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The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). There are also online calculators available specifically for Heat-transfer fluid applications. Experimental assessment of the heat transfer coefficient poses some challenges especially when small fluxes are to be measured (e.g. < 0.2 W/cm 2). [1] [2]
β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature). is the kinematic viscosity; α is the thermal diffusivity; T s is the surface temperature; T ∞ is the quiescent temperature (fluid temperature far from the surface of the object) Gr x is the Grashof number for characteristic length x
where ˙ is the heat transferred per unit time, A is the area of the object, h is the heat transfer coefficient, T is the object's surface temperature, and T f is the fluid temperature. [8] The convective heat transfer coefficient is dependent upon the physical properties of the fluid and the physical situation.
The lumped capacitance solution that follows assumes a constant heat transfer coefficient, as would be the case in forced convection. For free convection, the lumped capacitance model can be solved with a heat transfer coefficient that varies with temperature difference. [9]
First, the body must be at uniform temperature initially. Second, the Fourier's number of the analyzed object should be bigger than 0.2. Additionally, the temperature of the surroundings and the convective heat transfer coefficient must remain constant and uniform. Also, there must be no heat generation from the body itself. [1] [3] [4]
The Nusselt number is the ratio of total heat transfer (convection + conduction) to conductive heat transfer across a boundary. The convection and conduction heat flows are parallel to each other and to the surface normal of the boundary surface, and are all perpendicular to the mean fluid flow in the simple case.
The film temperature is often used as the temperature at which fluid properties are calculated when using the Prandtl number, Nusselt number, Reynolds number or Grashof number to calculate a heat transfer coefficient, because it is a reasonable first approximation to the temperature within the convection boundary layer.
As noted, a Biot number smaller than about 0.1 shows that the conduction resistance inside a body is much smaller than heat convection at the surface, so that temperature gradients are negligible inside of the body. In this case, the lumped-capacitance model of transient heat transfer can be used. (A Biot number less than 0.1 generally ...