Calculation of a heat transfer by radiation

         For two grey objects the quantity of transmitted heat is calculated under the formula:

q_e = C₀· e_n· [(T₁/100)⁴- (T₂/100)⁴] · H ,                                                  [1]

where

C₀ = 4,9 kcal/(m²·hour·K) – coefficient of radiation of a black object;

e_n – the reduced power of blackness of system;

H – a cross radiating surface;

T₁, T₂ – temperatures of interreacting objects (a radiator and heat receiver).

For recalculation between force systems it is used the following dependence: 1 cal = 4,1868 J.

          We consider, that surfaces have the concentric shape and the heating up surface is located in heated up. For this case of interaction of two objects the given degree of blackness of system calculated under the formula:

e_n = 1 / [1+ (1/e₁-1) · f₁₂+ (1/e₂-1) · f₂₁]                                                [2]

where

e₁, e₂   – degrees of blackness of a heater and the receiver accordingly;

f₁₂, f₂₁ – averages on a surface coefficients of a cross irradiance of a heater on heat and receiver on a heater.

         Averages on a surface irradiance coefficients (for interreacting surfaces) and quantity of a cross radiating surface are spotted by means of following dependences:

f₁₂ = 1; f₂₁ = F₁/F₂; H =f₁;                                                                    [3]

where

F₁, F₂ – the areas of surfaces of radiation and uptake accordingly.

         Let's substitute formulas (2) and (3) in the formula (1). We will gain the following resultant the formula:

q_e = C₀· [(T₁/100)⁴- (T₂/100)⁴] · F₁ / [1+ (1/e₁-1) + (1/e₂-1) · F₁/F₂],   [4]

         The thermal stream radiated by a surface in a surrounding medium, pays off under the formula:

q_e = C₀· e· (T/100)⁴ · F .                                                                          [5]

         Let's present calculation under the given formula in the form of the system of diagrammes constructed by means of an applet.

         For build-up of system of nomograhic charts we will converse the formula (4) to a following view:

q_e = C₀· [(T₁/100)⁴- ((T₁-dT)/100)⁴] · F₁ / [(1/e₁) + (1/e₂-1) · F₁/F₂],     [6]

where

dT = T₁-T₂ – a difference of temperatures of surfaces of a heating and uptake.

          The circuit design of nomographs is presented in drawing 1.

                            Drawing 1. The circuit design of system of nomographs for graphic-analytical calculation of heat transfer by radiation

         After applet start an auxiliary window will have the following appearance (drawing 2).

                           Drawing 2. An additional window of an applet on build-up of system of nomographs for graphic-analytical calculation of heat transfer by radiation

         In an auxiliary window the circuit design of disposing of nomographs is already shown, but she demands recurring feeding into, therefore on each small square which is marking out a nomograph "is clicked" by the right key of the mouse and the left key "clicked"on that place where there should be a colour flag indicator (a place of disposing of meaning of parametre Z of a nomograph). It is possible choose any other location of variable parametre Z. After recurring appointment of the circuit design of nomographs "is clicked" by the left key of the mouse on sign "[-]", had in left overhead to the angle of the circuit design of nomographs. It will change the aspect on "[+]". It means, that the circuit design of nomographs is fixed. .

  Drawing 3. An additional window of an applet on build-up of system of nomographs with the tuned circuit design of nomographs for graphic-analytical calculation of radiant heat transfer

          After attaching of the circuit design of nomographs, "is in succession clicked" on everyone sign, marking out a nomograph, and it is pushed three buttons "In the working memory" ("В ОЗУ"), "Substitution ID" ("Подстановка ИД"), "the Total formula" ("Итоговая формула") for entering of all parametres of a nomograph into an on-line storage and design formula formation.

          We transfer to the basic window and we induct meanings of steps on axes "X" and "Y". We push the button "to Build on ID" ("Построить по ИД").

       Drawing 4. The basic window of an applet for build-up of system of nomographs for graphic-analytical calculation of radiant heat transfer

          More detailed instruction on operation with an applet.

The topic of this section: calculation of heat transfer by radiation in radiant heat transfer (radiative heat transfer) between bodies.