Heat transferHeat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer.
Thermal conductionConduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its thermal conductivity, and is denoted k. Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it.
ProvenceProvence (prəˈvɒ̃s, USalsoprəʊˈ-, UKalsoprɒˈ-, pʁɔvɑ̃s) is a geographical region and historical province of southeastern France, which extends from the left bank of the lower Rhône to the west to the Italian border to the east; it is bordered by the Mediterranean Sea to the south. It largely corresponds with the modern administrative region of Provence-Alpes-Côte d'Azur and includes the departments of Var, Bouches-du-Rhône, Alpes-de-Haute-Provence, as well as parts of Alpes-Maritimes and Vaucluse.
Integral transformIn mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed function can generally be mapped back to the original function space using the inverse transform. An integral transform is any transform of the following form: The input of this transform is a function , and the output is another function .
Kernel (linear algebra)In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector. That is, given a linear map L : V → W between two vector spaces V and W, the kernel of L is the vector space of all elements v of V such that L(v) = 0, where 0 denotes the zero vector in W, or more symbolically: The kernel of L is a linear subspace of the domain V.
Present valueIn economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of zero- or negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow".
Laplacian matrixIn the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating the negative continuous Laplacian obtained by the finite difference method. The Laplacian matrix relates to many useful properties of a graph.
QuaternionIn mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative. Quaternions are generally represented in the form where a, b, c, and d are real numbers; and 1, i, j, and k are the basis vectors or basis elements.
Spectral theoryIn mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of systems of linear equations and their generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter.
Heat transfer coefficientIn thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ΔT ). It is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter per kelvin (W/m2/K).
