Theoretical Overview

The basic equations used to study heat transfer are:

• The general heat transfer equation:

            q = UADT

            where U is the overall heat transfer coefficient; A is the area over which heat transfer occurs; T is the temperature; and q is the heat transferred.

• The Nusselt number (which is used to find the heat transfer coefficient):

            Nu = hD/k

            Nu a Re

            Nu a Pr

            where h is the local heat transfer coefficient; D is the diameter; k is the thermal conductivity; Re is the Reynolds Number; Pr is the Prandtl Number; and Nu is the Nusselt Number.

• Reynolds Number

            Re = uD/v

            where u is the velocity of the fluid; and v is the kinematic viscosity.

• Prandtl Number

            Pr = v/a

            where a is the thermal diffusivity.

The diffusive-convective equation is an energy balance of the heat transferred in and out of the system. 

• The diffusive-conductive equation is presented below

            rC_pV(¶T/¶t)  =  k(¶²T/¶x²)+ Q

            where r is the density of the fluid; Cp is the heat capacity of the fluid; V is the volume of the fluid; (¶T/¶t) is the change in temperature with respect to time; (¶²T/¶x²) is the change of temperature with respect to position; Q is the rate of heat generation in the system.

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