A beaker contains a fluid of density ρ kg/m³, specific heat S J/kg °C and viscosity η. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area (Q/A) by convection when beaker is put on a hot plate, a student proposes that it should depend on η, ((SΔθ)/h) and (1/(ρ g…

Question

A beaker contains a fluid of density ρ kg/m³, specific heat S J/kg °C and viscosity η. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area (Q/A) by convection when beaker is put on a hot plate, a student proposes that it should depend on η, ((SΔθ)/h) and (1/(ρ g)) when Δθ (in °C) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for (Q/A) is

Accepted Answer

(1) η(SΔθ)/h. Given: Q/A is a power per unit area, [MT⁻³]. η=[ML⁻¹T⁻¹] and (SΔθ)/h=([L²T⁻²K⁻¹][K])/([L])=[LT⁻²]. Their product: [ML⁻¹T⁻¹][LT⁻²]=[MT⁻³]. That matches exactly, so no further factor is needed and Q/A=η(SΔθ)/h.

Step-by-step solution

Why the other options are wrong