Laminar Heat Transfer in a Channel With Unsteady Flow and Wall Heating Varying With Position and Time

1963 ◽  
Vol 85 (4) ◽  
pp. 358-365 ◽  
Author(s):  
R. Siegel ◽  
M. Perlmutter
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Heat Production ◽  
Fluid Velocity ◽  
Isothermal Condition ◽  
Convection Heat Transfer ◽  
Channel Cross Section ◽  
Fluid Temperature ◽  
Parallel Plates ◽  
General Relations

An analysis is made of incompressible laminar forced convection heat transfer between two parallel plates that have a specified heat production to be dissipated at their surfaces. The heat production can vary in an arbitrary manner with time and position along the channel, starting from an initially isothermal condition. The fluid velocity is assumed constant over the channel cross section, but can vary with time. The variation of fluid temperature over the channel cross section is accounted for. General relations are presented in closed form and their application is illustrated by carrying out some typical examples. The results are compared with previous analyses that have assumed constant temperatures over the channel cross section and a constant heat-transfer coefficient.

Optimization of Micro Channel Morphology

2006 ◽  
Author(s):  
Aleksander Vadnjal ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Media ◽  
Cross Section ◽  
Channel Morphology ◽  
Channel Cross Section ◽  
Micro Channel ◽  
Parallel Plates ◽  
Conservation Of Energy ◽  
Micro Channels

An increasing demand for a higher heat flux removal capability within a smaller volume for high power electronics led us to focus on micro channels in contrast to the classical heat fin design. A micro channel can have various shapes to enhance heat transfer, but the shape that will lead to a higher heat flux removal with a moderate pumping power needs to be determined. The standard micro-channel terminology is usually used for channels with a simple cross section, e.g. square, round, triangle, etc., but here the micro channel cross section is going to be expanded to describe more complicated and interconnected micro scale channel cross sections. The micro channel geometries explored are pin fins (in-line and staggered), parallel plates and sintered porous micro channels (see Fig.1). The problem solved here is a conjugate problem involving two heat transfer mechanisms; 1) porous media effective conductivity and 2) internal convective heat transfer coefficient. Volume averaging theory (VAT) is used to rigorously cast the point wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of the micro channel (porous media) morphology. Using the resulting VAT based field equations, optimization of a micro channel heated from one side is used to determine the optimum micro channel morphology. A small square of 1 cm 2 is chosen as an example and the thermal resistance, 0C/W, and pressure drop are shown as a function of Reynolds number.

scholarly journals Numerical investigation fluid velocity and heat transfer on the stretching sheet by VIM method and optimization fluid temperature and velocity parameter by Prandtl number and viscoelastic parameter

2021 ◽  
Author(s):  
Pooya Pasha ◽  
Ali Hosin Alibak ◽  
Hossein Nabi ◽  
Farzad tat Shahdost
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Iteration Method ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Convection Heat Transfer ◽  
Fluid Temperature ◽  
Viscoelastic Parameter ◽  
Velocity Changes ◽  
Variation Iteration Method

This study aimed at investigating the variation of heat transfer and velocity changes of the fluid flow along the vertical line on a surface drawn from both sides. In the beginning, the several parameters such as Prandtl number and viscoelastic effect evaluated for heat transfer and fluid velocity by variation Iteration method. The results were compared with the numerical method. The second part of the description relates to the use RSM method in the Design Expert software. In this paper by using the RSM method, optimized the fluid velocity and heat transfer passing from the stretching sheet. By increasing the Prandtl number, the convection heat transfer 43 % increased ratio the minimum Prandtl number. In accordance with balanced modes for Prandtl number and viscoelastic parameter and wall temperature, the best optimization occurred for fluid velocity and fluid temperature with f=0.67 and θ=0.606. The results of variation iteration method are accurate for the nonlinear solution. As the value of k increases, the value of fluid velocity indicates an increase and by increase Prandtl number, the value of Temperature decreases.

Unsteady Laminar Flow in a Duct With Unsteady Heat Addition

1961 ◽  
Vol 83 (4) ◽  
pp. 432-440 ◽  
Author(s):  
Morris Perlmutter ◽  
Robert Siegel
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Nuclear Reactor ◽  
Transient Processes ◽  
Channel Cross Section ◽  
Fluid Temperature ◽  
Parallel Plates ◽  
Reactor Shutdown ◽  
Thermal Entrance ◽  
Insight Into

An analysis is made of transient heat transfer with transient laminar flow between heated (or cooled) parallel plates. The transient processes are caused by simultaneously changing the fluid pumping pressure and either the wall temperature or the wall heat flux. The solution is obtained for both the thermal entrance and fully developed heat-transfer regions. The slug-flow simplification is made; that is, the velocity at any instant of time is taken as uniform throughout the channel. The fluid temperature distribution, however, depends on both the axial co-ordinate and the position within the channel cross section. A few numerical examples are carried out which give some insight into various transient processes such as those occurring during a nuclear-reactor shutdown.

Numerical Study of Flow and Heat Transfer of High Knudsen Number Flow Regimes in Nanochannels Filled with Porous Media

2011 ◽  
Vol 403-408 ◽  
pp. 5324-5329
Author(s):  
A.H. Meghdadi Isfahani ◽  
A. Soleimani
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Porous Media ◽  
Cross Section ◽  
Flow Model ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Circular Cross Section ◽  
Flow Regimes ◽  
Channel Cross Section

Considering the dependency of viscosity on Kn, a unified flow model for all flow regimes with different Kn was obtained. Applying the Dary Brinkman – Forchheimer flow model with the slip boundary condition, finite difference solutions for fully developed velocity distribution in a nanochannel of circular cross section, filled with porous media was presented. Convection heat transfer of the system, reflected in Nu was analyzed using the temperature jump boundary condition. It is shown that despite of the fact that in most of previous researches, Kn was assumed constant along the channel, the variations of Kn due to the pressure variations, have considerable effects on heat transfer and temperature distribution across the channel cross section.

Radiation and Convection Heat Transfer in a Porous Bed

1968 ◽  
Vol 90 (1) ◽  
pp. 51-54 ◽  
Author(s):  
W. A. Beckman
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Collection Efficiency ◽  
Convection Heat Transfer ◽  
Heat Fluxes ◽  
Fluid Temperature ◽  
Radiation Heat ◽  
Radiation Heat Flux ◽  
Flowing Fluid ◽  
Porous Bed

The one-dimensional steady-state temperature distribution within an isotropic porous bed subjected to a collimated and/or diffuse radiation heat flux and a transparent flowing fluid has been determined by numerical methods. The porous bed was assumed to be nonscattering and to have a constant absorption coefficient. Part of the radiation absorbed by the porous bed is reradiated and the remainder is transferred to the fluid by convection. Due to the assumed finite volumetric heat transfer coefficient, the bed and fluid have different temperatures. A bed with an optical depth of six and with a normal incident collimated radiation heat flux was investigated in detail. The radiation incident on the bed at the fluid exit was assumed to originate from a black surface at the fluid exit temperature. The investigation covered the range of incident diffuse and collimated radiation heat fluxes expected in a nonconcentrating solar energy collector. The results are presented in terms of a bed collection efficiency from which the fluid temperature rise can be calculated.

Inverse Boundary Design Combining Radiation and Convection Heat Transfer

2001 ◽  
Vol 123 (5) ◽  
pp. 884-891 ◽  
Author(s):  
Francis H. R. Franc¸a ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Linear Equations ◽  
Convection Heat Transfer ◽  
Parallel Plates ◽  
Heat Flux Distribution ◽  
Inverse Boundary ◽  
Value Decomposition ◽  
Non Linear Equations ◽  
Combined Mode

This work investigates inverse boundary design for radiation, convection and conduction combined-mode heat transfer. The problem consists of finding the heat flux distribution on a heater that satisfies both the temperature and the heat flux prescribed on a design surface of an enclosure formed by two finite parallel plates. A gray participating medium flows in laminar regime between the walls, which are gray, diffuse emitters and absorbers. All the thermal properties are uniform. This problem is described by an ill-conditioned system of non-linear equations. The solution is obtained by regularizing the system of equations by means of truncated singular value decomposition (TSVD).

Experimental and Numerical Investigation of Convection Heat Transfer of CO2 at Supercritical Pressures in a Vertical Mini Tube

2004 ◽  
Author(s):  
Pei-Xue Jiang ◽  
Yi-Jun Xu ◽  
Run-Fu Shi ◽  
S. He
Keyword(s):  
Heat Transfer ◽  
Wall Thickness ◽  
Fluid Pressure ◽  
Convection Heat Transfer ◽  
Local Heat Transfer ◽  
Fluid Temperature ◽  
Convection Heat ◽  
Transfer Coefficients ◽  
Bulk Fluid ◽  
Heat Transfer Coefficients

Convection heat transfer of CO2 at supercritical pressures in a vertical mini tube with a diameter of 0.948 mm was investigated experimentally and numerically. The local heat transfer coefficients, bulk fluid temperatures and wall temperatures were measured and presented. The effects of inlet fluid temperature, fluid pressure, mass flow rate, heat flux and wall thickness on the convection heat transfer in the mini tube were investigated. The experimental results were compared with calculated results using well-known correlations and numerical simulations. The results showed that the variable thermophysical properties of supercritical CO2 significantly influenced the convection heat transfer in the vertical mini tube and that for the studied conditions the influence of the wall thickness on the convection heat transfer in the mini tube was not great. For bulk fluid temperatures higher than the pseudo-critical temperature, the simulation results and the correlation results for the convection heat transfer coefficients in the mini tube corresponded well to the experimentally measured results.

Numerical Analysis of Vapor Bubble Growth and Wall Heat Transfer During Flow Boiling of Water in a Microchannel

2005 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Vapor Bubble ◽  
Bubble Growth ◽  
Stokes Equations ◽  
Flow Boiling ◽  
Navier Stokes ◽  
Channel Cross Section ◽  
Wall Heat Transfer ◽  
Wall Superheat

The present study is performed to analyze the wall heat transfer mechanisms during growth of a vapor bubble inside a microchannel. The microchannel is of 200 μm square cross section and a vapor bubble begins to grow at one of the walls, with liquid coming in through the channel inlet. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. The bubble grows rapidly due to heat transfer from the walls and soon turns into a plug filling the entire channel cross section. The average wall heat transfer at the channel walls is studied for different values of wall superheat and incoming liquid mass flux. The results show that the wall heat transfer increases with wall superheat but is almost unaffected by the liquid flow rate. The bubble growth is found to be the primary mechanism of increasing wall heat transfer as it pushes the liquid against the walls thereby influencing the thermal boundary layer development.

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