# Rate of heat transfer / specific heat

• charlotte7070
In summary, the conversation discusses the problem of determining the time required to heat or cool a concrete slab based on its dimensions and thermal properties. The estimated time for the process is several hours, according to the rule of thumb for characteristic heat diffusion times.

#### charlotte7070

I am digging back thorugh thermodynamics textbooks, and am seeing insulation values etc. but none on how to solve for time required to heat a material.

Here is the specific problem. I am trying to fgure out how long its takes to cool (or alternately heat) a concrete slab.

The slab is 8 in. with initial temp 60 degrees F. Temperature on top and bottom of slab is ambient air temp, 20 degrees.

k, concrete = 1.7 W / m - deg K
c, concrete = 750 Joules

the area of slab can be assumed to be very large (an acre? infinity?)
and the air can be assumed to not change as a result of the heat loss of the concrete.

So I have rate of heat transfer: dependent on the surface area,
H = -k A (dT / dX)

and specific heat of concrete, dependent on mass:
dQ = m c dT = Joules

t (seconds) to cool one inch thickness concrete by 22.2 deg C or K
= dQ / H = 637 seconds (this seems a little fast to me since concrete is fairly insulating material).

Does this look correct? (Assuming I have the heat capacity and conductivity of concrete correct). This would be derived into an integral to get the temp at a certain time and depth, but as a consultant would be laughed out of the room, and will simplify to some finite steps in time and thickness.
No need to get to technical! I won't get it! Thank you for your input.

Hi charlotte7070, welcome to PF. A good rule of thumb for characteristic heat diffusion times is $t\approx L^2/D$, where L is a characteristic length (I'd take 4 in, or 0.1 m, for this problem) and $D=k/c\rho$ is the thermal diffusivity, which looks like it's around 10-6 m2 s-1 for concrete. So I'd estimate it would take at least 104 s, or several hours, to heat most of the slab to close to 60°F.

thank YOU!

## What is the rate of heat transfer?

The rate of heat transfer is the amount of heat energy that is moved or transferred per unit of time. It is measured in units of watts (W) or joules per second (J/s).

## What factors affect the rate of heat transfer?

The rate of heat transfer is affected by several factors, including the temperature difference between the two objects, the thermal conductivity of the materials, and the surface area of contact between the two objects.

## What is specific heat?

Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is measured in units of joules per kilogram per degree Celsius (J/kg°C).

## How does specific heat affect the rate of heat transfer?

The specific heat of a material determines how much heat energy is needed to change its temperature. Materials with a higher specific heat will require more heat energy to raise their temperature, resulting in a slower rate of heat transfer.

## What is the formula for calculating rate of heat transfer?

The formula for calculating the rate of heat transfer is Q/t = kA(ΔT/Δx), where Q is the heat transferred, t is the time, k is the thermal conductivity, A is the surface area of contact, ΔT is the temperature difference between the two objects, and Δx is the distance between the two objects.