Calculation of Natural Convection Heat Transfer Coefficients Posted on Saturday, July 23, 2011 at 4:48 PM Introduction
If you want to obtain an Excel spreadsheet for natural convection heat transfer coefficient calculations, click here to visit our download page. Read on for information about natural convection heat transfer coefficients and Excel spreadsheets to obtain a value for them.
Convection heat transfer takes place between a solid surface and fluid that is at a different temperature and is in contact with the surface. If the fluid is flowing past the surface due to an external driving force like a fan or pump, then the heat transfer is called forced convection. When fluid motion is due to density differences within the fluid (caused by temperature variation), then the heat transfer is called natural convection or free convection.
Newton's Law of Cooling for Natural Convection Heat Transfer
Newton's Law of Cooling [ Q = hA(Ts - Tf) ] is a simple expression used for the rate for convective heat transfer with either forced or natural convection. The parameters in Newton's Law of Cooling are:
- Q, the rate of forced convection heat transfer (Btu/hr - U.S. or W - S.I.)
- Ts, the solid temperature (oF - U.S. or oC - S.I.)
- Tf, the fluid temperature (oF - U.S. or oC - S.I.)
- A, the area of the surface that is in contact with the fluid (ft2 - U.S. or m2 - S.I.)
- h, the convective heat transfer coefficient (Btu/hr-ft2-oF - U.S. or W/m2-K - S.I.)
Dimensionless Nusselt, Rayleigh, Grashof, and Prandtl Numbers
 Natural convection heat transfer coefficients typically are estimated using correlations of dimensionless numbers, specifically correlations of Nusselt number (Nu) with Prandtl number (Pr), Grashof number (Gr), and/or Rayleigh number (Ra), where Ra = GrPr. The Nusselt, Grashof and Prandtl numbers are defined in the box at the left.
Following is a list of the parameters that appear in these dimensionless numbers, with units are given for both the U.S engineering system and S.I. system of units:
- D, a characteristic length parameter (e.g. diameter for natural convection from a circular cylinder or a sphere or height of a vertical plate) (ft for U.S., m for S.I.)
- ρ, the density of the fluid (slugs/ft3 for U.S., Kg/m3 for S.I.)
- μ, the viscosity of the fluid (lb-sec/ft2 for U.S., N-s/m2 for S.I.)
- k, the thermal conductivity of the fluid (Btu/hr-ft-oF for U.S., W/m-K for S.I.)
- Cp, the heat capacity of the fluid (Btu/lb-oF for U.S., J/kg-K for S.I.)
- g, the acceleration due to gravity (32.17 ft/sec2 for U.S., 9.81 m/s2 for S.I.)
- β, the coefficient of volume expansion of the fluid ( oR for U.S., K for S.I.)
- ΔT, the temperature difference between the solid surface and the fluid ( oF for U.S., oC or K for S.I.)
The following sections provide equations for estimating the heat transfer coefficient for several common natural convection configurations.
Natural Convection from a Vertical Plane
 The box at the right shows two correlations for convection heat transfer between a vertical plane and a fluid of different temperature in contact with it. The first can be used for all values of Rayleigh number and the second is only for laminar flow, indicated by Ra < 109. The screenshot image below shows an example of an Excel spreadsheet to calculate the natural convection heat transfer coefficient for a vertical plate using the two equations shown here.
For low cost, easy to use Excel spreadsheet packages for calculating convection heat transfer coefficients for natural convection from a vertical plane, a horizontal plane, an inclined plane, a horizontal cylinder or a sphere in either U.S. or S.I. units, click here to visit our download page.
References
1. Incropera, F.P., DeWitt, D.P, Bergman, T.L., & Lavine, A.S., Fundamentals of Heat and Mass Transfer, 6th Ed., Hoboken, NJ, John Wiley & Sons, (2007).
2. Lienhard, J.H, IV and Lienhard, J.H. V, A Heat Transfer Textbook: A Free Electronic Textbook
3. Bengtson, Harlan H, Fundamentals of Heat Transfer, an online continuing education course for engineering PDH credit
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