# Does the convective heat transfer coefficient depend on temperature difference?

Consider a flat plate at a higher temperature than the fluid which is flowing over it, with some velocity. Forced convection is taking place. I'm convinced that the value of heat transfer coefficient h, depends on fluid properties, fluid flow regime, surface roughness and geometery of surface area. However, does it also depend on the temperature difference between the plate and the free stream? Does it also depend on the area of the flat plate?

Or the dependence of h on fluid properties, flow regime, surface roughness, geometery is given for a particular surface area and temperature difference?

The temperature dependence is embodied in the fluid properties. The local heat transfer coefficient is based on the local heat flux, which does not depend on the total area. The overall heat transfer coefficient is the average of the local heat transfer coefficient, integrated over the area.

• Oh I see, so the film temperature at which we evaluate the properties and assume them as being constants, changes as the temperature difference between flat plate and free stream changes. As film temperature changes, properties change and this change is properties increases or decreases h. Am I right? Aug 2, 2021 at 13:54
• I learnt another relation for heat transfer coefficient given by : h= [-k(dT/dy)y=0]/(Ts - Tf) k=thermal conductivity of fluid, y=0 represents slope at the surface of the plate of temperature profile, Ts= plate surface temperature, Tf= free stream fluid temperature. In this relation if the denominator increases, does the numerator also increase accordingly to keep h constant? Aug 2, 2021 at 13:59
• Well, in the correlations we use to determine h, we have certain specifications for what temperature(s) to use to evaluate that properties. Aug 2, 2021 at 14:01
• The equation you wrote assumes that you know h and are solving for the temperature variation within the medium. So, for a given h, if the denominator increases, the numerator increases too. The h in this equation is determined from the heat transfer correlations applied to the outside medium. Once you solve a few problems involving these concepts, you'll the idea of how all this works. Aug 2, 2021 at 16:20
• That was useful. Aug 3, 2021 at 16:00

The convection coefficient $$h$$ (W/m$$^2$$ K) appears in the heat transfer equation

$$\dot{q} = h A \Delta T$$

where $$\dot{q}$$ is the heat flow (W), $$A$$ is the area (m$$^2$$), and $$\Delta T$$ is the temperature difference (K or $$^o$$C). The coefficient $$h$$ expresses how effective a fluid is at transporting heat in the presence of mass flow.

• Fluid Properties -- Changing intrinsic fluid properties such as density can change $$h$$. 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.

• Surface Roughness -- Increasing surface roughness can change the local flow of the fluid, which can then affect the local $$h$$, which can then affect the overall $$h$$. Otherwise, roughness could in principle be argued to already be directly incorporated into what should be presented as $$A$$ and not truly be a factor that changes $$h$$.

• Geometry -- This can be more important in natural convection than in forced convection. The affect is to change the flow pattern that forms. Consider for example the difference in natural convection from a hot plate with fluid on it along a vertical wall versus that along a wall that is inclined over the hot plate. The convection flow will be higher in the former case.

• Area -- This is already a direct factor in the heat flow equation, so it is not in $$h$$.

• Temperature Difference -- This is already a direct factor in the heat flow equation, so it is not directly in $$h$$. An indirect influence can occur however when the intrinsic property (density) of the fluid depends on temperature.

• Oh, Got it, the temperature difference is accounted in fluid properties. Thanks, this was useful. Aug 2, 2021 at 14:17