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The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies (like Reynolds analogy , Prandtl–Taylor analogy) developed to directly relate heat transfer coefficients, mass transfer coefficients and friction factors, Chilton and Colburn J-factor analogy proved to be the most accurate.
The overall heat transfer coefficient takes into account the individual heat transfer coefficients of each stream and the resistance of the pipe material. It can be calculated as the reciprocal of the sum of a series of thermal resistances (but more complex relationships exist, for example when heat transfer takes place by different routes in ...
These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: (,) = = [ + ], [1]where T i is the initial uniform temperature of the slab, T ∞ is the constant environmental temperature imposed at the boundary, x is the location in the plane wall, λ is the root of λ * tan λ = Bi, and α is thermal diffusivity.
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot (1774–1862). The Biot number is the ratio of the thermal resistance for conduction inside a body to the resistance for convection at the surface of the body.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
describes heat transfer across a surface = Here, is the overall heat transfer coefficient, is the total heat transfer area, and is the minimum heat capacity rate. To better understand where this definition of NTU comes from, consider the following heat transfer energy balance, which is an extension of the energy balance above:
The convective heat transfer between a uniformly heated wall and the working fluid is described by Newton's law of cooling: = where represents the heat flux, represents the proportionally constant called the heat transfer coefficient, represents the wall temperature and represents the fluid temperature.
Q H = W + Q C = heat exchanged with the hot reservoir. η = W / (Q C + Q H) = thermal efficiency of the cycle If the cycle moves in a clockwise sense, then it is a heat engine that outputs work; if the cycle moves in a counterclockwise sense, it is a heat pump that takes in work and moves heat Q H from the cold reservoir to the hot reservoir.
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