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For example, all else being equal, gases are less effective than liquids at convective heat transfer. Flow Regime -- The convection coefficient depends on Reynolds number in various cases. For example, you certainly feel cooler on a windy day than on a day with no wind even though all else is the same.
Heat transfer coefficients are a bit tricky, for good reason. You need to know something about the conditions that exist on both sides of the pipe, and you only stated that you have water in a stainless steel pipe. For heat transfer to occur, you need a second fluid on the outside of the pipe that you can transfer heat with.
The free convective heat transfer coefficient depends strongly on the orientation of the surface and also on the surface geometry. Certainly, the free convection heat transfer coefficient from a flat horizontal surface will be very different from that from a flat vertical surface.
It's the rate of heat flow. The correct formula for convective heat transfer is $\dfrac{Q}{t}=h{A(T_2-T_1)}$ where h is the Heat Transfer Coefficient. As you can clearly see even in the Wikipedia page, the Q is mentioned with a dot above it implying the time derivative of the heat transferred or the rate of heat transfer.
The heat transfer coefficient between steel tube and gas is known, as well as the heat transfer coefficient between water and steel and the conductive heat transfer coefficient for the steel. To calculate the heat transfer between the gas and water is pretty straightforward, using Fouriers and Newtons law. The question is:
1) The heat transfer coefficient of the steam is normally substantially higher than that for water, so this coefficient will not be your limiting factor. If a similar heat exchanger exists, take measurements and calculate the overall heat transfer coefficient, which I expect will be in the range of 200-400 BTU/hr-ft^2-degF.
So, out here, we've got a constant temperature that doesn't depend on any heat transfer physics and is essentially imposed on the situation as an independent boundary condition. Therefore, it is the ideal choice to use as a temperature baseline, because it is independent , constant and stable , compared to what is happening inside the thermal ...
Transport Phenomena by Bird, Stewart, and Lightfoot provides extensive information on correlations to determine the convective heat transfer coefficient in various situations. Convective heat transport in flow past a sphere is specifically covered. This is a very well-known situation, and has been analyzed extensively.
Short answer to the orientation question: It depends on many factors, but a vertical surface generally transfers heat faster. Only one type of heat transfer coefficient is strongly affected by gravity: the convection coefficient for natural convection; the reason is that warmer air is less dense than cooler air. Natural convection describes hot ...
If you were interested in the temperature variation within a fluid with convective heat transfer, you want to solve a more general heat equation that contains a convective term that then couples its solution with a solution for the motion of the fluid (e.g. Navier Stokes), $$ \frac{\partial T}{\partial t} + \tilde{u} \cdot \nabla T= k\nabla^2T ...