Natural Convection Heat Transfer from a Horizontal Plate
Editor's Note: It was reported to us by a Plant Engineer that the following spreadsheet contains some errors. We are working on verifying the contents. In the mean time we wanted to inform our readers of the following possible problems:
"1. The Fluid Thermal Expansion Coefficient "beta" is taken as the inverse of the absolute temperature. This is only correct if the fluid is a gas. The correlation is in error for use of water.
2. The Prandtl number calculation is wrong. The units as in the spreadsheet come out to (sec^2-ft)/(ft-slug) and this is supposed to be a dimensionless number. You must change the density input to units of lb/ft^3 and viscosity units to lb-sec/ft^2.
3. The Grashoff number calculation is wrong. The units as in the spreadsheet come out to (ft^2-slugs^2)/(sec^4-lb^2) and this is supposed to be a dimensionless number. You must change the density input to units of lb/ft^3 and viscosity units to lb-sec/ft^2. Then it will work."
The author of the article has a new website where he may have provided corrections for some of these issues. You may follow him at www.engineeringexcelspreadsheets.com or www.engineeringexceltemplates.com. The original article continues below.
An Excel spreadsheet for natural convection heat transfer between a fluid and a horizontal plate is shown at the right. The dimensionless number correlations for this natural convection configuration, and the applicable range of Rayleigh number for each, are as follows:
For heat transfer from the upper surface of a plate hotter than the fluid or to the lower surface of a plate that is cooler than the fluid:
Nu = 0.54 Ra1/4 ( 104> Ra > 107 )
Nu = 0.15 Ra1/3 ( 107> Ra > 1011 )
For heat transfer from the lower surface of a plate hotter than the fluid or to the upper surface of a plate that is cooler than the fluid:
Nu = 0.27 Ra1/4 ( 105> Ra > 1010 )
The input parameters for this Excel spreadsheet are similar to those needed for natural convection from a vertical plate. One difference is the definition of the length parameter, L, for use in the Nusselt number and the Rayleigh number. For a horizontal plate, the length parameter is defined as: L = area of plate/perimeter of plate, as noted on the spreadsheet. The Excel formulas calculate the Nusselt number and natural convection heat transfer coefficient, h, for each of the three correlations given above. You then need to choose the correct correlation based on the heat transfer configuration and the value of the Rayleigh number.
To download this Excel spreadsheet in either U.S. or S.I. units, click on one of the links below:
Click here to download this spreadsheet template in U.S. units.
Click here to download this spreadsheet template in S.I. units.