An approximate solution for a steady-state problem involving conditions of convective heat transfer

1968 ◽  
Vol 15 (2) ◽  
pp. 685-688 ◽  
Author(s):  
R. A. Pavlovskii
Keyword(s):  
Heat Transfer ◽  
Approximate Solution ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
State Problem ◽  
Steady State Problem

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

Role of blood as heat source or sink in human limbs during local cooling and heating

1994 ◽  
Vol 76 (5) ◽  
pp. 2084-2094 ◽  
Author(s):  
M. B. Ducharme ◽  
P. Tikuisis
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Steady State ◽  
Heat Source ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Total Heat Loss ◽  
Partial Immersion ◽  
Thermal Steady State

The objective of the present study was to investigate the relative contribution of the convective heat transfer in the forearm and hand to 1) the total heat loss during partial immersion in cold water [water temperature (Tw) = 20 degrees C] and 2) the heat gained during partial immersion in warm water (Tw = 38 degrees C). The heat fluxes from the skin of the forearm and finger were continuously monitored during the 3.5-h immersion of the upper limb (forearm and hand) with 23 recalibrated heat flux transducers. The last 30 min of the partial immersion were conducted with an arterial occlusion of the forearm. The heat flux values decreased during the occlusion period at Tw = 20 degrees C and increased at Tw = 38 degrees C for all sites, plateauing only for the finger to the value of the tissue metabolic rate (124.8 +/- 29.0 W/m3 at Tw = 20 degrees C and 287.7 +/- 41.8 W/m3 at Tw = 38 degrees C). The present study shows that, at thermal steady state during partial immersion in water at 20 degrees C, the convective heat transfer between the blood and the forearm tissue is the major heat source of the tissue and accounts for 85% of the total heat loss to the environment. For the finger, however, the heat produced by the tissue metabolism and that liberated by the convective heat transfer are equivalent. At thermal steady state during partial immersion in water at 38 degrees C, the blood has the role of a heat sink, carrying away from the limb the heat gained from the environment and, to a lesser extent (25%), the metabolic and conductive heats. These results suggest that during local cold stress the convective heat transfer by the blood has a greater role than that suggested by previous studies for the forearm but a lesser role for the hand.

Numerical and Experimental Study of Flow and Convective Heat Transfer on a Rotor of a Discoidal Machine with Eccentric Impinging Jet

2019 ◽  
pp. 1-29
Author(s):  
Chadia Haidar ◽  
Rachid Boutarfa ◽  
Mohamed Sennoune ◽  
Souad Harmand
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Air Flow ◽  
Impinging Jet ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Air Jet

This work focuses on the numerical and experimental study of convective heat transfer in a rotor of a discoidal the machine with an eccentric impinging jet. Convective heat transfers are determined experimentally in steady state on the surface of a single rotating disk. The experimental technique is based on the use of infrared thermography to access surface temperature measurement, and on the numerical resolution of the energy equation in steady-state, to evaluate local convective coefficients. The results from the numerical simulation are compared with heat transfer experiments for rotational Reynolds numbers between 2.38×105 and 5.44×105 and for the jet's Reynolds numbers ranging from 16.5×103 to 49.6 ×103. A good agreement between the two approaches was obtained in the case of a single rotating disk, which confirms us in the choice of our numerical model. On the other hand, a numerical study of the flow and convective heat transfer in the case of an unconfined rotor-stator system with an eccentric air jet impinging and for a dimensionless spacing G=0.02, was carried out. The results obtained revealed the presence of different heat transfer zones dominated either by rotation only, by the air flow only or by the dynamics of the rotation flow superimposed on that of the air flow. Critical radii on the rotor surface have been identified

Casing Convective Heat Transfer Coefficient and Reference Freestream Temperature Determination Near an Axial Flow Turbine Rotor

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
C. Camci ◽  
B. Gumusel
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Heat Transfer Coefficient ◽  
Axial Flow ◽  
Reference Temperature ◽  
Steady State Heat Transfer

The present study explains a steady-state method of measuring convective heat transfer coefficient on the casing of an axial flow turbine. The goal is to develop an accurate steady-state heat transfer method for the comparison of various casing surface and tip designs used for turbine performance improvements. The freestream reference temperature, especially in the tip gap region of the casing, varies monotonically from the rotor inlet to rotor exit due to work extraction in the stage. In a heat transfer problem of this nature, the definition of the freestream temperature is not as straightforward as constant freestream temperature type problems. The accurate determination of the convective heat transfer coefficient depends on the magnitude of the local freestream reference temperature varying in axial direction, from the rotor inlet to exit. The current study explains a strategy for the simultaneous determination of the steady-state heat transfer coefficient and freestream reference temperature on the smooth casing of a single stage rotating turbine facility. The heat transfer approach is also applicable to casing surfaces that have surface treatments for tip leakage control. The overall uncertainty of the method developed is between 5% and 8% of the convective heat transfer coefficient.

Evaluation of a Hue Capturing Based Transient Liquid Crystal Method for High-Resolution Mapping of Convective Heat Transfer on Curved Surfaces

1993 ◽  
Vol 115 (2) ◽  
pp. 311-318 ◽  
Author(s):  
C. Camci ◽  
K. Kim ◽  
S. A. Hippensteele ◽  
P. E. Poinsatte
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Steady State ◽  
Liquid Crystals ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Bottom Surface ◽  
Curved Surfaces ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

Accurate determination of convective heat transfer coefficients on complex curved surfaces is essential in the aerothermal design and analysis of propulsion system components. The heat transfer surfaces are geometrically very complex in most of the propulsion applications. This study focuses on the evaluation of a hue capturing technique for the heat transfer interpretation of liquid crystal images from a complex curved heat transfer surface. Impulsively starting heat transfer experiments in a square to rectangular transition duct are reported. The present technique is different from existing steady-state hue capturing studies. A real-time hue conversion process on a complex curved surface is adopted for a transient heat transfer technique with high spatial resolution. The study also focuses on the use of encapsulated liquid crystals with narrow color band in contrast to previous steady-state hue based techniques using wide band liquid crystals. Using a narrow band crystal improves the accuracy of the heat transfer technique. Estimated uncertainty for the heat transfer coefficient from the technique is about 5.9 percent. A complete heat transfer map of the bottom surface was possible using only seven liquid crystal image frames out of the 97 available frames during the transient experiment. Significant variations of heat transfer coefficients are quantitatively visualized on the curved surfaces of the transition duct.

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