Question Solved1 Answer Consider two dimensional laminar boundary layer flow over a flat isothermal surface. Very close to the surface, the velocity components are very small. If the pressure changes are assumes to be negligible in the flow being considered, derive an expression for the temperature distribution near the wall. Viscous dissipation effects should be included in the analysis.

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Transcribed Image Text: Consider two dimensional laminar boundary layer flow over a flat isothermal surface. Very close to the surface, the velocity components are very small. If the pressure changes are assumes to be negligible in the flow being considered, derive an expression for the temperature distribution near the wall. Viscous dissipation effects should be included in the analysis.
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Transcribed Image Text: Consider two dimensional laminar boundary layer flow over a flat isothermal surface. Very close to the surface, the velocity components are very small. If the pressure changes are assumes to be negligible in the flow being considered, derive an expression for the temperature distribution near the wall. Viscous dissipation effects should be included in the analysis.
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Answer:Consider the fluid flow in laminar Boundary layer.Flow is steady and two dimensional.Taking a differential volume of length dx, height dy and unit depth in the z-direction.Applying Consenvation of energyEnergy in - Enengy out = Change in Energyy of the SystemEin - Eout = DsystemAt steady flow{:[Delta" Esystem "=0],[" Ein "=" Eout "]:}No work is involued here. Energy transfen will takes placl by heat and mass.The rate of energy transfer to the control volume by mass in x-directionLet m^(m)= mass flow rate of fluid{:[=" mass flow rate of fluid "],[=" P.uty ")" (velocity)(areal "],[=(dy.1)]:}e= Energy of the fluid per unit mass CSScanned with CamScanner =h=C_(p)TWhere,{:[h=" Specific enthalpy "],[c_(p)=" Specific neat capacity at constant "],[],[T=" Pressure "],[" Temperature "]:}Now,{:[(" Ein "-" Eout ")_("mass ",x){:=me_(x)-[(m^(˙))e_(x)+(del(me)/(del x))_(x)*dx]],[=-(del((me^(˙)))_(x))/(del x)*dx],[=-rho(del)/(del x)[rho u(dy*1)C_(p)T]dx],[=-rhoC_(p)(u(del T)/(del x)+T(del u)/(del x))dxdy]:}Rate of energy transfer to the control volume by mass in y-direction(E_("un ")-" Eout ")_("mass "y)=(me^(˙))_(y)-[((me^(˙)))_(y)+(del((m^(˙))e)_(y))/(del y)dy]Here,m^(˙)=p theta(dx*1){:[=>=-(del((m^(˙))e)_(y))/(del y)*dy],[=-(del(Pv(dx*1)C_(P))/(del y)dy],[=-PC_(P)(v(del T)/(del y)+T(del v)/(del y))dxdy]:}Adding eqn (1) and eqn (II)En ... See the full answer