# Question:How to solve the BVP and draw a 3 D plot for skin fiction and nusselt number

## Question:How to solve the BVP and draw a 3 D plot for skin fiction and nusselt number

Maple

eq1 := diff(f(eta), eta, eta, eta, eta)+(2*f(eta)*(diff(f(eta), eta, eta, eta))+2*g(eta)*(diff(g(eta), eta)))*(1-phi)^2.5*(1-phi+phi*rhos/rhof)-sigmanf*M*(diff(f(eta), eta, eta))*(1-phi)^2.5/sigmaf = 0

eq2 := diff(g(eta), eta, eta)-(1-phi)^2.5*(1-phi+phi*rhos/rhof)*(2*(diff(f(eta), eta))*g(eta)-2*(diff(g(eta), eta))*f(eta))-sigmanf*M*g(eta)*(1-phi)^2.5/sigmaf = 0

eq3 := k[nf]*(diff(theta(eta), eta, eta))/(Pr*k[f])+((1-phi+phi*rhos*cps/(rhof*cpf))*2)*f(eta)*(diff(theta(eta), eta))-4*lambda*(1-phi+phi*rhos*cps/(rhof*cpf))*(f(eta)^2*(diff(theta(eta), eta, eta))+f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta)))+sigmanf*M*Ec*((diff(f(eta), eta))^2+g(eta)^2)/sigmaf = 0

eq4 := (1-phi)^2.5*(diff(chi(eta), `\$`(eta, 2)))+2*Sc*f(eta)*(diff(chi(eta), eta))-sigma*Sc*(1+delta*theta(eta))^n*exp(-E/(1+delta*theta(eta)))*chi(eta) = 0

Boundary Conditions

f(0) = 0, (D(f))(0) = A1+gamma1*((D@@2)(f))(0), f(10) = 0, (D(f))(10) = 0, g(0) = 1+gamma2*(D(g))(0), g(10) = 0, theta(0) = 1+gamma3*(D(theta))(0), theta(10) = 0, chi(0) = 1, chi(10) = 0

Parameters

lambda = 0.1e-1, sigma = .1, Ec = .2, E = .1, M = 5, delta = .1, n = .1, Sc = 3, A1 = .5, gamma1 = .5, gamma2 = .5, gamma3 = .5, Pr = 6.2, phi = 0.1e-1, rhos = 5.06*10^3, rhof = 997, cps = 397.21, cpf = 4179, k[nf] = .6358521729, k[f] = .613, sigmanf = 0.5654049962e-5, sigmaf = 5.5*10^(-6)

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