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Modelling of Heat Transfer During Deep Fat Frying of Food
Published in Surajbhan Sevda, Anoop Singh, Mathematical and Statistical Applications in Food Engineering, 2020
KK Dash, Maanas Sharma, MA Bareen
Fourier number represents the dimensionless time. It may be interpreted as the ratio of current time to time to reach steady-state. The Fourier number is a dimensionless number that characterizes heat conduction. It is the ratio of diffusive/conductive transport rate by the quantity storage rate and arises from non-dimensionalization of the heat equation. Fourier number can be obtained by multiplying the dimensional time by the thermal diffusivity and dividing by the square of the characteristic length: () Fo=αtL2
Time-Dependent Nuclear Heat Transfer
Published in Robert E. Masterson, Nuclear Reactor Thermal Hydraulics, 2019
Thus, the Fourier number measures the amount of heat conducted through an object relative to the amount of heat stored in the object. Consequently, a large value for the Fourier number indicates that heat propagates relatively quickly through an object. Now the terms in Equations 12.52(a), 12.52(b), and 12.52(c) converge rapidly when t is large, but when τ > 0.2, keeping the first term and neglecting all of the remaining terms results in a maximum error of less than 2%. Thus, when τ > 0.2, the Heisler charts provide excellent predictions of the time-dependent temperature profiles as long as a object is spatially uniform; that is, spatially homogeneous.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
on the surface S, where h is the heat transfer coefficient from the surface of the body, then Equation (51.5) can be nondimensionalized with the following variables: the Fourier number, Fo =αtL2 (i.e., the dimensionless time variable), the dimensionless heat generation variable g(r,t)L2/κTo-T∞, and the Biot number, Bi=hL/κ, where L and To are suitable length and temperature scales, respectively. The Fourier number denotes the ratio of the heat transferred by conduction to the heat stored in the body and is useful in solving transient problems. When the Fourier number is very large, transient terms in the solution of the diffusion equation may be neglected. The Biot number is a measure of the relative magnitudes of the heat transfer due to conduction and convection (or radiation) in the body. When the Biot number is very small (<0.1), the temperature in the body may be assumed to be a constant, and the lumped form of the energy equation may be used.
Mechanical and thermal couplings in helical strands*
Published in Journal of Thermal Stresses, 2019
Dansong Zhang, Martin Ostoja-Starzewski, Loïc Le Marrec
With Eqs. (61) and (55), the perturbations for the longitudinal and torsional wave solutions are with or , respectively. This solution contains an imaginary coefficient through , hence there is damping in the elastic waves. Since all other variables are real, the amount of damping is controlled by Γ. In particular, two situations are considered, (where , or ), and . The physical meanings of these two conditions can be elucidated with the Fourier number. The Fourier number is defined as where is the thermal diffusivity, Tc is the characteristic time scale, and Lc the characteristic length scale. For the wave-form solution Eq. (51), the time scale is and the length scale is the wavelength , so
Modeling horizontal storage tanks with encapsulated phase change materials for building performance simulation
Published in Science and Technology for the Built Environment, 2018
Katherine D'Avignon, Michaël Kummert
Here, the Fourier number, Fo, represents the ratio of the conductive heat transfer rate to the rate of heat storage while the Biot number, Bi, is the ratio of the heat transfer resistances inside and at the surface of the material. The PCM's specific heat, cp, pcm, varies during its change of phase so the minimum value over the expected temperature range must be used.