The performance of the heat sink is governed by this simple heat transfer equation: 1 where: is the heat from the source(s) being cooled is the convection coefficient of the heat sink is the total surface area of the heat sink is the temperature of the source being cooled is the ambient...
Moldoveanu, and Minea [52] conducted an experimental study to develop a single equation for the estimation of the specific heat of three different unitary and two different hybrid nanofluids, see Table 4.5. They performed their experiments for Al2O3, SiO2, and TiO2 nanoparticles and their hybrid...
(see definition 6.1 ), \(t>0\) . moreover, let \(\tilde{u}\in w^{1,1}_{loc}(\mathbb {r}^{n-1}\times (0,t))\) be the solution to heat equation $$\begin{aligned} \tilde{u}(x):= \left\{ \begin{array}{lll} \tilde{u}_t(x,t)=\delta u (x,t), &{}\quad...
If one performs this operation on the simplified χ equation, (97), an identical result is obtained. If one does not ignore only the internal modes in Eq. (94) represented by f(T) then one has for the partial of ln(P/Ps), with respect to 1/T, (122)−RT∂ ln(P/Ps)∂...
For the case, note that ifvsolves the initial value problem for the ordinary heat equation with initial valuea, then the functionsolves the initial value problem above. Hence, blow-up does not occur in this case. Intuitively, this can be explained by the fact that forthe reaction is stronge...
Simple equations in matrix form can be written as below. In this equation; M is 2D matrix (2 bars shows that it is 2D matrix), U is 1D matrix form of unknown parameters from the each node, q is 1D matrix form of right side of the equation. ...
The field (geometrical) theory of specific heat is based on the universal thermal sum, a new mathematical tool derived from the evolution equation in the Euclidean four-dimensional spacetime, with the closed time coordinate. This theory made it possible
(Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three ...
(1991)developed such models by discretizing the heat exchanger into small elements of fixed area. They discretized the hyperbolic first order heat transfer equation for both hot and cold streams inside each element. Even though their model assumes constantheat transfer coefficientsand constant heat ...
the heater. By heating the working fluid with saturated water steam, due to highcondensation heat transfercoefficient at the hot side, the wall temperature would very close to thesaturation temperatureof water steam. The local bulk temperature of the fluid can be obtained from the energy equation...