4 Phenomenologi al Equation Closure. 7 4 1 Examples 8 Example: River Flow 8 Quasi-equilibrium approximation 8 Example: TraÆ Flow 9 Example: Heat Condu tion 10 Fi k's Law 10 Thermal ondu tivity, difusivity, heat equation 10 Example: Granular Flow 11 Example: Invis id Fluid Flow 12 In ompressible Euler Equations 12 In ompressible Navier-Stokes Equations 12 Gas Dynami s 13 Equation of State 13 Ise...

We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise. Then we settle this question by proving that solutions to the linear equation have negative moments of all orders. Supported by NSA...

We consider the heat equation with a multiplicative Gaussian potential in dimensions d ≥ 3. We show that the renormalized solution converges to the solution of a deterministic diffusion equation with an effective diffusivity. We also prove that the renormalized large scale random fluctuations are described by the Edwards-Wilkinson model, that is, the stochastic heat equation (SHE) with additive...

The present article focuses on the evaluation of a first-moment closure model applicable to film cooling flow and heat transfer computations. The present first-moment closure model consists of a higher level of turbulent heat flux modeling in which two additional transport equations for temperature variance kθ and its dissipation rate εθ are ...

We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line x = 1, where the solution is wanted f...

in this paper, the effects of baffle on thermal characteristics of combined convection-radiation heat transfer in laminar flow adjacent to an inclined backward facing step (bfs) in a horizontal duct are investigated. a baffle is mounted on the top wall of channel downstream side of step. in this study, the fluid is treated as a gray, absorbing, emitting and scattering medium; therefore, in the ...

Let (M, g(t)), 0 ≤ t ≤ T , ∂M 6= φ, be a compact n-dimensional manifold, n ≥ 2, with metric g(t) evolving by the Ricci flow such that the second fundamental form of ∂M with respect to the unit outward normal of ∂M is uniformly bounded below on ∂M × [0, T ]. We will prove a global Li-Yau gradient estimate for the solution of the generalized conjugate heat equation on M × [0, T ]. We will give an...

In this paper we employ linear combinations of n heat kernels to approximate solutions to the heat equation. We show that such approximations are of order O(t ( 1 2p− 2n+1 2 ) in Lp-norm, 1 ≤ p ≤ ∞, as t → ∞. For positive solutions of the heat equation such approximations are achieved using the theory of truncated moment problems. For general sign-changing solutions, this type of approximations...

in this paper, we investigate the application of the homotopy perturbation method (hpm) for solving a one-dimensional nonlinear inverse heat conduction problem. in this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. furthermore, the temperature histories are unknown at the end point of the interval. this problem is ill-po...