This article deals with a Markov process related to the fundamental solution of a heat equation on the direct product ring Q_S, where Q_S is a finite direct product of p-adic fields. The techniques developed here are different from the well known ones: they are geometrical and very simple...
The first law of thermodynamics states that changes in internal energy can be accounted for by heat losses: ΔE = Q – W, where ΔE is change in internal energy (Δ is the Greek letter "delta," and means "difference" here), Q is the amount of thermal energy t...
The heat diffusion equation obtained from the energy balance applied to a differential element is (4.11)1r∂∂rkr∂T∂r+1r2∂∂ϕk∂T∂ϕ+∂∂zk∂T∂z+q.v=ρcp∂T∂t. 4.3.3 Spherical coordinates Fourier’s law for the spherical coordinates is (4.12)q=−k...
The equation can also be formatted as {eq}q = m * L_f {/eq}. The units of each variable in this equation are: The units for q can be any energy unit: Joule, Calorie, BTU, kilojoules, and so on. The energy unit of q must be in agreement with the energy unit of the heat ...
2.2 Heat conduction equation The heat conduction equation is a partial differential equation for conduction of heat through a body. The solution of the equation gives the temperature distribution in the body at different instances of time. As discussed in Chapter 1, differentiation of the temperature...
Specific heat refers to the amount of heat required to raise unit mass of a substance's temperature by 1 degree. The Specific Heat formula is: c = ΔQ / (m ×ΔT) Where: c: Specific Heat , in J/(kg.K) ΔQ: Heat required for the temperature change, in J ΔT: Temperature ...
equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generict≠1is a non-stationary Schrodinger equation wheretparametrizes shift in time. In this paper we make the non-stationary equation explicit for theq,t-Virasoro block with one degenerate and...
Chuanqiang Chen, Xinan Ma, and Paolo Salani, On space-time quasiconcave solutions of the heat equation, arXiv preprint arXiv:1405.6373 (2014).C.Q. Chen, X.N. Ma, P. Salani, On space-time quasiconcave solutions of the heat equation, arXiv:1405.6373 [math.AP]....
1-DHeatTransfer(cont.)RecallFourier'sLaw:dTq=-kA,Ifthetemperaturegradientisaconstantdxq=constent(heattransferrateisaconstant)dTT2T1,whereT(x0)T1,T(xL)T2dxL T1T2 T1T2T1T2dTqkAkAdxL(L/kA)T1T2Lq,whereR:thermalresistanceRkA q(I)T1(V1...
Thus, in the porous media, it is wise to select the Forchheimer equation for the description of the nonlinear flow. (6.59)−∂p∂x=AQ+BQ2 The dimensions of Q, ∂p∂x, A, and B are L3T− 1, ML− 2T− 2, ML− 5T− 1, and ML− 8, respectively....