Analytical Solutions of Heat-Conduction Problems with Time-Varying Heat-Transfer Coefficients

2015 ◽  
Vol 88 (3) ◽  
pp. 688-698 ◽  
Author(s):  
V. A. Kudinov ◽  
A. V. Eremin ◽  
E. V. Stefanyuk
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solutions ◽  
Time Varying ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

scholarly journals Heat and mass transfer in the process of heat treatment and drying of natural leather with the convective method of energy supply

2021 ◽  
Vol 66 (1) ◽  
pp. 84-92
Author(s):  
A. O. Ol’shanskii ◽  
A. M. Gusarov ◽  
S. V. Zhernosek
Keyword(s):  
Heat Transfer ◽  
Heat Treatment ◽  
Mass Transfer ◽  
Heat Conduction ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Unsteady Heat Conduction

In the work, the authors investigated the possibility of using the results of analytical solutions of the linear differential equations of unsteady heat conduction with constant heat transfer coefficients to calculate the temperature of the material during heat treatment of leathers. Heat treatment of natural leathers as heat-sensitive materials is carried out under mild temperature conditions and high air moisture contents, the temperature does not undergo significant changes, and the heat transfer coefficients change almost linearly. When using analytical solutions, the authors made the assumptions that for small temperature gradients over the cross section of a thin body, the thermal transfer of matter can be neglected and for values of the heat and mass transfer Biot criteria less than unity, the main factor, limiting heat and mass transfer, is the interaction of the evaporation surface of the body with the environment; so, in solving the differential heat equation we can restrict ourselves to one first member of an infinite series. In this case, a piecewise stepwise approximation of all thermophysical characteristics with constant values of these coefficients at the calculated time intervals was applied, which made it possible to take into account the change in the transfer coefficients throughout the entire heat treatment process. Processing of experimental data showed that in low-intensity processes with reliable values of the transfer coefficients, it is possible to use the results of solutions of differential equations of unsteady heat conduction in heat transfer calculations. The results of the study of heat transfer during drying of leather confirm the laws of temperature change established experimentally. Together with experimental studies of drying processes, analytical studies are of great practical importance in the development of new methods for calculating heat and mass transfer in wet bodies.

Inverse Determination of Steady Heat Convection Coefficient Distributions

1998 ◽  
Vol 120 (2) ◽  
pp. 328-334 ◽  
Author(s):  
T. J. Martin ◽  
G. S. Dulikravich
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Measurement Data ◽  
Cost Effective ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Simple Modification ◽  
Heat Transfer Coefficients ◽  
Thermal Boundary Conditions

An inverse Boundary Element Method (BEM) procedure has been used to determine unknown heat transfer coefficients on surfaces of arbitrarily shaped solids. The procedure is noniterative and cost effective, involving only a simple modification to any existing steady-state heat conduction BEM algorithm. Its main advantage is that this method does not require any knowledge of, or solution to, the fluid flow field. Thermal boundary conditions can be prescribed on only part of the boundary of the solid object, while the heat transfer coefficients on boundaries exposed to a moving fluid can be partially or entirely unknown. Over-specified boundary conditions or internal temperature measurements on other, more accessible boundaries are required in order to compensate for the unknown conditions. An ill-conditioned matrix results from the inverse BEM formulation, which must be properly inverted to obtain the solution to the ill-posed problem. Accuracy of numerical results has been demonstrated for several steady two-dimensional heat conduction problems including sensitivity of the algorithm to errors in the measurement data of surface temperatures and heat fluxes.

A Numerical Evaluation of a Simple Procedure for Using Transient Surface Temperature Measurements to Determine Local Convective Heat Transfer Rates

1999 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
David Naylor
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Inverse Heat Conduction ◽  
Transfer Coefficients ◽  
Transfer Rates ◽  
Heat Transfer Coefficients

Abstract A transient method, based on an inverse heat conduction solution, for experimentally determining the distribution of local heat transfer rates on the surface of a body has been numerically evaluated. The particular interest is in situations in which the heat transfer coefficients are relatively low and in which there are relatively large changes in the heat transfer coefficient over the surface of the body being considered. In the method, a solid body of the shape being investigated, constructed from a low conductivity material, is heated to a uniform temperature and then exposed to a test flow. Using a layer of temperature sensitive crystal placed over the surface of this model or by other means, the time taken for the temperature at a relatively small number of selected points on the surface to reach a selected value is determined. The surface heat flux rate distribution is then found from these measured times using a simple inverse heat conduction method. The feasibility of this method has been evaluated by considering relatively low Reynolds number flow over a square cylinder and natural convective flow over a circular cylinder. Known local heat transfer coefficient distributions for these situation have been applied as boundary conditions in the numerical solution of the transient cooling of a the “experimental” models. These solutions are used to generate “measured” data i.e. to generate simulated experimental data. The inverse heat transfer method has then been used to predict the local heat transfer coefficient distribution over the surface and the predicted and input distributions have been compared. The effect of uncertainties in the experimental measurements on this comparison has then been evaluated using various assumed uncertainty values. The results of the study indicate that the proposed method of measuring local heat transfer coefficients is capable of giving results of good accuracy.

Reconstruction of the heat transfer coefficients and heat fluxes in heat conduction problems

2021 ◽  
Author(s):  
Talaat Abdelhamid ◽  
Ammar H. Elsheikh ◽  
Olatunji Mumini Omisore ◽  
N.A. Saeed ◽  
T. Muthuramalingam ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Heat Fluxes ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

Numerical Analysis of Heat Conduction in Cooling of Aluminum Extrusion

2002 ◽  
Author(s):  
Nicola Bianco ◽  
Oronzio Manca
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Cooling System ◽  
Heat Conduction Problem ◽  
Aluminum Extrusion ◽  
Transfer Coefficients ◽  
Lower Velocity ◽  
Heat Transfer Coefficients ◽  
Water Sprays ◽  
Volume Method

A thermal analysis of the cooling of an extruded aluminum alloy by means of water sprays is carried out. The heat conduction problem has been solved numerically by means of a finite volume method. The heat transfer coefficients used in the boundary conditions has been evaluated by means of spray heat transfer correlations, which relate these coefficients to the spray hydrodynamic parameters. The influence of the number of sprays and of the solid velocity has been investigated. Results show that the efficiency of the cooling system decreases as the number of jets increases. The efficiency of each spray increases with the velocity for the same number of sprays. As the workpiece velocity increases it needs to increase the number of sprays to obtain the same temperature difference between the entry and the exit of the cooling system. The greater the number of sprays related to the case with lower velocity, the smaller the increase of the number of sprays.

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