Heat transfre for a domestic radiator

[nickbone59]

Any suggestions anyone? Really struggling with this one !

Homework Statement

A domestic radiator is 2.5 m long and 0.6m high and is sited in a room whose temperature is 14C. Hot water is circulating through the radiator at a temperature of 90c. The radiator is convecting heat from both sides but only radiating from one side. Given that the surface emissivity is 0.7, calculate the total heat transfer from radiator to the room.

Homework Equations

Stefan-Boltzmann Constant = 5.67x10^-8

Nu = 0.59(Gr.Pr)^0.25 for laminar flow (GR.Pr)<10^9
Nu = 0.129(Gr.Pr)^0.33 for turbulent flow (GR.Pr)>10^9
where,
Grashof no. Gr= ($$\rho$$^2$$\beta(\theta$$1-$$\theta$$2)l^3)/$$\mu$$^3

Nusselt No. Nu= hl/k

Prandtl No. Pr=Cp$$\mu$$/k

The Attempt at a Solution

Q= $$\sigma\epsilon$$A(T1^4-T2^4)

= 5.67x10^-8 x 0.7 x 1.5 x (1.736x10^10-6.785x10^9)

= 629.8W

 

[Astronuc]

Looks like you got the radiated heat correct. It would be preferable to include units with the numbers.

Now find the convective heat. One needs a formula for the convective heat transfer coefficient.

 

[piercas]

Assuming that the radiator is made of a material with a surface emissivity of 0.7, the total heat transfer from the radiator to the room can be calculated using the Stefan-Boltzmann law. The equation takes into account the surface area of the radiator, the difference in temperatures between the radiator and the room, and the surface emissivity.

However, this calculation only takes into account the radiative heat transfer. Since the radiator is also convecting heat from both sides, the convective heat transfer must be considered as well. This can be calculated using the Nusselt number, which takes into account the flow conditions and fluid properties.

The Grashof number can be calculated using the given dimensions and temperatures, and the Prandtl number can be estimated based on the properties of water. Once the Nusselt number is determined, the convective heat transfer coefficient (h) can be calculated using the thermal conductivity of air.

Once both the radiative and convective heat transfer are determined, they can be added together to get the total heat transfer from the radiator to the room. This will give a more accurate and comprehensive understanding of the heat transfer in this system.

Some suggestions to consider for this problem could be to double check the calculations and units used, as well as to make sure all relevant factors (such as the convective heat transfer) are taken into account. Also, it may be helpful to break down the problem into smaller steps and calculations to make it easier to understand and solve. Additionally, consulting with a professor or fellow classmates for further clarification or assistance could be beneficial.