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Fourier heat flux

The Fourier heat flux model under macroscopic continuum formulation is given as... [Pg.310]

The failure of thermodynamic equilibrium and continuum is not well defined for liquids. Therefore, the validity of no-slip, no-temperature-jump, linear stress-strain relation and Fourier heat flux-temperature relationship are unknown for liquids. [Pg.335]

The Fourier law gives the rate at which heat is transferred by conduction through a substance without mass transfer. This states that the heat flow rate per unit area, or heat flux, is proportional to the temperature gradient in the direction of heat flow. The relationship between heat flux and temperature gradient is characterized by the thermal conductivity which is a property of the substance. It is temperature dependent and is determined experimentally. [Pg.346]

The constant of proportionality k is known as the thermal conductivity of the material and the above relationship is known as Fourier s law for conduction in one dimension. The thermal conductivity k is the heat flux which results from unit temperature gradient in unit distance. In s.i. units the thermal conductivity, k, is expressed in Wm"1 K. Integration of Fourier s law yields... [Pg.313]

Fourier s law for thermal conduction An equation describing the relationship between the rate of heat flux and the temperature gradient. See Eq. (23). [Pg.37]

The first step in the process is to relate heat flow to a temperature gradient, just as a diffusive flux can be related to a concentration gradient. The fundamental law of heat conduction was proposed by Jean Fourier in 1807 and relates the heat flux (q) to the temperature gradient ... [Pg.703]

The other mode of heat transfer is conduction. The conductive heat flux is, by Fourier s law,... [Pg.16]

Prior to any test, the system was controlled for 8-10 hours to make sure that steady state was achieved. Once steady state was reached, the temperatures of all the thermocouples were measured and recorded to determine the temperature drop across the sample material. Because the heat flux is proportional to the temperature difference, the through-plate thermal conductivity across the material can be determined using Fourier s law [141] ... [Pg.274]

Heat can be transferred by conduction, convection, or radiation and/or combinations thereof. Heat transfer within a homogeneous solid or a perfectly stagnant fluid in the absence of convection and radiation takes place solely by conduction. According to Fourier s law, the rate of heat conduction along the y-axis per unit area perpendicular to the y-axis (i.e., the heat flux q, expressed as W in - or kcal m 2 h ) will vary in proportion to the temperature gradient in the y direction, dt/dy (°C m or K m ), and also to an intensive material property called heat or thermal conductivity k (W m K or kcal h m °C ). Thus,... [Pg.14]

Fourier s law states that heat flux (W/m2 or J/s-m2) is proportional to the negative gradient of the temperature field, with the constant of proportionality being a material property called the thermal conductivity A.,... [Pg.103]

In this form Fourier s law is substituted for the heat flux. The thermal conductivity X is the average conductivity of the fluid mixture. In subsequent chapters we discuss the details of how the thermal conductivity is determined and the process to calculate the mixture-averaged values. [Pg.114]

In the Couette-Poiseuille problem, which considered fluid flow alone, the drag on the surfaces could be determined from the velocity gradients. Similarly the heat flux from the fluid to the walls can be determined from Fourier s law, using the calculated temperature gradient ... [Pg.166]

The heat flux at the wall at any z position can be determined from the radial temperature profiles using Fourier s law as... [Pg.190]

Using the empirical laws displayed in Table 2.1, the entropy production can be identified for a few special cases. For instance, if only heat flow is occurring, then, using Eq. 2.15 and Fourier s heat-flux law,... [Pg.29]

From a microscopic standpoint, thermal conduction refers to energy being handed down from one atum or molecule in the next one. In a liquid or gas, ihese particles change their position continuously even withoul visible movemeni and they transport energy also in this way. From a macroscopic or continuum viewpoint, thermal conduction is quantitatively described by Fourier s equation, which states that the heat flux q per unit time and unit area through an area element arbitrarily located in the medium is proportional to the drop in temperature, -grad T. per unit length in the direction normal to the area and to a transport property k characteristic of the medium and called thermal conductivity ... [Pg.758]

For Equations (3.6) and (3.7), Fourier s law can be used to relate the heat flux to the temperature gradient in a continuum medium ... [Pg.55]

Conductive heat transfer does not require any motion of atoms or molecules, as only the interactions between atoms or molecules transfers heat. The heat flux expressed in W rn 2 can be described using Fourier s law ... [Pg.341]

We have previously reported that the destabilizing force is a consequence of the heat diffusion mechanism (for details see ref. [36]). The diffusive heat flux across a medium with thermal conductivity k is given by Fourier s law. [Pg.14]

When a temperature gradient exists in a material, energy in the form of heat is conducted from a high-temperature region to a low-temperature region through intermolecular and atomic impacts, lattice vibrations, and transport of electrons. This type of thermal energy transfer is called conductive heat transfer. The relation between heat flux induced by thermal conduction and temperature can be described by Fourier s law as... [Pg.33]

The energy equation expressed in terms of temperature is convenient for evaluating heat fluxes. Let e = cyT with cv the specific heat at constant volume and T the absolute temperature of the fluid. Assuming the heat flux Jq obeys Fourier s law, Eq. (5.18) takes the form... [Pg.170]

The heat flux can be expressed in terms of temperature gradient by the Fourier equation ... [Pg.56]

The heat flux into the solid is obtained by differentiating Eq. E5.2-9 with respect to x, and using Fourier s law... [Pg.188]

Rate of Heat Transfer. Fourier s Law may be integrated and solved for a number of geometries to relate the rate of heat transfer by conduction to the temperature driving force. Equations are given below that allow the calculation of steady-state heat flux and temperature profiles for a number of geometries. [Pg.98]

The superposition principle for heat flow as measured by power-compensated DSC should apply—just as it would be expected that the water flow into one tank from two pipes would be additive. Assuming Fourier s law holds (steady state heat flow proportional to temperature gradient), the temperature differences measured in DTA (and heat-flux DSC) are additive via contributions from multiple transformation sources within the sample material. [Pg.143]

The local heat flux from the surface to the fluid at any x value may be computed by Fourier s heat conduction law,... [Pg.146]

Using Fourier s law, thq boundary condition on temperature at the wall in the specified heat flux case is ... [Pg.138]

This equation allows the 0,. values to be found. The boundary conditions give 0,1 = 0, 2 and either 0,jy = 1 or0,jv = 0, -1 + AY depending on whether the wall temperature or the wall heat flux is specified. Once these values are determined, the heat transfer rate can be found. The local heat transfer rate at the wall at any value of Z is given by using Fourier s law as ... [Pg.216]


See other pages where Fourier heat flux is mentioned: [Pg.189]    [Pg.189]    [Pg.722]    [Pg.726]    [Pg.36]    [Pg.703]    [Pg.708]    [Pg.9]    [Pg.56]    [Pg.319]    [Pg.27]    [Pg.247]    [Pg.787]    [Pg.267]    [Pg.88]    [Pg.758]    [Pg.472]    [Pg.156]    [Pg.60]    [Pg.510]    [Pg.92]    [Pg.115]   
See also in sourсe #XX -- [ Pg.310 , Pg.335 ]




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