(Mild solution) A functionu :I \rightarrow L_{+}^p(X, m)is a mild solution of (IVP) inIifu(t) \in D(f)for allt \in I \setminus \{0\},f \circ u \in L^1((0,t]; L^p(X, m))for everyt \in I \setminus \{0\}, andusatisfies the variation of constants formula \b...
By plugging this expressions into the lengthy formula that results from applying Wick’s theorem to the integrand of Eq. (1) and performing the time integral, after some cumbersome but straightforward algebra we get Eq. (3). A full derivation of Eqs. (3–5) is presented in the ...
Within the GK theory of linear response, the thermal conductivity is given by the celebrated GK formula13,14,15,16,19 $$\kappa \propto \int\nolimits_{0}^{\infty }\langle {{{\bf{J}}}_{E}(t)\cdot {{{\bf{J}}}_{E}(0)\rangle {{{\rm{d}}}t,$$ (5) where the energy ...
PURPOSE: A heat-radiating cathode structure is provided to prevent leakage current from flowing between the external face of a heater and the inner surface of a metal base even at a temperature of above 1000 deg.C. CONSTITUTION: A heat-radiating cathode structure includes an electron emitting me...
The thesis built special calculation formula of heating strip for frontal jet preheat furnace(JPF) in vertical-type continue annealing furnace.The thesis e... J Min - 《China Metallurgy》 被引量: 2发表: 2011年 Furnace for heating particles A bottom-up cocurrent combustion furnace for the prod...
By applying a certain current I and voltage U to the mat over a defined time period [t1,t2] the total supplied heat is: (6.17)ΔQ=∫t1t2U⋅I dt A sandwich layout must be used, where the heater mat (area smaller than the cell surface area) is placed tightly between several ...
by a range of factors such as stability, lack of good theoretical model and mechanism understanding, production complexity, high production cost etc. In this regard, a comprehensive review of nanofluid research will enable researchers to understand the current research gap and recent developments of ...
The thermal efficiency of a typical unfired combined cycle plant may be found by using the following formula: (7.40)η=(Wout−Win)GT+(Wout−Win)STQTOTAL where (Wout –Win)GT: net work output of gas turbine (Wout –Win)ST: net work output of steam turbine QTOTAL: total heat supplied...
The coal oxygen combustion reaction is considered as a primary reaction, and E/RT ≥ 1, 1-2RT/E is approximately to 1, which is simplified by Formula (3) into Formula (5). $$n = 1,\ln \left[ {\frac{{ - \ln \left( {1 - \alpha } \right)}}{{T^{2} }}} \right]...
Its calculation formula is given in Equation (16): 𝑄𝑟=𝐼𝑇𝛥𝑆𝑛𝐹Qr=ITΔSnF (16) where I represents the charge–discharge current, A; T is the operating temperature of the battery, K; ΔS is the change in entropy before and after the chemical reaction, J/(mol·K)...