Forced Convection Heat Transfer for Cylinder in Crossflow
Background:
Forced convection heat transfer occurs when a fluid flows along a heated or cooled body. In the forced convection heat transfer process the dimensionless convective heat transfer coefficient (Nusselt number) is a function of the Reynolds and Prandtl numbers. The fluid flow field may be laminar or turbulent and a primary parameter is the fluid velocity. As an example, the forced convection heat transfer coefficient for flow over a cylinder can be determined by a transient lumped thermal capacitance experiment.
When the Biot number (h L/k) for a transient heating/cooling process is less than about 0.1 the spatial temperature in the body at any instant is approximately constant as the body temperature increases or decreases with time. Generally this applies to situations where the thermal conductivity is large and/or the convective heat transfer coefficient is small, but as indicated by the Biot number the body dimensions are equally important. In the case of small Biot number (less than about 0.1) and where the heat transfer coefficient 'h' is constant, the body' temperature variation with time is described by:
where T is temperature, t is time, h is the convective heat transfer coefficient, r is material density, c is body specific heat, A is body surface area, V is body volume, and ¥ and i are the fluid and initial body temperatures, respectively.
Objectives:
To demonstrate a forced convective heat transfer process and to determine the forced convective heat transfer coefficient using the transient lumped thermal capacitance process for flow across a cylindrical surface.
Materials and Equipment:
Copper rod (and possibly a rod of an other material) of about 1/2 inch diameter with hole in one end for a dial thermometer and another to attach a cord.
Dial thermometer.
Cord to support the rod.
Means to heat copper rod (hot bath or oven).
Experiment:
First measure the room temperature with the thermometer. Place the copper rod in a hot bath or oven and heat to between 100 and 200 C. Using gloves, remove the rod, attach the cord, and insert the dial thermometer in the end with hole. Holding the string above your head, begin swinging the rod around you at a steady rate, counting the rotation rate and noting the approximate circle diameter. Every 15 or 20 seconds momentarily stop the rotation and quickly record the temperature and time and then resume the rotation and repeat until the temperature drops to within about 20 oC of the room temperature. The time record could later be adjusted to account for the short periods when rotation was interrupted to measure the temperature, but these periods should be relatively small.
Repeat this experiment with the larger aluminum rod but for this rod attempt to have a higher velocity (higher rotation rate) than was achieved for the copper rod. The reason will be apparent later.
Results:
Graph your results in terms of the natural log of the left-hand side of the above equation against time (t) on semi-log paper. The result should be approximately a straight line and the slope of the line should equal -hA/r cV. Using the density and specific heat of the rod material and the surface area and volume of the rod, determine the forced convection heat transfer coefficient 'h'. Do the same for the aluminum rod results.
After determining 'h', compute the Biot number (hA/r cV) to determine if the value is below the required value of approximately 0.1. If it is, the process was lumped thermal capacitance and the computed value of 'h' will be a reasonably accurate determination of the actual convection heat transfer coefficient. (If the Biot number is much larger than 0.1, then the process deviates from one that is lumped thermal capacitance and the computed value of 'h' will not be valid, and will be increasingly in error the larger the Biot number.) Do the same for the aluminum rod. Are these the same or different and why? Do the different materials in themselves influence the heat transfer coefficients?
Compare your determined values of 'h' with those based on an accepted empirical correlation for forced convection from cylinders. Note that the velocity can be determined from the rotation rate and the diameter of rotation.
[Note that this will be a homework problem to be assigned later.]
Comments:
In this experiment, in addition to forced convection, there will be some radiation heat transfer and thus the computed value of 'h' will be somewhat high, however, the radiation heat transfer contribution should be relatively small in this experiment since forced convection should predominate. One could estimate the radiation heat transfer contribution to determine if it is significant.
The forced convection heat transfer coefficient is essentially independent of temperature difference so this transient experiment should provide a fairly accurate measure of the forced convection heat transfer coefficient for flow over a cylinder.