method of Patankar and Spalding. These distributions are compared with those available in the literature. Calculated heat flux distributions show that the internal thermal layer is only likely to reach self-preserving conditions when x exceeds 40 δ0.

Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of a Nanofluid Over Non-Isothermal Stretching Sheet

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Wubshet Ibrahim ◽  
B. Shanker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Surface Temperature ◽  
Stretching Sheet ◽  
Lewis Number ◽  
Flow And Heat Transfer ◽  
Layer Flow

The boundary-layer flow and heat transfer over a non-isothermal stretching sheet in a nanofluid with the effect of magnetic field and thermal radiation have been investigated. The transport equations used for the analysis include the effect of Brownian motion and thermophoresis. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., thermal radiation parameter R, Prandtl number Pr, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order nonlinear ordinary differential equations. These equations were numerically solved using a fourth-order Runge–Kutta method with shooting technique. The analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to see the effects of governing parameters for various physical conditions. Numerical results are obtained for distribution of velocity, temperature and concentration, for both cases i.e., prescribed surface temperature and prescribed heat flux, as well as local Nusselt number and Sherwood number. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nt and Lewis number Le. Besides, it is found that the surface temperature increases with an increase in the Lewis number Le for prescribed heat flux case. A comparison with the previous studies available in the literature has been done and we found an excellent agreement with it.

Protuberances in a Turbulent Thermal Boundary Layer

2011 ◽  
Author(s):  
Steven R. Mart ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Boundary Layers ◽  
Thermal Boundary Layer ◽  
Leading Edge ◽  
Heated Plate ◽  
Fluid Temperature ◽  
Constant Flux ◽  
Thermal Boundary Layers

Recent efforts to evaluate the effects of isolated protuberances within velocity and thermal boundary layers have been performed using transient heat transfer approaches. While these approaches provide accurate and highly resolved measurements of surface flux, measuring the state of the thermal boundary-layer during transient tests with high spatial resolution presents several challenges. As such, the heat transfer enhancement evaluated during transient tests are presently correlated to a Reynolds number based either on the distance from the leading edge or on the momentum thickness. Heat flux and temperature variations along the surface of a turbine blade may cause significant differences between the shapes and sizes of the velocity and thermal boundary layer profiles. Therefore, correlations are needed which relate the states of both the velocity and thermal boundary layers to protuberance and roughness distribution heat transfer. In this study, a series of three experiments are performed for various freestream velocities to investigate the local temperature details of protuberances interacting with thermal boundary layers. The experimental measurements are performed using isolated protuberances of varying thermal conductivity on a steadily-heated, constant flux flat plate. In the first experiment, detailed surface temperature maps are recorded using infrared thermography. In the second experiment, the unperturbed velocity profile over the plate without heating is measured using hot-wire anemometry. Finally, the thermal boundary layer over the steadily heated plate is measured using a thermocouple probe. Because of the constant flux experimental configuration, the protuberances provide negligible heat flux augmentation. Consequently, the variation in protuberance temperature is investigated using the velocity boundary layer parameters, the thermal boundary layer parameters, and the local fluid temperature at the protuberance apices. A comparison of results using plastic and steel protuberances illuminates the importance of the shape of the thermal and velocity boundary layers in determining the minimum protuberance temperatures.

scholarly journals Thermal-Boundary-Layer Response to Convected Far-Field Fluid Temperature Changes

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
Hongwei Li ◽  
M. Razi Nalim
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Thermal Boundary Layer ◽  
Steady State Solution ◽  
Step Change ◽  
Far Field ◽  
Fluid Temperature ◽  
Constant Wall Temperature

Fluid flows of varying temperature occur in heat exchangers, nuclear reactors, nonsteady-flow devices, and combustion engines, among other applications with heat transfer processes that influence energy conversion efficiency. A general numerical method was developed with the capability to predict the transient laminar thermal-boundary-layer response for similar or nonsimilar flow and thermal behaviors. The method was tested for the step change in the far-field flow temperature of a two-dimensional semi-infinite flat plate with steady hydrodynamic boundary layer and constant wall temperature assumptions. Changes in the magnitude and sign of the fluid-wall temperature difference were considered, including flow with no initial temperature difference and built-up thermal boundary layer. The equations for momentum and energy were solved based on the Keller-box finite-difference method. The accuracy of the method was verified by comparing with related transient solutions, the steady-state solution, and by grid independence tests. The existence of a similarity solution is shown for a step change in the far-field temperature and is verified by the computed general solution. Transient heat transfer correlations are presented, which indicate that both magnitude and direction of heat transfer can be significantly different from predictions by quasisteady models commonly used. The deviation is greater and lasts longer for large Prandtl number fluids.

Heat transfer from surfaces of non-uniform temperature

1958 ◽  
Vol 4 (1) ◽  
pp. 22-32 ◽  
Author(s):  
D. B. Spalding
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Temperature Distribution ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Total Heat Flux ◽  
Uniform Temperature ◽  
Steady Heat ◽  
Arbitrary Velocity

The paper deals with the calculation of steady heat transfer from a surface of arbitrary temperature distribution to a laminar semi-infinite stream of arbitrary velocity distribution. Lighthill's method is improved by a correction which accounts for the departures from linearity of the velocity profile within the thermal boundary layer, and which comprehends the influences of Prandtl number, pressure gradient, body forces, and non-coincident start of velocity and thermal layers. Methods are given for evaluating the total heat flux directly, and for integrating the differential equations for the growth of the boundary layer thickness by means of quadratures.

Instantaneous Heat Flux Simulation of a Motored Reciprocating Engine: Unsteady Thermal Boundary Layer With Variable Turbulent Thermal Conductivity

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Abdalla Agrira ◽  
David R. Buttsworth ◽  
Mior A. Said
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Thermal Boundary Layer ◽  
Combustion Engine ◽  
Turbulent Viscosity ◽  
Spark Ignition Engine ◽  
Turbulent Prandtl Number

Due to the inherently unsteady environment of reciprocating engines, unsteady thermal boundary layer modeling may improve the reliability of simulations of internal combustion engine heat transfer. Simulation of the unsteady thermal boundary layer was achieved in the present work based on an effective variable thermal conductivity from different turbulent Prandtl number and turbulent viscosity models. Experiments were also performed on a motored, single-cylinder spark-ignition engine. The unsteady energy equation approach furnishes a significant improvement in the simulation of the heat flux data relative to results from a representative instantaneous heat transfer correlation. The heat flux simulated using the unsteady model with one particular turbulent Prandtl number model agreed with measured heat flux in the wide open and fully closed throttle cases, with an error in peak values of about 6% and 35%, respectively.

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